For the given arch bridge loaded, as shown above, determine the following;
(a) The support reactions (b) The bending moment diagram of the girder (c) The shear force diagram of the girder (d) The axial force diagram of the girder
Typical structures are rarely supported only on a single pile. Therefore, the number and spacing of piles required to support a given structure is an important aspect of the design. The number of piles required to support a given load is dependent on the magnitude of the load and the load-carrying capacity of the piles, while the spacing of piles in a group is dependent on the type of pile, soil properties, method of installation, and the size of the pile.
However, in some cases, lightly loaded columns in a building or other structures can be supported on a single pile, provided the piles and pile caps are eventually chained together with continuous ground/plinth beams. In such cases, the load-carrying capacity analysis of the pile can be based on the case of a single pile.
In other cases, the group of piles are typically positioned in close spacing beneath the structures they support, thereby necessitating the consideration of the collective behaviour of the entire group of piles. This is especially important when friction piles are used. The bearing capacity of a pile group does not solely depend on the capacity of each individual pile multiplied by the number of piles in the group. This difference in capacity is attributed to the phenomena known as ‘Group action of piles’.
Grouping of Piles
It is typical to avoid the exclusive usage of driven piles beneath a column or wall due to the tendency of the pile to deviate horizontally during installation, leading to uncertainty in aligning the pile accurately beneath the foundation. Failure can occur either at the interface between the pile and column or within the pile itself, when unexpected eccentricities arise.
Therefore, it is usual practice to construct piles for walls in a staggered configuration on both sides of the wall’s centre line. When a single pile configuration is not feasible, a higher number of piles are utilized in a specific configuration for supporting a column. If the needed capacity exceeds three piles, the piles will be arranged symmetrically around the point or area where the load is applied. Figure 1 illustrates the representative configurations of pile groups for column loads.
Figure 1: Typical pile spacing and configuration for column loads
Typically, column and wall loads are transmitted to the pile group by means of a pile cap. This pile cap is a thick reinforced concrete slab that is connected to the pile heads, facilitating the collective behaviour of the group (see Figure 2).
The requirement for the collective arrangement of driven piles does not extend to bored piles. Drilled shafts can be placed with a high degree of precision. Residential buildings can utilize a single, large-diameter drilled shaft pile to provide support for its columns. This can be utilized when the arrangement of three piles results in an excessive amount of additional load capacity, particularly in the scenario of driven piles.
In a typical scenario, the number of piles required to support any load is calculated using the serviceability limit state loads. This is then compared with the stated safe load-carrying capacity of a given pile with known diameter and embedment depth. For instance, if the calculated service axial load is 2450 kN, and the load carrying capacity of a 600 mm diameter pile at an embedment depth of 15 m is 724 kN, the number of piles required is given by;
Number of piles = Service Axial Load/Allowable pile load capacity = 2450/724 = 3.38 (Adopt 4 piles)
Spacing of Piles
The spacing of piles in a group is determined by several criteria, including the overlapping of stresses between adjacent piles, the cost of the foundation, and the intended efficiency of the pile group. The stress isobars of a single pile supporting a focused load will resemble the illustration in Figure 2(a).
Figure 2: Stress isobars of single piles and groups of piles
When piles are driven in close proximity, there is a potential for the stress isobars of neighbouring piles to overlap, as illustrated in Figure 2(b). To prevent potential failure due to either shear or excessive settlement, it is advisable to increase the space between the overlapping elements, as seen in Figure 2(c). Wide spacing is disadvantageous as it necessitates a larger pile cap, hence increasing the overall cost of the foundation.
Driven piles result in increased stress overlap owing to soil displacement. When piles are driven into loose sands, compaction occurs, resulting in smaller spacing. However, in the case of piles being driven into saturated silt or clay, compaction does not occur, but the piles may undergo uplift. To mitigate this issue, one can increase the pile spacing.
Reduced spacings can be employed for cast-in-situ piles due to a decreased tendency for disturbance. End-bearing piles can be positioned at a closer spacing compared to friction piles. Different building codes typically stipulate the minimum spacing between piles. The spacing of straight uniform cylindrical piles may range from 2 times the diameter (2d) to 6 times the diameter (6d). The required minimum distance for friction piles is three times the diameter of the pile (3d).
When point-bearing piles pass through a compressible stratum, the minimum spacing required is 2.5 times the diameter of the piles if they are resting on compact sand or gravel. However, if the piles are resting on stiff clay, the minimum spacing should be 3.5 times the diameter of the piles. The minimum distance required for compaction piles may be 2 times the diameter (2d).
In general, piles should be driven starting from the centre and moving outward, unless the soil is soft clay or very soft. In such cases, the pile driving should start from the edges of the foundation and go towards the centre to prevent the sideways movement of dirt during the driving process.
Take Away
The primary considerations for determining the number of piles include the load-bearing capacity of the soil, the expected loads on the structure, and the desired safety factors. Pile capacity can be estimated through various methods such as static load tests, dynamic load tests, or geotechnical analysis.
Engineers must also consider the distribution of loads across the piles and assess how they interact to distribute the structural loads effectively. Additionally, the structural design of the piles themselves, including their type (e.g., driven piles, drilled shafts, or micropiles), size, and material, may also affect the number of piles needed.
The spacing of piles is equally important. It influences the overall performance of the foundation system, affecting factors like settlement, cost, and load-carrying capacity. When piles are spaced so closely such that the stress isobars overlap, the pile group will undergo higher settlement than previously envisaged. From experience, you rarely go wrong by placing your spacing between 2.5d to 3d. Proper spacing design involves a balance between load distribution and economic considerations.
In conclusion, determining the number and spacing of piles for a foundation system demands careful engineering consideration of soil characteristics, structural loads, safety margins, and economic implications. The chosen arrangement must guarantee the structure’s stability and performance while keeping construction expenses within budget. Selecting the right number and spacing of piles is an important aspect of deep foundation design and has a substantial impact on the overall success of a construction project.
When replacing or installing a new roof hatch, making the right selection is important for safety and functionality. A wide range of hatches exist for different weight ratings and use cases. This blog post lets you explore the key factors, like material, latching systems, and dimensions, to help you select the ideal roof hatch solution for your specific house or commercial establishment project’s needs.
7 Essential Factors to Check When Purchasing Roof Hatch
Picking a roof hatch that meets your structure project’s requirements and demands takes some planning. Below are seven crucial factors to check when buying the most suitable roof hatch for your home or commercial building’s access necessities.
Size and Dimensions
Measuring the roof area size is crucial. You must make sure the hatch will fit in that space properly. Consider what needs to go through the opening, like tools, supplies, and people. You want to choose a hatch big enough that nothing gets stuck when moving it in or out of the roof.
Materials
Manufacturers commonly make roof hatches out of three materials—aluminum, steel, and fiberglass. Aluminum-built hatches, like BA-ALRF-LA aluminum roof hatch, are light but easily dent if bumped. Steel is tough but will rust over time in some weather conditions. Fiberglass is very sturdy and can handle rain and sun without issues.
It would be best if you chose based on what climate you live in. If it rains a lot where you are, fiberglass or steel would be better since they don’t rust. Aluminum would work well in dry areas. Remember to also think about how much bumping and banging the hatch may get, as steel could take more abuse than aluminum before getting damaged.
Door Style
Hatches come with doors of multiple panels or a single solid piece. Panel doors are lighter to open and close since they have separate sections that move. However, wind and cold air can blow through the cracks between panels.
Solid doors, on the other hand, grant better insulation since they are one solid piece that seals tightly. But they are very heavy to lift open and shut. You should also consider whether drafts will be an issue for your use and whether you can effortlessly handle the weight of a solid door, given that ensuring safety is vital. Pick the door style best suited to your work needs and ability.
Insulation
For temperature control, seek out insulated hatch options. Insulation helps maintain a stable temperature in the roof area, allowing building occupants and employees to work throughout all seasons.
In very hot or cold places, insulation makes a big difference in keeping enclosed spaces livable year-round. It prevents outside heat or chill from easily transferring through the hatch material. Hence, you must highly consider this, especially if the condition sees major temperature swings from season to season.
Lifting System
Hatches have presented various alternatives for helping lift the door open and closed. Common systems include gas shocks, springs, and pulley setups. Gas shocks and springs provide power to assist with lifting.
Meanwhile, pulleys make raising or lowering the door easier while keeping balance. Consider your strength and pick a lifting system you can work with safely using only one hand. That way, your other hand will be free for holding tools, supplies, or other items when going in and out of the hatch opening.
Safety Railings
Railings play an important safety role. They help guard against accidental falls through the open hatch area. Be sure any railings surround the perimeter of the hatch opening.
It protects you while in or around the space. These railings must match the hatch size so protection extends across the access area. Also, double-check its compliance with building codes for fall safety measures to ensure security from injuries and tumbles off the roof.
Hardware
The hinges, latching mechanisms, and other small parts on a hatch are important to guarantee the component’s proper functioning over the long run. Hatches need hardware strong enough to stand firm against heavy usage over time. Among hardware materials, stainless steel weathers environmental elements like extreme heat, cold, rain, and snow better than alternatives.
Using stainless steel avoids common issues, such as rust that can weaken other metal parts quicker than expected. So, when looking for hatches, consider the hardware’s quality, too. Adequate sturdiness guarantees the hatch continues operating seamlessly for all seasons as required for roof access.
Pick What’s Best for Your Project
Choosing the right hatch requires considering your building’s unique access needs and environment. Taking the time to measure and assess materials and systems compatibility will save costs. A hatch is an important safety investment that also enhances work efficiency. With so many options, the essential factors listed in this blog aim to help you purchase a hatch solution tailored for reliable, durable performance on your job sites for years to come.
Cylindrical steel tanks are important structures used for the storage of different kinds of fluids. They are more popular in the petrochemical industry where it used for storing petroleum products, water, chemicals etc. Storage tanks are containers, either above or below the ground, that are used to store chemicals, petroleum, and other liquid products. This article is focused on the design of above above-ground cylindrical steel storage tank.
Cylindrical steel tank farms are usually constructed using a series of steel plates which are welded together on site. The thickness of the plates usually varies, usually being maximum at the bottom and minimum at the top. When the diameter of the tank is very large, internal steel columns are introduced to support the roof rafters and shell cover.
A cylindrical tank or shell may be described as thin or thick depending upon the thickness of the plate in relation to the internal diameter of the cylinder. Above-ground cylindrical tanks are typically thin-walled structures that are prone to buckling, or losing their stability, especially when they are empty or have a low liquid level. This is because external loads, such as wind and earthquakes, can more easily cause these tanks to collapse.
Traditionally, the ratio of t/d = 0.05 has been considered a suitable line of demarcation between thick and thin cylinders. If the thickness of the shell is equal to or greater than the internal diameter/20, the shell is regarded as a thick shell. In thin cylinders, the stress is usually assumed to be uniformly distributed over the wall thickness. When these storage cylinders are subjected to internal static pressure due to the stored fluid, the following types of stresses are developed.
(1) Hoop or circumferential stresses. These stresses act in a tangential direction to the circumference of the cylinder. (2) Longitudinal stresses. These act parallel to the longitudinal axis of the shell (3) Radial stresses. They act radially to the circumference of the shell.
The design of cylindrical steel tanks such as tank farms usually involves the determination of the proper thickness of the tank shell that will resist the bursting force from the stored fluid, and also remain stable under the action of other external forces.
If the bursting force (pressure) = Resisting strength
Therefore, pdl = 2ltσc
σc = pd/2t
Where; d = internal diameter of the cylinder t = thickness of the cylinder p = internal pressure in the cylinder σc = circumferential or hoop stress in the cylinder
Similarly for longitudinal stress for tanks with both ends covered with two end plates;
σl = pd/4t
Where σl = longitudinal stress
The maximum shear stress in a cylindrical shell is given by;
τmax = (σc – σl)/2 = pd/8t
Therefore, if it is required to determine the wall thickness of a thin cylindrical shell so that it can withstand a given internal pressure p, we have to determine that the maximum stress developed in the shell does not exceed the permissible tensile stress of the shell material (fy). Therefore,
t ≥ pd/2fy
Design of Cylindrical Steel Tanks
The document EN 14015:2005 provides the specifications for the structural design and verification of flat-bottomed, above-ground, welded steel tanks for the storage of liquid at ambient temperature. The EN14015 design standard uses a simplified approach to determine the thickness of tank shell courses.
This approach is based on the tank’s geometry, the liquid level, the material used, the liquid’s density, and a corrosion allowance. It aims to limit the tensile stresses in the shell due to hydrostatic pressure. However, it does not explicitly consider tank shell buckling.
Fluid Action
When a tank is in operation, the pressure load from the liquid inside it must be considered, from the maximum liquid level to when the tank is empty. The internal pressure load must also be considered, including the load due to the specified test pressure and test internal negative pressure.
For a full tank, the design hydrostatic pressure is the highest liquid pressure that acts at the bottom of the tank shell course. This is calculated as the product of the liquid’s specific weight and the maximum height of the liquid, measured from the top of the tank shell. This fluid pressure is resisted by making the bottom shell courses thicker.
In other words, the design hydrostatic pressure is the maximum pressure that the tank shell course must be able to withstand when the tank is full. This pressure is calculated based on the weight of the liquid and the height of the liquid column. The bottom shell courses are made thicker to resist this pressure.
The computation of the thickness of the tank shells is influenced by factors like the geometry of the tank, material to be contained, material strength, corrosion allowance, design pressure and height of shell courses from the top of the tank shell. Furthermore, the design of the shell for external wind loads and internal negative pressure, which is the buckling resistance of the tank shell, is prevented by providing ring stiffeners and determining the minimum spacing of secondary rings using an equivalent minimum shell thickness.
According to EN 14015:2004, the maximum allowable design stress in shell plates shall be two-thirds of the yield strength of the material with a maximum design stress of 260 MPa (when the temperature is equal to less than 100 degrees celsius). The specified thickness of the shell plates shall not be less than the specified nominal thicknesses specified in Table 16 of the code.
Tank Diameter D (m)
Minimum nominal shell thickness (mm) for carbon and carbon manganese steels
D < 4
5
4 ≤ D < 10
5
10 ≤ D < 15
5
15 ≤ D < 30
6
30 ≤ D < 45
8
45 ≤ D < 60
8
60 ≤ D < 90
10
90 ≤ D
12
Table 1: Minimum nominal shell thickness
The code specifies that in no case should the specified thickness of the shell or the reinforcing plate be greater than 40mm (clause 9.1.6). Also the minimum circumferential dimensions of a shell plate shall be 1m.
The required minimum design thickness of the shell plates is derived from equation (1) below or the secified values provided in Table 1, whichever is the greatest.
ec = D/20S[98W(Hc – 0.3) + p] + c —— (1)
where: c is corrosion allowance, for the shell assumed fully painted (c = 0), D is tank diameter in [m], Hc is the distance from the bottom of the considered course to the design liquid height [m], W is the maximum design density of the contained liquid under storage conditions, in kg/l p is the design pressure [mbar], S is the allowable design strength [MPa].
According to EN14015, 9.1.1a, the allowable design stress, S is a minimum of 2/3 of the yield strength of the shell material or 260 MPa, P is the design pressure [MPa], and W is the density of the liquid to be contained.
Hp1 = K(emin5/D3)0.5 —— (2)
where: Hp is the minimum spacing between the stiffeners, emin is the minimum shell thickness, and K is a factor determined by an empirical formula in equation (3).
K = 95000/(3.563VW2 + 580PV) —— (3)
where: VW is a 3-second gust wind speed and PV is the design internal negative pressure.
For the specified nominal thickness of the bottom plates shall not be less than 6mm for lap welded bottoms or 5mm for butt welded bottoms (Carbon and Manganese Carbon steels) excluding the corrosion allowance. In addition, the bottom plate thicknesses in the corroded condition shall be sufficient to resist uplift due to the design internal negative pressure.
Bottom of tanks greater than 12.5m diameter shall have a ring of annular plates, having a minimum nominal thickness ea, excluding corrosion allowance either;
(a) not less than that given by the following equations; ea = 3.0 + e1/3 where e1 is the thickness of the first course excluding corrosion allowance in mm.
But must not be greater than 6mm. Bottom of tanks up to and including 12.5m diameter may be constructed without a ring of annular plates.
Conclusion
Cylindrical steel storage tanks are one of the most common types of tanks used for storing a wide variety of liquids, including petroleum products, chemicals, and water. These tanks are typically designed to be above ground, although below-ground tanks are also used in some applications.
The design of a cylindrical steel storage tank is based on a number of factors, including the type of liquid to be stored, the tank’s capacity, and the operating conditions. The tank must be strong enough to withstand the hydrostatic pressure of the liquid, as well as any external loads, such as wind, earthquake, and snow.
The tank shell is typically made of steel plates that are welded together. The thickness of the shell plates is determined based on the design pressure and the allowable stress of the steel. The bottom of the tank is typically thicker than the sides and top to withstand the higher hydrostatic pressure at the bottom of the tank.
The tank roof can be either fixed or floating. Fixed roofs are typically used for tanks storing volatile liquids, such as gasoline, to prevent the release of vapours. Floating roofs are typically used for tanks storing non-volatile liquids, such as water, to reduce evaporation.
The construction of a cylindrical steel storage tank typically involves the following steps:
Site preparation: The site is prepared to provide a level and stable foundation for the tank.
Tank assembly: The tank shell is assembled by welding together the steel plates.
Roof assembly: The tank roof is assembled and installed on the tank shell.
Internal and external coatings: Internal and external coatings are applied to the tank to protect it from corrosion.
Piping and instrumentation: Piping and instrumentation are installed to allow the tank to be filled and emptied, and to monitor the liquid level and pressure.
After the tank is constructed, it must be tested to ensure that it meets the design specifications. This typically involves a hydrostatic test, in which the tank is filled with water and the pressure is gradually increased to the design pressure.
We often focus on aesthetics, functionality, and safety when designing commercial buildings. However, we also often overlook one crucial aspect: the access doors. These hidden doors provide convenient entry to concealed plumbing and electrical systems, offering surprising benefits for commercial buildings.
This article will explore why removable drywall access doors are becoming increasingly popular and how they can enhance efficiency, aesthetics, security, and compliance in commercial building design.
Benefits of Removable Drywall Access Doors
Convenient Accessibility for Repairs and Maintenance
Removable drywall access doors serve a simple but vital purpose: they provide access to hidden plumbing and electrical systems in commercial buildings. These systems can be quite complex and spread out into commercial structures. In the past, the usual way to access them was by cutting through the drywall, which took time and cost a lot in labor and materials.
But with removable drywall access doors, you don’t need to go through all that trouble. You can open and close these doors easily, allowing maintenance workers to access the systems without causing much damage to the nearby walls. This makes it much cheaper and faster for businesses in the building, saving them money and reducing downtime.
Seamlessly Blending with Aesthetics
People often have one concern when thinking about access doors: how they’ll look in a space. But removable drywall access doors are designed to blend with the walls around them. Removable drywall access doors can be customized to perfectly match the surrounding drywall’s texture, color, and design. This makes them virtually invisible and ensures they blend seamlessly with the wall when not being used.
This ability to fit in with the aesthetics means these access doors will maintain the overall look of the space. In a business setting, where first impressions matter a lot, this careful attention to detail can make the building look better while still being useful.
Enhanced Safety Measures
Security is a major worry in commercial building design, and access doors are crucial in addressing this concern. Removable drywall access doors can have strong locks, stopping unauthorized people from entering. This extra security layer is essential for protecting valuable items and keeping people in the building safe.
Additionally, these doors can meet strict fire safety rules, ensuring they don’t undermine the fire-resistant quality of walls. This dual function makes them vital for maintaining safety and security in commercial properties.
Versatile Design Solutions
Commercial buildings come in various shapes, materials, and sizes—each with unique design needs. Also, there are numerous technical systems running behind the scenes, such as cabling for internet connectivity, HVAC systems, and electrical wiring for various devices. Maintenance and upgrades are inevitable, and this is where the clever integration of Babcock-Davis BRGBR removable drywall access door becomes essential.
Additionally, removable drywall access doors are incredibly versatile, allowing architects and designers to incorporate them into different layouts and setups easily. Whether it’s a tiny office, a bustling retail shop, or a vast industrial facility, these access doors can be adapted to fit the space’s specific needs precisely.
This flexibility also applies to the size of the access doors, making it possible to tailor them for different entry points. This means no area becomes off-limits when maintenance or repairs are needed, ensuring that every part of the building remains accessible as necessary.
Long-Term Financial Benefits
While installing removable drywall access doors might seem like an extra cost initially, it’s a smart long-term investment. These doors simplify repairs and maintenance, cutting down on labor costs. Moreover, they’re designed to be long-lasting, reducing the need for frequent replacements.
Additionally, considering the increasing emphasis on energy efficiency in commercial buildings, you can insulate these access doors. This insulation prevents heat from escaping or entering them, lowering energy consumption and utility bills.
Compliance with Building Regulations
Compliance with regulations is a non-negotiable requirement in commercial construction. Removable drywall access doors adhere to these codes, guaranteeing that the building remains safe and in line with standards.
This compliance not only prevents legal issues but also enhances the overall safety and functionality of the space. It ensures that the building is aesthetically pleasing, structurally sound, and secure, meeting all legal requirements.
Final Thoughts
The benefits of removable drywall access doors in commercial building design extend far beyond their unassuming appearance. They offer easy access for repairs and maintenance, seamlessly integrate with the aesthetics of a space, enhance security, provide design versatility, and contribute to long-term cost savings. Moreover, they ensure compliance with building codes and minimize disruption during installation.
These surprising advantages make removable drywall access doors essential in creating efficient, functional, and aesthetically pleasing commercial spaces. Architects, designers, and building owners should consider their inclusion as a fundamental aspect of any commercial building project, ultimately leading to more efficient and sustainable buildings.
A beam and raft foundation is a special type of shallow foundation where ground beams are incorporated into the raft slab along the column lines to enhance the structural performance of the slab and to reduce cost. Therefore, the design of a beam and raft foundation involves the provision of adequate member sizes and reinforcement for the ground beams and slab, while ensuring that the bearing capacity of the soil is not exceeded.
In flat raft slab design, punching shear is a major design requirement that influences the thickness of the slab. This often leads to an excessive thickness of slab members that will be economically detrimental to the owner of the building. However, by introducing ground beams along the column gridlines, the problem of punching shear is eliminated as the column bears on the ground beams. This may lead to the use of thinner slabs and bigger heavily reinforced ground beams.
Figure 1: Schematic representation of beam and raft slab action
The beams in a beam and raft foundation may be upstand or downstand. The general theory in the design of beam and raft foundations is that the earth pressure intensity as a result of the superstructure load is first resisted by the raft slab, which then transfers the load to the ground beams. Therefore, the uniformly distributed load used in the design of the ground beams is assumed to be transferred from the raft slab.
Since the pressure load on the raft slab is coming from the ground, it follows that the top fibre of the slab is in tension in the sagging areas (span), while the support regions are in tension at the bottom fibre. This is a typical reverse of what is obtainable in the design of suspended solid slabs.
Therefore, for the theory and assumptions made in the design of a beam and raft foundation to be valid, the slab must be in direct contact with the ground, and be stiff enough to resist the earth pressure intensity. This is one of the scepticism of professionals on the use of downstand ground beams in raft foundations.
In the case of down-stand beams, the ground beams are constructed into the natural soil, with a height that rises above the natural ground level, in order to make up the architectural level for the ground floor slab. As a result, the foundation must be filled with imported earth material to the ground beam level, before the raft slab concrete is done.
Completed ground beam casting waiting to be filled
If the imported material is not properly compacted and eventually settles, the raft slab will behave like a suspended slab and the design philosophy will eventually be defeated. Additionally, the foundation slab will bear on a filled ground with unknown bearing capacity. Therefore, the fill material for raft slabs must be high-quality earth materials (preferably granular materials) and must be properly compacted.
Filling of beam and raft foundation with laterite
Therefore, upstand ground beams are theoretically more certain since the raft slab bears directly on the natural ground, however, they will be more expensive since another oversite concrete will have to be done. However, down-stand ground beam construction provides an economical advantage to the building owner since the raft slab also functions as the oversite concrete floor. An Investigation on the Analysis of Beam and Raft Foundation Using Staad Pro
Design Example
The axial forces in the ground floor columns have been presented below, and have been used to demonstrate how to carry out the design of the beam and raft foundation manually.
Design Data Allowable bearing capacity of soil = 40 kN/m2 Dimension of all columns = 230 x 230 mm Dimension of ground floor beams = 1200 x 250 mm Thickness of ground floor slab = 150 mm Concrete cover to ground beams = 50 mm (sides and bottom) Cover to slab = 30 mm fck = 25 MPa fyk = 500 MPa
Analysis of the raft slab by rigid approach A little consideration of Figure 3 will show that the foundation is loaded is symmetrically in the x-direction, therefore we will compute the eccentricity of the load in the z-direction.
Sum of load on gridline D = 79 + 168 + 168 + 79 = 494 kN Sum of load on gridline C = 173 + 384 + 384 + 173 = 1114 kN Sum of load on gridline B = 225 + 498 + 498 + 225 = 1446 kN Sum of load on gridline A = 108 + 235 + 235 + 108 = 686 kN
Fig 5: Load on the raft slab
Resultant of loads R = 686+ 1446 + 1114 + 494 = 3740 kN
Taking moment about the centroid of the base;
M = (-686 x 7.5) – [1446 x (7.5 – 6)] + [1114 x (7.5 – 4)] + (494 x 7.5) = 290 kNm
Eccentricity of the load e = M/R =290/3740 = 0.0775 m to the right hand side
The base dimensions are taken as follows; L = 6 + 6 + 6 + 0.25 = 18.25 m B = 6 + 5 + 4 + 0.25 = 15.25m
Pressure distribution Pi= (R/A) ± (6Re/LB2)
On substituting and solving; Pmax = 13.847 kPa Pmin = 13.028 kPa
These values are way below the allowable bearing capacity of the soil, therefore there is no need to increase the dimensions of the base. Also, due to the close values of Pmax and Pmin, instead of using a trapezoidal pressure distribution, we can assume a rectangular pressure distribution using the maximum pressure.
Note Pressure distribution calculation is carried out using SLS load, but we used ULS here. You can convert from ULS to SLS for simple buildings when using Eurocode by using a factor of 1.37 (Ubani, 2017).
Therefore, using a pressure of 13.847 kPa, we can design the raft slabs and the ground beams using the conventional methods which I believe that we are familiar with.
Design of the raft slab
The design of the raft slab is done just like the design of a normal suspended floor, but there is usually no need to check for deflection. For raft foundations without ground beams, punching shear is also very critical.
Self weight of the slab = 25 kN/m2 x 0.15 m = 3.75 kN/m2
Design pressure for the raft slab = 13.85 – 3.75 = 10.1 kN/m2 (note that it will be improper to factor the self-weight of the ground floor slab since it is favourable in this case)
Effective depth of the slab d = h – Cc – ϕ/2 = 150 – 30 – 10/6 = 115 mm
Where Cc = concrete cover of the raft slab, and ϕ is the diameter of the reinforcement to be used.
Moment coefficient for two adjacent edges discontinuous
Short Span
Long Span
Mid-span
0.059
0.034
Continuous edge
0.078
0.045
Short Span – Mid span
MEd= 9.5 kN.m k = 0.028 Since k < 0.167 No compression reinforcement required z = 0.95d As1 = 193 mm2/m ASmin = 153 mm2/m Check if ASmin < 0.0013 b d (187.2 mm2/m) Therefore, provide H10 @ 250 c/c TT (Asprov = 314 mm2/m)
Short Span – Continuous Edge MEd = 12.6 kNm; Asreq = 254 mm2/m Therefore, provide H10 @ 250 c/c BB (Asprov = 314 mm2/m)
Long Span – Mid span MEd = 5.5 kNm; Asreq = 127 mm2/m Therefore, provide H10 @ 250 c/c NT (Asprov = 314 mm2/m)
Long Span – Continuous Edge MEd = 7.3 kNm; Asreq = 161 mm2/m Therefore, provide H10 @ 250 c/c TT (Asprov = 314 mm2/m)
Design of the ground beams
The figure above shows the assumed load distribution from the raft slab to the ground beams. For simplicity of hand calculations, we are going to use the formula for load transfer to the ground beams. This gives unconservative results, especially for shear forces induced in the beam. But can be used for design purposes.
Slab load from Panel 1 and 2 w1 = w2 = nlx/3 = (10.1 × 4)/3 = 13.467 kN/m
Slab load from Panel 3 and 4 w3 = w4 = nlx/3 = (10.1 × 5)/3 = 16.833 kN/m
Slab load from Panel 5 and 6 w5 = w6 = nlx/3 = (10.1 × 6)/3 = 20.2 kN/m
Total load on the spans wC-D = 13.467 + 13.467 = 26.93 kN/m wB-C = 16.833 + 16.833 = 33.67 kN/m wA-B = 20.2 + 20.2 = 40.4 kN/m
The self-weight of the beam in this case is beneficial (favourable), and can be ignored. We can therefore analyse the ground beam as a continuous beam as follows;
We know that MA = MD = 0 since we are treating it as a simple support.
Let us use the stiffness method for the analysis of the structure. The adopted basic system is shown below.
The canonical equation for the beam is given below;
To determine the support moments; Mi = Mf + M1Z1 + M2Z2
At support B MBL = 182.25 – [90.161/EI× 3EI/6] = 137.17 kNm MBR = -70.145 – [90.161/EI× 4EI/5] + [12.761/EI× 2EI/5]= -137.17 kNm
At support C MCL= +70.145 – [90.161/EI× 2EI/5] + [12.761/EI× 4EI/5]= 44.289 kNm MCR = -53.86 + [12.761/EI× 3EI/4] = -44.289 kNm
Using the principles of statics, the span moments and shear force diagrams can be drawn.
Structural Design
Span A – B MEd = 120.2 kNm
h = 1200 mm Effective depth d = 1200 – 50 – 10 – (16/2) = 1132 mm (assuming ϕ16 mm reinforcement will be used for the main bars, and ϕ10mm for the links). Beam width (bw) = 250 mm
k = MEd/(fckbd2) = (120.12 × 106)/(25 × 250 × 11322) = 0.0149 Since k < 0.167 No compression reinforcement required
To calculate the minimum area of steel required; fctm = 0.3 × fck2⁄3 = 0.3 × 252⁄3 = 2.5649 N/mm2 (Table 3.1 EC2)
ASmin = 0.26 × fctm/fyk × bt × d
Where bt is the width of the beam in tension. A little consideration will show that the flange of the beam is in tension. If we are to use the flange of the beam the way it is in tension,
ASmin = 0.26 × 2.5649/500 x 2290 x 1132 = 3457 mm2
In BS 8110-1:1997, the minimum area of steel required when the flange is in tension is; Asmin = (0.26bwh)/100 = (0.26 ×250 ×1200)/100 = 780 mm2
Eurocode experts have suggested using the area of the T-section for the calculation of the minimum reinforcement Such that the ASmin = 0.26 × fctm/fyk × Ac Ac = (2290 x 150) + (1050 x 250) = 60600 mm2 ASmin = 0.26 × 2.5649/500 x 60600 = 819 mm2 (this is acceptable).
Therefore provide 5H16 Top (Asprov = 1005 mm2)
Design of support B MEd = 137.71 kNm Note that at support B, the web is in tension and we will need to consider the flange width in the calculation of the area of steel required. l0 = 0.15 (l1 + l2) = 0.15(6000 + 6000) = 1800 mm b1 = b2 = (6000 – 250)/2 = 2875 mm l0 = 0.85l1 = 0.85 x 6000 = 5100 mm
beff,1 = beff,2 = (0.2 x 2875) + (0.1 x 1800) = 755 mm which is not less than 0.2l0 = (0.2 x 1800) = 360 mm Hence, beff,1 = beff,2 = 360 mm < 755 mm beff = 250 + 360+ 360 = 970 mm k = MEd/(fck bd2 ) = (137.71 × 106)/(25 × 970 × 11322) = 0.00443 Since k < 0.167 No compression reinforcement is required
On looking at the internal stresses diagram, this reinforcement provided can go all the way in the beam.
Shear Design Using the maximum shear force for all the spans Support B; VEd = 144.46 kN VRd,c = [CRd,c.k. (100ρ1 fck )1/3 + k1.σcp]bw.d ≥ (Vmin + k1.σcp) bw.d
CRd,c = 0.18/γc = 0.18/1.5 = 0.12
k = 1 +√(200/d) = 1 +√(200/1132) = 1.42 > 2.0, therefore, k = 1.42
σcp = NEd/Ac < 0.2fcd (Where NEd is the axial force at the section, Ac = cross-sectional area of the concrete), fcd = design compressive strength of the concrete.) Take NEd = 0
VRd,c = [0.12 × 1.42(100 × 0.00142 × 25 )1/3] 250 x 1132 = 73564 N = 73.564 kN Since VRd,c (73.564 kN) < VEd (144.46 kN), shear reinforcement is required.
The compression capacity of the compression strut (VRd,max) assuming θ = 21.8° (cot θ = 2.5) VRd,max = (bw.z.v1.fcd)/cotθ + tanθ V1 = 0.6(1 – fck/250) = 0.6(1 – 25/250) = 0.54 fcd = (αcc fck)/γc = (0.85 × 25)/1.5 = 14.167 N/mm2 Let z = 0.9d
References Ubani O.U. (2017): Practical Structural Analysis and Design of Residential Buildings Using Staad Pro V8i, CSC Orion, and Manual Calculations. Ist Edition, Volume 1. Structville Integrated Services
To download the above-named textbook, click on the image below;
The Leaning Tower of St. Moritz is a 12th-century church tower located in the Swiss Alps. It is one of the most iconic landmarks in the town of St. Moritz and is known for its distinct tilt. The tower is 33 meters high and leans 5.5 degrees to the north. The Leaning Tower of St. Moritz has been associated with the landslide occurring in the area.
For the past 30 years, the Institute of Geotechnical Engineering at ETH Zurich has been actively involved in all aspects of the problem related to geotechnical engineering, both through research and by providing expert services to the community.
According to Alonso et al. (2010), the slope above the village of St. Moritz is unstable and can be divided into two parts: the Gianda Laret rockfall and the Brattas landslide as shown in Figure 1. The Gianda Laret rockfall is located at the top of the slope and extends down to an altitude of 2100 meters.
Figure 1: The geology of Brattas Landslide (Alonso et al., 2010)
The Brattas landslide is located below the rockfall and is composed of a thick layer of soil. The landslide is moving downhill but is blocked by a ridge. The Brattas landslide is 600 meters wide and has an average slope of 20 degrees (see Figure 2). The main sliding surface of the landslide is about 50 meters deep. The Brattas landslide is made up of different layers of soil, which vary in thickness and properties.
The road Via Maistra is getting narrower by about 0.5 centimetres per year at the point where it is closest to the Brattas landslide. The displacement rate of the landslide increases uphill from Via Maistra. The movement of the landslide has only been measured in the developed areas, so it is not known if there is any interaction between the Gianda Laret rockfall and the Brattas landslide.
Figure 2: An aerial photo of St. Moritz landslide (Alonso et al., 2010)
The Leaning Tower of St. Moritz
The effects of the Brattas landslide are most evident in the behaviour of the oldest structures in the area. The Leaning Tower of St. Moritz Church, which was built in the 12th century at the foot of the landslide, leans 5 degrees off-centre. The church itself was demolished in 1893 due to excessive differential settlement.
Since 1908, regular measurements have been taken to track the tilt and displacement of the tower. Stabilization efforts in 1928 and 1968 were not successful in the long term. In 1976, the tower reacted alarmingly to an earthquake in Friaul, Italy. As a result, another stabilization attempt was undertaken in 1983.
Figure 3: Geological profile of the Leaning Tower (Alonso et al., 2010)
In 2013, the Leaning Tower of St. Moritz underwent a major renovation to reduce its tilt and improve its stability. The renovation involved removing some of the weight from the top of the tower and reinforcing the foundation. The renovation was successful, and the tower is now considered to be safe and stable.
The Problem
The Brattas landslide is caused by a combination of geological and hydrological factors. The landslide is located in a region where the Mesozoic sediments of the Bernina nappe have been pushed over the crystalline rock of the Err nappe. A nappe is a large sheet of rock that has been moved a long distance from its original position.
The landslide is also affected by the presence of deep aquifers, which create independent water tables. When the snow melts in the spring, the water pressure in the aquifers increases. This can reduce the shear strength of the soil and lead to landslides. Small landslides occur in the Brattas area every year, but larger landslides can also occur less frequently.
Landslide Stability Analysis
Puzrin and Sterba (2006) developed a simple model of a constrained landslide to assess the long-term stability and displacements of the St. Moritz landslide. The model is based on an inverse analysis, which means that the safety factor is determined by fitting the model to the observed displacement data.
In 2005, Puzrin performed a preliminary stability analysis of the Brattas landslide using the displacement data that was available at the time. The data was collected from the lower 200 meters of the landslide. Puzrin assumed that the two parts of the landslide were connected, and that the total length of the landslide was 1500 meters. He then used the equation developed by Puzrin and Sterba (2006) to fit the displacement data. This produced a ratio of b/a = 0.39.
Puzrin then assumed that the effective angle of internal friction was within the range of 28 to 35 degrees, as suggested by Vermeer (1997). For the average slope of 20 degrees, this gave a value of pa′/pp′ = 0.28 − 0.15. The corresponding safety factor was calculated to be Fs = 0.78 −1.46.
Puzrin’s preliminary analysis suggested that the Brattas landslide was marginally stable, but it did not exclude the possibility of failure. To improve the accuracy of the prediction, more data was collected from the middle and upper parts of the landslide. This data showed that the movement rate at the top of the landslide was significantly higher than at the bottom of the Gianda Laret rockfall.
This suggests that the rockfall movement is stopped by a rock ridge and does not fully transfer earth pressures to the Brattas landslide. However, the upper boundary of the Brattas landslide is slowly shifting upwards as blocks from the rock ridge collapse into the sliding mass.
Based on the latest data, the authors assume that there is no interaction between the Gianda Laret rockfall and the Brattas landslide. They then use a revised version of the Puzrin and Sterba (2006) equation to fit the displacement data. This gives a ratio of b/a = 0.15 and a safety factor of Fs = 2.49 − 4.63.
This suggests that the Brattas landslide is stable and that there is no risk of failure in the near future. However, the authors caution that this conclusion is preliminary, as the observations over the past two years are not sufficient for long-term analysis.
Leaning Instability
In addition to predicting the long-term stability and displacements of the Brattas landslide, the authors also want to answer another important question: is the Leaning Tower of St. Moritz tilting due to the landslide, or is it due to a leaning instability or a bearing capacity failure?
To answer this question, the authors need to know the soil strength and stiffness in the vicinity of the tower. They collected this data using two different types of dilatometer tests. They also installed an inclinometer and a piezometer in the vicinity of the tower.
Before it was stabilized, the Leaning Tower of St. Moritz had a square foundation and the following geometry:
Height of the centre of gravity: Hc ≈ 13.0 m
Half-width of the square foundation: b = 3.0 m
The average radius of the square ring foundation: r = 1.5 m
The tower’s high slenderness ratio of Hc/r = 8.7 requires a check against leaning instability. The tower is built on a 15 m thick layer of gravelly clay. The properties of this clay were derived from the dilatometer tests:
Compression index: Cc = 0.12
Swelling index: Ce = 0.02
In-situ void ratio: e0 = 0.5
The tower’s slenderness ratio Hc/r = 8.7 is much smaller than the calculated critical value of 19. This means that the tower’s excessive inclination is not due to leaning instability. So, could the tower’s inclination be due to a bearing capacity failure?
Bearing Capacity
The authors calculated the bearing capacity of the tower when it was still standing straight. They used the available parameters to calculate the bearing capacity of the soil as 1040 kN/m2. The weight of the tower is 1264 tons, which results in an average contact stress of 344 kPa. This means that the safety factor against bearing capacity failure for the tower when it was not inclined was 3.0. This is a sufficient safety factor to ensure that bearing capacity failure was not possible.
The authors also considered the case of the tower when it was inclined. In this case, the pressure under one of the footings was much higher than the average, leading to a contact pressure of 606 kPa. However, even in this case, the safety factor against bearing capacity failure was still significantly greater than unity (1.72). This means that bearing capacity failure can also be excluded as the source of the tower’s inclination.
Conclusion
The authors have established that the excessive inclination of the Leaning Tower of St. Moritz is not due to leaning instability or bearing capacity failure. They also note that other structures in the landslide area are also inclined, even though they have much lower height-to-width ratios and contact pressures. This suggests that the most likely reason for the tower’s inclination is the landslide displacement.
The authors conclude that, although the landslide is not likely to fail catastrophically, its movements are still damaging the structures in the area. There are two ways to mitigate this damage:
Stabilize the structures locally and let them “swim” with the landslide.
Stabilize the landslide globally by drainage.
References
Alonso E.E, Pinyol N.M., Puzrin A. M. (2010). Geomechanics of Failure. Advanced Topics. Springer. Puzrin, A.M., and Sterba, I. (2006) Inverse long-term stability analysis of a constrained landslide. Géotechnique 56 (7), 483 − 489. Vermeer, P.A. (1997) PLAXIS Practice I: The leaning Tower of St. Moritz. PLAXIS Bulletin, No. 4, 4 − 7.
Glass is a significant and popular material in contemporary architecture, whether it is used to facilitate the entry of natural light into indoor areas, contribute to exterior aesthetics, or build facades/curtain walls for highrise buildings. It is an inorganic solid with a non-crystalline (amorphous) atomic structure and is produced from a wide variety of constituent materials. However, glass is a relatively new structural material, and its use in this area is a significant development.
Over the past 25 years, there has been a lot of progress in the use of glass as a structural material. This can be seen in the growing number of buildings that use glass for structural elements. One example of a significant implementation from this period is the extension of the Broadfield House Glass Museum in Kingswinford.
Figure 1: Glass staircase and decking in a building
The development of glass structures has been driven by advances in glass technology and our understanding of its mechanical and strength properties. The use of structural glass has also led to the development of standards for its design. Today, there are standards covering the design of glass structures, but historically there have been a variety of national regulations that were often contradictory, incomplete, outdated, or not aligned with the European basis of design of EN 1990 (2010).
The European Commission issued a mandate in 2012 for a new generation of Eurocodes, including a new Eurocode for the design of glass structures. This work has resulted in the development of a harmonized European standard, Eurocode 10, which is expected to be published in early 2024.
Types of Glass
Annealed Glass
Annealed glass, also known as float glass, is the most common type of glass. It is made by floating molten glass on a bath of molten tin. After the glass is formed, it is annealed, which is a process of slow heating and cooling to remove internal stresses. Annealed glass is relatively weak and susceptible to impact, bending, and thermal stresses. It also breaks into large, sharp shards, which can be dangerous (see Figure 2).
Figure 2: Typical fractured annealed glass
The way annealed glass breaks depends on the flaws in the glass, the stress level, the stressed surface area, and the duration of the load. Flaws in the glass can be caused by the manufacturing process, cutting, grinding, or drilling, or by the environment in which the glass is used (e.g., humidity can promote crack growth).
Heat Strengthened Glass
Heat-strengthened glass is made by heating annealed glass to a temperature slightly above its annealing point and then cooling it quickly. This causes the surface of the glass to cool and solidify first, while the interior of the glass remains hotter. As the interior cools, it tries to shrink, but the surface is preventing it from doing so. This creates a compressive stress on the surface of the glass and a tensile stress in the interior.
This heat treatment makes heat-strengthened glass stronger than annealed glass and more resistant to fracture. When heat-strengthened glass does break, it breaks into smaller pieces than annealed glass, which reduces the risk of injury.
The surface compressive stress of heat-strengthened glass must be greater than 24 MPa but less than 52 MPa. This is to ensure that the glass is strong enough to resist breakage, but not so strong that it is susceptible to spontaneous fracture.
Tempered Glass
Tempered glass, also known as fully tempered or thermally toughened glass, is made in the same way as heat-strengthened glass, but it is cooled more quickly. This causes the surface of the glass to be in more compression and the interior to be in more tension. The surface compressive stress of tempered glass must be greater than 69 MPa.
When tempered glass breaks, it shatters into small, roughly cubic pieces. This is because the tension in the interior of the glass is so great that it causes the glass to break into very small pieces (see Figure 3).
Figure 3: Typical fracture pattern of tempered glass
Tempered glass is susceptible to spontaneous breakage due to nickel sulfide (NiS) inclusions. NiS inclusions are small particles of nickel sulfide that can get trapped in the glass during manufacturing. If these inclusions are heated to a certain temperature, they can transform into a larger and more stable form of nickel sulfide. This transformation can cause the glass to break spontaneously.
To reduce the risk of spontaneous breakage, tempered glass should be inspected for NiS inclusions before it is installed. Tempered glass should also be treated carefully during handling and installation to avoid damaging the surface, which could lead to cracks and subsequent breakage.
Mechanical and Strength Properties of Glass
Glass is a brittle material, which means that it is more likely to break suddenly and without warning when compared with other common structural materials. This is because glass contains tiny cracks, which can concentrate stress and cause the glass to fail.
Glass is weak in tension because it is a brittle material. Brittle materials have a strong atomic structure, but they are also very susceptible to cracks. When glass is loaded in tension, it can’t deform like other structural materials, such as steel or concrete. Instead, it fails suddenly at its ultimate tensile strength as shown in Figure 4. This means that there is no warning before glass breaks, which is why it is important to design carefully when using glass as a structural material.
Figure 4: Stress-strain behaviour of glass, steel and aluminium alloy
Despite its brittle nature, glass has a theoretical strength of 25-30 GPa, which is very high. However, in real-world applications, the strength of glass is much lower. This is because even small cracks can significantly reduce the strength of glass. The Griffith Theory of Fracture explains why glass is so susceptible to failure. This theory states that the strength of a brittle material is limited by the presence of cracks. The larger the crack, the lower the strength of the material.
To use glass as a structural material, it is important to design structures that minimize the risk of crack formation and propagation. This can be done by using thick glass, avoiding sharp corners, and using appropriate supports.
The typical physical properties of glass are shown in Table 1;
Property
Symbol
Value
Modulus of Elasticity
E
70,000 N/mm2
Shear modulus
G
𝐸 [2(1 + 𝜐)]
Poisson’s ratio
𝜐
0.22
Coefficient of thermal expansion
𝛼
9 × 10-6 /°C
Density
𝜌
2,650 kg/m3
Table 1 – Typical physical properties of glass
Glass is a strong material with a Young’s modulus of 70,000 MPa, which is comparable to aluminium. Its key strength is its bending strength, which is 45 MPa for annealed float glass according to EN 572-1. This value can be increased using thermal or chemical modification processes. Thermal treatment can produce thermally toughened safety glass with a strength of 120 MPa or heat-strengthened glass with a strength of 70 MPa. Chemical treatment can produce glass with a strength of 150 MPa.
As discussed earlier, the fracture pattern of a glass depends on how it has been treated. Annealed float glass breaks into large, sharp shards, while thermally toughened safety glass breaks into a fine mesh of small pieces. Heat-strengthened glass falls somewhere in between. Laminated glass, which is made up of two or more glass panes bonded together with adhesive layers, is the safest type of glass for use in structures because it does not shatter into sharp pieces when it breaks.
Figure 5: Fracture pattern of different types of glass
Structural Design of Glass Elements
Ultimate limit state
According to the current European standards, the basic method for verification of structural glass is the limit state method. This design concept is also included in the EN 16612 standard for lateral load resistance of linearly supported glazing used as infill panels. The design methodology presented here shall be in accordance with EN 16612 standard, pending the final release of Eurocode 10.
It is subjected to examination for two main conditions: – determination of the maximum bending stress 𝜎max calculated for the most unfavourable load combinations, which cannot exceed the design value of bending strength fgd: 𝜎max ≤ fgd – determination of the maximum deflection 𝑤max for the most unfavourable load combinations, which cannot exceed the design value of deflection wd: 𝑤max ≤ wd
The EN 16612 standard requires that the maximum bending stress in the ultimate limit state (ULS) be examined. This is done by calculating the design value of bending strength, fgd. The EN 16612 standard provides methods for calculating fgd for annealed glass and prestressed glass.
fgd = (ke × ksp × kmod × fgk)/γM,A
where:
fgk is the characteristic value of bending strength for annealed glass (45 MPa) γM,A is the material partial factor for annealed glass (1.8) ke is the factor for edge strength (typically 1.0) ksp is the factor for the glass surface profile (typically 1.0) kmodis the factor for the load duration (typically 1.0)
The design value of bending strength for prestressed glass is obtained from the following formula:
where; 𝑓𝑔𝑑 – design value of the bending strength, 𝑓𝑏𝑘 – characteristic value of the bending for prestressed glass (70 MPa for heat-strengthened glass and 120 MPa for tempered glass). 𝛾𝑀𝑉 – material partial factor for prestressed glass 𝛾𝑀𝑉 = 1.2, 𝑘𝑉 – factor for strengthening of prestressed glass, for float glass 𝑘𝑉 = 1.0.
In the design formula for bending strength (formula 4.3), the edge strength factor (ke) is used to account for the location of the stresses. The value of ke depends on the type of glass and the quality of the edges. If the glass is supported on all four edges, ke is equal to 1.0. However, if the glass is supported on only two edges, ke may be less than 1.0.
Another important factor in determining the design value of bending strength is the load duration factor (kmod). This factor can be calculated using the following formula;
kmod = 0.663t(-0.0625)
where t is the load duration in hours. The value of kmod ranges from 0.29 to 1.0. Table 4 shows the basic values of kmod for different load durations. The load duration factor is important because glass is a viscoelastic material, which means that its strength decreases over time under sustained load. The kmod factor accounts for this decrease in strength.
Action
Load duration
Value of kmod
Wind gust
5s (or less)
1.0
Wind storm load
10 min
0.74
Maintenance loads
30 min
0.69
Snow load – external canopies and roofs of unheated buildings
3 weeks
0.45
Snow load – roofs of heated buildings
5 days
0.49
Dead loads, self-weight, altitude load on insulating glass units
Permanent (50 years)
0.29
Table 4. Value of 𝑘mod for load duration according to EN 16612 standard
Figure 6: Glass decking in a building
Solved Examples
(1) Calculate the bending strength of annealed glass for the following load conditions;
The lowest design value of bending strength occurs for permanent loads and annealed glass. In this case, the design value is only 18% of the characteristic value of bending strength for annealed glass. The design value is higher for thermally strengthened glass (41%) and thermally toughened safety glass (70%).
However, it is important to note that glass elements are usually subjected to a combination of loads. The standard recommends that the kmod factor be taken at the highest possible value, i.e., for the shortest duration load, when considering combinations of loads. However, all relevant load combinations must be considered. The kmod factor can also be determined as a weighted average.
Figure 7:Glass staircase structure
Serviceability Limit State
The deflection of a glass pane in a structural system should not be so large that it compromises the structural integrity or serviceability of the system. The deflection of a glass pane can be calculated using the finite element method, which can account for large deflections if necessary.
The limit value for the deformation of glass products can vary depending on the type of glass component used. This is because glass is a more sensitive material than other building materials, and even small deformations can be noticeable and uncomfortable for users. Additionally, glass structures can be designed to withstand specific loads and deflections, and exceeding these limits can compromise the structural integrity of the structure.
In other words, the amount of deformation that is allowed for a glass product will depend on a number of factors, including the type of glass, the intended use of the product, and the aesthetic and structural requirements. For example, a glass window will have different deflection limits than a glass staircase.
The serviceability limit state (SLS) in EN 16612 defines different deformation classes for different levels of criticality. 1. SLS as deflections or displacements of pure aesthetical relevance, 2. SLS as deflections or displacements affecting integrity, functionality or durability of the glass component in the unfractured state, 3. SLS as deflection or displacements or effect thereof affecting safety.
The first class 1-SLS is not considered under this standard. For the second class 2-SLS, a typical deflection limit for glass components was defined, which are presented below.
Deflection limit of glass structures
Continuously supported along all edges = L/50 (where L is the length of the short edge) Continuously supported along 2 or 3 edges = L/100 (where L is the length of the unsupported edge) Locally clamped at 2 or 3 edges (centre) = L/50 (where L is the length of the short edge) Locally clamped at 2 or 3 edges (free edge) = L/100 (where L is the length of the unsupported edge)
In HongKong, the deflection of rectangular glass plates can be calculated using the equation below;
Four sides simply supported; 𝛿 = 𝑡∙er0+r1𝑥+r2𝑥2
Where 𝑥 = In [In (p(ab)2/Et4)]
For two sides simply supported; 𝛿 = 5/32 (pa4/Et3)
where; 𝛿 = Centre deflection (mm) a = Length of shorter side of glass pane (mm) or loaded span in two-side simply supported case (mm). 𝑏 = Length of longer side of glass pane (mm) 𝑡 = Minimum glass pane thickness (mm) 𝑝 = Design pressure on individual glass pane (kPa) 𝐸 = Modulus of elasticity of glass pane (kPa)
The deflection limit (𝛿limit) of the glass pane should be taken as follows:
Four-side simply supported: 𝛿limit = 1/60 of the short span
Three-side simply supported: 𝛿limit = min. [b/60 , a/30]
Two-side simply supported: 𝛿limit =1/60 of the loaded span
Cantilever: 𝛿limit = 1/30 of the span
Point supported: 𝛿limit = 1/60 of the longer span between supports
Conclusion
Glass structures are a prominent feature of modern architecture, serving both aesthetic and functional purposes. They showcase the versatility and transparency of glass, which is used to create entire facades, roofs, and even floors in buildings. Glass structures allow natural light to permeate interior spaces, creating a unique design aesthetic.
However, it is important to design glass structures carefully to ensure that they are safe and durable. This is because glass is a brittle material that can break if it is not properly supported. Glass structures need to be designed to withstand all of the loads that they will be subjected to during their lifetime. This includes both the permanent loads (such as the weight of the glass itself) and the variable loads (such as wind and snow loads.
The design of glass structures requires careful consideration of load-bearing capabilities, thermal expansion, and resistance to various stresses, such as wind and seismic forces. Engineers and architects use advanced materials and engineering techniques, such as laminated or tempered glass, to ensure the strength and safety of these structures.
In the design of reinforced concrete buildings, it is essential to consider how changes in moisture and temperature can affect the volume of the structure. The magnitude of the stresses generated and the extent of the movement resulting from these volume alterations are directly related to the length of the building. To mitigate the effects of moisture or temperature-induced changes and prevent cracking, expansion joints are employed to divide buildings into distinct sections.
Expansion joints (also known as movement joints) are gaps in structures that allow different parts of the structure to move independently. They represent a disruption in both reinforcement and concrete, making them effective for accommodating both shrinkage and temperature variations. This is important because all materials expand and contract when their temperature changes. Without expansion joints, this movement could cause the structure to crack or fail.
This is especially true for building materials, such as concrete and steel, which can experience significant temperature changes throughout the day and year. Without expansion joints, these temperature changes would cause buildings to crack.
Joints in a building can serve as weak points to control crack locations (contraction joints) or create complete separation between segments (expansion joints). Currently, there is no universally agreed-upon design approach for accommodating building movements due to temperature or moisture variations. Many designers rely on “rule of thumb” guidelines that specify the maximum permissible distance between building joints.
Expansion joints are typically made of flexible materials, such as rubber or metal, which can compress and expand to absorb the movement of the structure. They are often sealed to prevent water and other elements from entering the structure.
The Need for Joints in Buildings
Expansion joints allow thermal expansions to occur in a building with minimal stress buildup. The greater the spacing between these joints, the higher the stresses they can accommodate. Typically, expansion joints divide a structure into segments, offering sufficient joint width to accommodate the building’s expansion as temperatures rise. In addition to mitigating contraction-induced cracking, expansion joints serve a dual purpose by providing relief from such cracking.
Controlling cracks in reinforced concrete structures is motivated by two main factors. Firstly, aesthetics are a significant consideration; noticeable cracks can mar the appearance, especially when the concrete is meant to be the final surface.
Cracks in crucial structural components like beams and columns can also lead to questions about the overall structural soundness, even if they don’t inherently jeopardize the building’s stability. Secondly, large crack widths can create pathways for air and moisture to infiltrate the structural framework, potentially leading to durability problems.
As a result, there is a genuine need for crack control in reinforced concrete structures. The main questions revolve around how to manage the extent of cracking, achieved through contraction joints, and how to restrict stresses in members to an acceptable level, accomplished through expansion joints.
Expansion Joints
Temperature changes induce stress within a structure, but this only occurs when the structure is restrained. In the absence of constraints, there are no resulting stresses. For instance, temperature difference has no effect on statically determinate structures.
In reality, almost all buildings have some level of restraint. The magnitude of temperature-induced stresses varies with the extent of temperature change; substantial temperature fluctuations can lead to significant stresses that must be considered during the design process, while minor temperature changes may result in negligible stresses.
These temperature-induced stresses occur due to changes in the volume of a structure between points where it is restrained. To estimate the amount of elongation caused by temperature increases, one can roughly multiply the coefficient of concrete expansion (approximately 12 x 10-6 /℃) by the length of the structure and the temperature change.
For example, a 200-foot-long building exposed to a temperature rise of 25 degrees Fahrenheit (14 degrees Celsius) will elongate by about 3/8 inch (9.5 millimetres). Expansion joints are employed to mitigate the forces imposed by thermally induced volume changes.
Expansion joints allow distinct sections of a building to expand or contract independently without negatively impacting its structural integrity or functionality. These joints should have sufficient width to prevent contact between portions of the building on either side of the joint when the structure experiences the maximum expected temperature rise.
The width of expansion joints can range from 1 to 6 inches or more, with 2 inches being the typical width. Wider joints are used to accommodate additional differential movement resulting from settlement or seismic forces. These joints should extend throughout the entire structure above the foundation level and can be either covered or filled. Filled joints are mandatory for fire-rated structures.
Spacing of Expansion Joints
There can be some debate about whether expansion joints should be included in building design and, if so, what spacing they should have. The spacing of expansion joints depends on the acceptable level of movement, as well as the allowable stresses and/or capacity of the structural elements. It also depends on the length and stiffness of frame members and the seasonal temperature fluctuations experienced at the construction site.
The design temperature change is calculated based on the difference between the extreme values of the daily maximum and minimum temperatures. In addition to general guidelines, various methods have been developed to calculate the appropriate spacing for expansion joints.
Author
Spacing of expansion joint
Lewerenz (1907)
75 ft (23 m) for walls.
Hunter (1953)
80 ft (25 m) for walls and insulated roofs, 30 to 40 ft (9 to 12 m) for uninsulated roofs.
Billig (1960)
100 ft (30 m) maximum building length without joints. Recommends joint placement at abrupt changes in plan and at changes in building height to account for potential stress concentrations
Wood (1981)
100 to 120 ft (30 to 35 m) for walls.
Indian Standards Institution (1964)
45 m (≈ 148 ft) maximum building length between joints
PCA (1982)
200 ft (60 m) maximum building length without joints
ACI 350R-83
120 ft (36 m) in sanitary structures partially filled with liquid (closer spacings required when no liquid present).
Table 1 — Expansion joint spacings
Similar to contraction joints, practical guidelines have been established, as outlined in Table 1. These guidelines vary depending on the type of structure and span a range of 30 to 400 feet (9 to 122 meters). In addition to these rule-of-thumb recommendations, several methodologies have been devised to determine the appropriate spacing for expansion joints. This section introduces three such methods, all rooted in the research conducted by Martin and Acosta in 1970, Varyani and Radhaji in 1978, and the National Academy of Sciences in 1974.
Some recommendations propose placing movement joints in masonry structures at approximately 7 meters apart, matching the spacing of the frame elements. For concrete floor slabs, the suggested spacing is approximately 20 to 30 meters, according to Deacon (1986), Bussell and Cather (1995), and the Concrete Society (2003). This implies that continuous multi-bay frames should also incorporate movement joints at similar intervals.
Consequently, a decision must be made: either incorporate movement joints throughout the entire height of the structure, necessitating full wind bracing in each portion of the structure or design the structure to withstand the forces generated by such movements.
Calculation of Expansion Joint Spacing (Single Storey Buildings)
In 1970, Martin and Acosta introduced a technique for determining the maximum allowable spacing between expansion joints in single-story frames with spans that are approximately equal. Their approach assumes that, with appropriate joint spacing, the load factors related to gravity loads will offer sufficient safety margins against the impact of temperature variations.
Martin and Acosta derived a unified formula to calculate the expansion joint spacing, denoted as “Lj,” which relies on the structural stiffness characteristics of the frame and the designated temperature change, ∆T. This equation was developed through a study of frame structures designed in accordance with ACI 318-63 standards. The formula for expansion joint spacing is as follows:
where: r = ratio of stiffness factor of column to stiffness factor of beam = Kc/Kb; Kc = column stiffness factor = Ic/h, in.3(m3) Kb = beam stiffness factor = Ib/L, in.3 (m3) h = column height, in. (m) L = beam length, in. (m) Ic = moment of inertia of the column, in.4(m4) Ib = moment of inertia of the beam, in.4 (m4) Ts = 30 F (17 C)
Values for Tmax and Tmin can be obtained from the Environmental Data Service for a particular location. The design temperature change ∆T is based on the difference between the extreme values of the normal daily maximum and minimum temperatures. An additional drop in temperature of about 30 F (17 C) is then added to account for drying shrinkage.
Length between expansion joints versus design temperature change, ∆T (Martin & Acosta 1970)
Conclusion
In the construction industry, expansion joints play a critical role in ensuring the longevity, safety, and functionality of the building structures. Their design and placement require careful consideration of various factors, including temperature variations, structural movement, and material characteristics. By providing controlled gaps to accommodate movement and stresses, expansion joints can be used to create robust and resilient structures in the face of dynamic forces and environmental challenges.
References
ACI Committee 350, “Concrete Structures (ACI 350R83),” American Concrete Institute, Detroit, 1983, 20 pp Billig, Kurt, “Expansion Joints,” Structural Concrete, London, McMillan and Co., Ltd., 1960, pp. 962-965. Code of Practice for Plain and Reinforced Concrete, IS 456-1964, 2nd Revision, Indian Standards Institution, New Delhi, 1964 Hunter, L.E., “Construction and Expansion Joints for Concrete,” Civil Engineering and Public Works Review, V. 48, No. 560, Feb. 1953, pp. 157-158, and V. 48, No. 561, Mar. 1953, pp. 263-265. Lewerenz, A.C., “Notes on Expansion and Contraction of Concrete Structures,” Engineering News, V. 57, No. 19, May 9, 1907, pp. 512-514 Wood, Roger H., “Joints in Sanitary Engineering Structures,” Concrete International, V. 3, No. 4, April 1981, pp. 53-56.
Due to the poor tensile strength of concrete, some degree of cracking in reinforced concrete is inevitable. Contraction joints are designed to create predetermined weak points where cracks can develop. The weakened section at a contraction joint can be created through forming or sawing, either with no reinforcement or by allowing a portion of the total reinforcement to pass through the joint. Through careful architectural planning, these joints can be strategically placed to ensure that any resulting cracks are less noticeable within a building and ideally out of plain view.
Crack forming through a contraction joint
There are two primary reasons for controlling cracks in reinforced concrete buildings. Firstly, aesthetics play a significant role; visible cracks are unsightly, particularly when the concrete is intended to be the final finished product. Cracks in major structural elements like girders and columns can raise concerns about the structure’s structural integrity, even if they don’t necessarily pose a structural risk. Secondly, cracks of significant width can allow air and moisture to penetrate the structure’s framework, potentially causing durability issues.
As a result, there is a genuine need for crack control in reinforced concrete structures. The main questions revolve around how to manage the extent of cracking, achieved through contraction joints, and how to restrict stresses in members to an acceptable level, accomplished through expansion joints.
The following sections offer recommendations for contraction joint spacing. Once the joint locations are chosen, it’s crucial to construct the joint in a manner that fulfils its intended purpose.
Contraction Joints
Drying shrinkage and variations in temperature result in tensile stresses within a concrete mass, especially when the material is restrained. Cracks will develop when these tensile stresses exceed the tensile strength of the concrete, which is relatively low.
Given this inherent limitation of concrete, cracking of concrete sections is usually quite likely. Contraction joints serve as predetermined weak points where cracks can form without adversely affecting the overall appearance of a structure. Typically, contraction joints are primarily employed in walls and slabs-on-grade.
It’s important to note that the greater the spacing between contraction joints, the more significant the forces generated within a structure due to volume changes. To withstand these forces and minimize the extent of cracking in the concrete, additional reinforcement is needed.
Joint Configuration
Contraction joints are normally constructed as concrete sections with reduced cross-sectional area and reinforcement. To ensure the weakness of the section is sufficient for crack formation, it is recommended that the concrete cross-section be reduced by at least 25 percent. In terms of reinforcement, there are currently two types of contraction joints in use, referred to as “full” and “partial” contraction joints according to ACI 350R guidelines.
Full contraction joints, the preferred choice for most building construction, are established with a complete disruption in reinforcement at the joint. All reinforcement is terminated approximately 2 inches (51 mm) away from the joint, and if the joint serves as a construction joint, a bond breaker is placed between successive placements.
Partial contraction joints, on the other hand, are constructed with no more than 50 percent of the reinforcement passing through the joint. Partial contraction joints find application in liquid containment structures. In both types of joints, water stops may be employed to ensure water tightness.
Joint Location
Once the decision to employ contraction joints is made, the next consideration is determining the necessary spacing to control the extent of cracking between these joints. As detailed in Table 1, various recommendations are provided for contraction joint spacing. The suggested spacings range from 15 to 30 feet (approximately 0.6 to 9.2 meters) and from one to three times the height of the wall.
Author
Recommended contraction joint spacing
Merrill (1943)
20 ft (6 m) for walls with frequent openings, 25 ft (7.5 m) in solid walls.
Fintel (1974)
15 to 20 ft (4.5 to 6 m) for walls and slabs on grade. Recommends joint placement at abrupt changes in plan and at changes in building height to account for potential stress concentrations.
Wood (1981)
20 to 30 ft (6 to 9 m) for walls
PCA (1982)
20 to 25 ft (6 to 7.5 m) for walls depending on number of openings.
ACI 302.1R
15 to 20 ft (4.5 to 6 m) recommended until 302.1R-89, then changed to 24 to 36 times slab thickness.
ACI 350R-83
30 ft (9 m) in sanitary structures.
ACI 350R
Joint spacing varies with amount and grade of shrinkage and temperature reinforcement.
ACI 224R-92
One to three times the height of the wall in solid walls
Table 1 – Contraction joint spacings
For sanitary structures, Rice (1984) offers contraction joint spacings based on specific reinforcement percentages (as outlined in Table 2).
Contraction joint spacing in ft.
Minimum percentage of shrinkage and temperature reinforcement (fy = 276 MPa)
Minimum percentage of shrinkage and temperature reinforcement (fy = 413 MPa)
less than 30
0.30
0.25
30 – 40
0.40
0.30
40 – 50
0.50
0.38
greater than 50
0.60
0.45
Table 2 – Contraction joint spacings for sanitary engineering structures based on reinforcement percentage (Rice 1984)
It’s important to note that the limits specified by Rice in Table 2 extend the recommendations outlined in ACI 350R, taking into account factors such as reinforcement grade and minimum bar size. It’s worth mentioning that when employing a “partial” contraction joint, the spacing should be roughly two-thirds of that used for a full contraction joint, as per ACI 350R guidelines.
Additionally, Wood (1981) suggests that any joint within a structure should traverse the entire structure in a single plane. Misalignment of joints may result in movement at one joint causing cracking in an unjointed portion of the structure until the crack intersects another joint.
For slabs-on-grade and concrete pavements, contraction joints are usually placed at depths ranging from 1/4 to 1/3 of the slab’s thickness and are commonly spaced at intervals of 3.1 to 15 meters (approximately 12 to 50 feet). Thinner slabs tend to have more closely spaced joints. According to the Portland Cement Association (PCA), contraction joints are spaced at intervals ranging from 24 to 30 times the thickness of the slab. When the spacing between joints exceeds 15 feet (4.5m), the inclusion of load transfer mechanisms such as dowels or diamond plates becomes necessary.
Contraction joint cracking
It is also common to have, a semi-random pattern for joint spacing in pavements to reduce their impact on vehicle resonance. Such patterns often involve a recurring sequence of joint spacings, such as 2.7 meters (9 feet), followed by 3.0 meters (10 feet), then 4.3 meters (14 feet), and subsequently 4.0 meters (13 feet).
Conclusion
In conclusion, contraction joints play an important role in the construction of concrete structures. These strategically placed joints serve as planned weak points, allowing for controlled cracking in response to factors like temperature variations and drying shrinkage. Properly designed and spaced contraction joints are essential for maintaining the structural integrity and aesthetic appeal of buildings and other concrete structures.
The choice of joint type, spacing, and reinforcement is crucial, as it directly impacts the extent of cracking and the overall durability of the structure. By adhering to recommended guidelines and considering the specific needs of the project, engineers and builders can effectively manage and control cracking, ensuring that the structure remains safe, functional, and visually pleasing for years to come.
References
ACI Committee 224, “Control of Cracking in Concrete Structures,” ACI 224R-80, Concrete International, V. 2, No. 10, Oct. 1980, pp. 35-76. ACI Committee 302, “Guide For Concrete Floor and Slab Construction (ACI 302.1R-89),” American Concrete Institute, Detroit, 1989, 45 pp. ACI Committee 318, “ACI Standard Building Code Requirements for Reinforced Concrete (ACI 318-63),” American Concrete Institute, Detroit, 1963, 144 pp. ACI Committee 350, “Concrete Structures (ACI 350R83),” American Concrete Institute, Detroit, 1983, 20 pp. Fintel, M. (1974). “Joints in Buildings,” Handbook of Concrete Engineering, New York, Van Nostrand Reinhold Company, 1974, pp. 94-110. Merril, W. S. (1943). “Prevention and Control of Cracking in Reinforced Concrete Buildings,” Engineering News-Record, V. 131, No. 23, Dec. 16, 1943, pp. 91-93 Rice, P.F. (1984). “Structural Design of Concrete Sanitary Structures,” Concrete International, V. 6, No. 10, Oct. 1984, pp. 14-16. Wood, R. H. (1981). “Joints in Sanitary Engineering Structures,” Concrete International, V. 3, No. 4, April 1981, pp. 53-56.
