Vibration (or Oscillation) is a time-dependent, repeated motion which a body undergoes when it is excited in its natural state or by an external force. Frequency is the number of cycles of vibration the system undergoes in a unit of time which is expressed in Hertz (Hz) or (cycles per second). When a structural system is undergoing undamped vibration in its natural state (under self excitation), it is said to be undergoing free vibration. A structure has as many natural frequencies as its degree of freedom, but the frequency with the highest mass participation is often regarded as the natural frequency.
In the video shown above, a ten storey frame of total height of 30 m (each storey height = 3m) was analysed to determine the natural frequency under a floor load of 40 kN/m at each level. All the columns are 400 mm x 400 mm in dimension while the beams are 600 mm x 400 mm. The support conditions were treated as fixed. When analysed using the steps described in the video, the results below were obtained;
The horizontal natural frequency was observed to be 0.587 Hz, with a period of 1.705 seconds. The mass participation factor for this mode vibration was found to be 81.89%. The implication of this is that when carrying out the wind load analysis, the frequency of the wind action should not be close to 0.587 to avoid resonance.
The vertical frequency of the structure was observed to be 5.854 Hz with a period of 0.171 seconds, and mass participation factor of 70.981%. This can be important when evaluating human-structure interaction if the building will be subjected to crowd action.
Here are some textbooks you can purchase from Amazon that will help your understanding of the subject:
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In the design of bridges, environmental actions such as wind, snow, and temperature should also be considered alongside traffic actions. In this article, we are going to show how to apply wind action on bridge decks according to the procedures described in EN 1991-1-4. The specifications in this code apply to bridges of constant cross-section with one or more spans. Different bridge deck sections are permitted such as mono-cell box sections, closed box sections, beam and slab deck systems, etc (see Fig 8.1 of EN 1991-1-4).
In EN 1991-1-4, wind load on bridge decks are considered to be coming from the longitudinal (y-direction) or from transverse (x-direction) axes, and these actions generate stresses in the x,y,z directions of the bridge deck (see Figure 1). During analysis, you can only consider the wind coming in one direction only (either x or y direction) for each load combination.
Fig 1: Wind direction on bridge deck (Fig 8.2 EN 1991-1-4)
Wind forces acting on a bridge deck Wind forces acting in the x-direction of a bridge deck is given by the simplified equation (1);
Fwk= 0.5ρVb2C.Aref,x —– (1)
Where; ρ = density of air = 1.25 kg/m3 Vb = basic wind speed of the site C = Wind load factor for the bridge Aref,x = Reference area
In the absence of traffic, the reference area Aref,x should take into account the total height d of projection on a vertical plane of all beams, including the part of one cornice or footway or ballasted track projecting over the front main girder, plus the sum d1 of solid parapets, noise barriers, windshields, and open safety barriers installed on the bridge. In the case of truss girders, the total height d of the projection on a vertical plane of all truss members should be considered.
In the presence of traffic, the reference area Aref,x should be assumed as the larger between the area evaluated considering the absence of traffic, and the area obtained taking into account the presence f traffic. For road bridges, the lateral surface of vehicles exposed to wind is represented by a rectangular area 2m in height starting from the carriageway level.
The wind load factor C is given by equation (2);
C = cecf,x —–(2)
Where ce is the exposure coefficient for kinetic pressure and cf,x is the force coefficient which is the drag coefficient without free end flow. The exposure coefficient can be evaluated by considering a reference height ze given by the distance from the lowest point of the ground and the center of the bridge deck disregarding additional parts, parapets, barriers, etc.
For bridges with solid parapets and/or solid barriers and/or traffic, the force coefficient cf,x can be determined using equation (3);
cf,x = min {2.4; max[2.5 – 0.3(b/dtot); 1.3]} —- (3)
Where b is the total width of the bridge and dtot is the height considered in the evaluation of Aref,x = dtot.L
From the above considerations, equation (1) can also be given as equation (4);
Fwk= qp(ze)Cf,x.Aref,x —– (4)
Analysis Example Evaluate the wind load on the bridge deck with the profile shown in Figure 2. The bottom of the bridge deck is 7m above the ground (see Figure 3), and it is located in a category III area.
Fig 2: Bridge deck profile
Fig 3: Height of the bridge deck above ground level
We will therefore take our reference height ze = 7.0 + 1.25 = 8.25 m
For the area under consideration, let the basic wind velocity Vb,0 = 40 m/s. Therefore; Vb = Cdir . Cseason . Vb,0 = 1.0 × 1.0 × 30 = 40 m/s
The mean wind velocity Vm(z) at a height z above the terrain depends on the terrain roughness and orography, and on the basic wind velocity, Vb, and should be determined using the expression below;
Vm(z) = cr(z). co(z).Vb
Where; cr(z) is the roughness factor (defined below) co(z) is the orography factor often taken as 1.0
The terrain roughness factor accounts for the variability of the mean wind velocity at the site of the structure due to the height above the ground level and the ground roughness of the terrain upwind of the structure in the wind direction considered. Terrain categories and parameters are shown in Table 1. We will assume that the tank support we are designing is located in an area that can be described as Category III.
Table 1: Terrain Categories and parameters (Table 4.1 EN 1991-1-4:2005)
cr(z) = kr. In (z/z0) for zmin ≤ z ≤ zmax cr(z) = cr.(zmin) for z ≤ zmin
Where: Z0 is the roughness length Kr is the terrain factor depending on the roughness length Z0 calculated using Kr = 0.19 (Z0/Z0,II)0.07
Where: Z0,II = 0.05 m (terrain category II) Zmin is the minimum height Zmax is to be taken as 200 m kr = 0.19 (0.3/0.05)0.07= 0.215
cr(z) = kr. In (z/z0) cr(8.5 m) = 0.215 × In(8.5/0.3) = 0.605
Therefore; Vm(8.5 m) = cr(z). co(z).Vb = 0.605 × 1.0 × 40 = 24.2 m/s
Wind turbulence The turbulence intensity Iv(z) at height z is defined as the standard deviation of the turbulence divided by the mean wind velocity. The recommended rules for the determination of Iv(z) are given in the expressions below;
Iv(z) = σv/Vm = k1/[c0(z).In (z/z0)] for zmin ≤ z ≤ zmax Iv(z) = Iv.(zmin) for z ≤ zmin
Where: k1 is the turbulence factor of which the value is provided in the National Annex but the recommended value is 1.0 Co is the orography factor described above Z0 is the roughness length described above.
From Figure 2, we can verify that dtot = 2.5 m + 1.0 m = 3.5 m b = 10.5 m
cf,x = min {2.4; max[2.5 – 0.3(b/dtot); 1.3]} = min {2.4; max[2.5 – 0.3(10.5/3.5)]; 1.3} = min {2.4; max[1.6; 1.3]} The minimum value of 1.3 recommended is always deemed unsafe sided, therefore take cf,x = 1.6
Fwk= 1.132 x 1.6 x 3.5 = 6.3392 kN/m
Fig 4: Application of wind load on the deck without vehicle
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Concreting or casting days are usually big days for site engineers. It is very typical to see engineers and project managers work very hard to ensure that nothing goes wrong on such days. Thinking ahead is an important skill in construction site management as it gives room for the elimination of all factors that may cause glitches during construction. In this article, we are going to provide some important checklists to help you know whether you are fully ready to cast concrete on site.
A lot of activities precede concrete casting on site such as formwork installation, reinforcement installation and fixing, quality control checks etc. Having gone through these processes to get everything right, the final stage is concreting. It is important to make a checklist in order to ensure that you have done everything properly. Omitting any of these checklists might cause a delay you will not expect on your day of casting.
Here are some important checklists before concreting in a low scale – low-cost construction project:
(1) Formwork The formwork installation must be checked and approved by a third party. Checks should include dimensions and tolerances, bracings, location of props, tightness of formwork to prevent excessive loss of cement slurry etc.
(2) Reinforcement The reinforcement works must be checked and approved by the structural engineer and other relevant agencies. Checks should ensure that the correct grade and sizes of bars have been used, the rebar spacings are according to the drawings, lap lengths and positioning of bars are appropriate etc. The inspector should also check the concrete covers, and certify them as adequate.
(3) Levels The levels for concreting should be established and checked using available instruments. The levels can be established using nails, markers, pegs etc. It is not ideal to start establishing casting levels on the day of concreting. It will lead to delays.
(4) Scaffolds, walkways, and platforms Sometimes site engineers may forget to make provisions for walkways and platforms and start running around on a casting day. If you are casting at a height, make sure you provide safe benches, walkways, scaffolds, and platforms to enable the casters to walk freely and pour concrete in a safe manner.
(5) Personal Protective Equipment(PPE) All PPEs must be available on-site prior to the day of casting and given to workers before the commencement of casting. Safety officers should stop the casting operation if safety precautions are not taken seriously.
(6) Materials All the materials needed for casting should be available before the day of casting. These include sand, granite, cement, admixtures, and water. As practically as possible, ensure that all the materials you need to complete the casting are on the ground a day prior to the casting date.
Suppliers may disappoint you on the casting day or there might be a breakdown of vehicles or unforeseen interruptions. This will completely ruin your big day and you will not meet your target. Also, make sure that you have calculated the quantity of materials you need properly, and verify that the suppliers did not undersupply. Lack of water on site can ruin your casting day too. Therefore, you must pay careful attention to the materials you need.
(7) Equipment/Machinery Ensure that all tools, equipment, and machinery you need for the job are on stand-by prior to the day of casting. You should have at least two vibrators and two concrete mixers on-site, depending on the size of the job to be done. Breakdown of equipment can completely ruin your day. Also make sure that ancillary equipment such as your concrete cube moulds, buckets, headpans, shovels, trowels, etc are all available.
(8) Personnel Make calls and confirm the availability of all personnel you will need for the job at least 24 hours before the casting day. This includes all supervisors, safety officers, operators, foremen, labourers, etc. Also, make sure that at least one iron bender, one carpenter, and one mechanic (technician) are available on your casting day for quick fixes just in case something goes wrong.
(9) Casting sequence/planning Plan your casting operations very well before the actual casting date. You may want to look at the areas that you will cast before the others. Factors that may influence these are the location of materials, location of concrete mixers, concrete thermal cracking considerations, ease of access and pouring, construction methodology etc.
A site manager must work out these details properly and discuss them with the foremen and supervisors. Their inputs will be helpful for a successful casting operation. Also based on the size of the job, you can request two or more gangs (two or more concrete mixers with different casting teams) working simultaneously so that you can finish on time. Make provisions for adequate lighting on site if the casting must finish in one day, and you anticipate it might creep into dusk.
With all these checklists certified, you can be sure that your casting can progress without many problems.
Spherical tanks (Horton Sphere) are used in several applications such as water storage, nuclear cooling, and storage of liquefied gases such as liquefied natural gas (LNG) and liquefied petroleum gas. One of the most common utilization of spherical vessels in the industry is pressurized gas storage because they can withstand higher internal pressure and have fewer size limitations than cylindrical pressure vessels. Horton Spheres usually contain pressurized gas inside the steel shell. The shell is supported by heavy steel columns which transmit the load to a reinforced concrete foundation.
Fig 1: Typical LPG spherical tank
Spherical tanks have high rigidity and durability. According to Khan (2015), the performance of a 200 m3 liquefied petroleum gas (LPG) tank with a wall thickness of 24 mm under 1.7 MPa pressure was evaluated after it had been in operation for three years. The result showed high resistance to micro cracking and shell deformation, with minimal wall thinning.
Fig 2: LPG Tank farm under construction in Lagos, Nigeria
Fig 3: Author at an LPG tank farm construction site in Lagos
In this article, we are going to evaluate the potentials of Staad Pro software in the modeling and analysis of LPG sphere tanks. We are not going to deeply evaluate the design considerations for such structures but you should know that the tank shell should be able to withstand the vapour pressure from the liquefied petroleum gas.
This pressure is dependent on temperature and the design temperature is selected from the environment under consideration. For example, LPG gas cylinder pressure (LPG gas bottle pressure) is 0 kPa at -43ºC and goes up to 2482 kPa at 70ºC.
In this article, let us model and analyse an LPG sphere tank on Staad Pro with the following data;
(1) Diameter of tank = 20 m (2) Thickness of tank shell = 25 mm (3) Columns – Hollow circular steel columns of external diameter 900 mm (thickness = 40 mm) (4) Design pressure = 1700 kPa
Fig 4: Spherical LPG model on Staad Pro
Fig 5: 3D rendering of LPG tank model
When analysed on Staad Pro for a gas pressure of 1700 kPa, the following results were obtained.
Fig 6: Lateral bending moment on the tank shell due to gas pressure
Fig 7: Longitudinal bending moment on the tank shell due to gas pressure
Fig 8: Twisting moment on the tank shell due to gas pressure
Fig 9: Lateral shear stress on the tank shell due to gas pressure
Fig 10: Longitudinal shear stress on the tank shell due to gas pressure
Fig 11: Lateral axial tension on the tank shell due to gas pressure
Fig 12: Longitudinal axial tension on the tank shell due to gas pressure
The video tutorial for this modeling and analysis is available on special request by sending an e-mail to ubani@structville.com. Also free contact us for special designs related to infrastructures in oil and gas facilities and tank farms.
References Khan F.A. (2015): Spherical tanks in energy storage systems. A PhD thesis subimtted to the Department of Mechanical Engineering, WORCESTER POLYTECHNIC INSTITUTE .
In civil engineering construction works, contractors bidding for a job are always required to specify the rate they will use in executing a given item of work. In a competitive bidding, the client will review the rates supplied by the bidders, and award the contract to the person he finds most suitable.
Concrete is a common construction material that is basically made from cement, sand, gravel, and water. The main aim of this article is to teach you how to build up your rate, and quote for concrete in construction works.
The unit of concrete in construction is specified in cubic metres (m3). For instance, if a floor slab has a net area of 250 m2, and a thickness of 150 mm, the volume of concrete required will be stated as (250 x 0.15 = 37.5 m3). In the bill, a contractor is expected to state the cost of casting a cubic metre of the specified grade concrete (say grade 25), which can be used to relate the cost of casting the entire slab.
Note that the rate supplied by the contractor is expected to include the cost of materials, plant, transportation, labour, and contractor’s profits.
There are basic considerations to make while quoting for concrete because you should not bid too high or too low. It is possible for contractors to have a wide difference in their rates for the same job. For a competitive tender without bias, a company that is going to hire equipment will likely bid higher than a company that has its own equipment. The same goes with labour, transport facilities, etc.
Bidding for a job should be an intelligent process, and the contractor should know his capacity as it will likely influence his cost and profitability. The cost of casting concrete in one day is not the same with casting it for two days. Therefore, a contractor’s capacity can enable him bid higher or lower depending on the context.
To make it simpler, let us give an idea on how you can build up your rate for grade 25 concrete.
In the past, we have made a post on how you can achieve grade 25 concrete on site. We were able to show that the mix ratio of 1:2.5:3.5 can yield grade 25 concrete. Let us assume you wish to use this mix ratio in building your rate.
The total volume in the mix ratio is given by; 1 + 2.5 + 3.5 = 7
Cement Ratio of cement by volume = 1/7 Density = mass/volume Mass of cement required = (1/7) x 1440 = 205.7 kg Making allowance for shrinkage = 1.54 x 205.7 = 316.77 kg Number of bags of cement required per of concrete = 316.77/50 = 6.33 bags (use 7 bags)
Sand Ratio of sand by volume = 2.5/7 Density = mass/volume Mass of sand required = (2.5/7) x 1650 = 589.285 kg Making allowance for shrinkage = 1.54 x 589.285 = 907.498 kg Making allowance for waste = 1.2 x 907.498 = 1088.99 kg/m3
Granite Ratio of granite by volume = 3.5/7 Density = mass/volume Mass of granite required = (3.5/7) x 1650 = 825 kg Making allowance for shrinkage = 1.54 x 825 = 1270.5 kg Making allowance for waste = 1.15 x 1270.5 = 1461.075 kg/m3
Market Prices of Materials including transportation to site; Cement = ₦4100 per bag Sharp sand = ₦ 3500 per tonne Granite aggregate = ₦ 16000 per tonne (the current basic rate of granite is about NGN 9000 per tonne, but the cost of transportation is currently so high)
Cost of materials Cost of cement per cubic metre concrete = 7 x 4,100 = ₦28,700 Cost of sharp sand per cubic metre of concrete = 3500 x 1.08899 = ₦3,812 Cost of granite per cubic metre of concrete = 16000 x 1.461 = ₦23,376 Total Material Cost = ₦55,888 per cubic metre of concrete
(b) Plant Rate of Concrete mixer per cubic metre of concrete = ₦600 Rate of vibrator per cubic metre of concrete = ₦350 Operator = ₦500 Total Plant Cost = ₦1,450 per cubic metre of concrete
(c) Labour Labour output (production and placement) per cubic metre of concrete = ₦7,000
Total cost of production = ₦55,888 + ₦1,450 + ₦7,000 = ₦64,388
(d) Profit and Overhead (20%) 1.2 x ₦64,388 = ₦77,205
Therefore thecost of producing one cubic metre of grade 25 concrete is ₦64,388
The West African Standard (WAS) compaction test is a type of compaction procedure that utilises intermediate compaction energy (compactive effort) for densification of soils. It has been recommended for densification of soils for highway construction in Nigeria and some other West African Countries. The compaction energy of WAS lies between the compaction energy of BS Light (Standard Proctor) and BS Heavy (Modified Proctor).
The details of the West African Standard compaction test using BS Mould are as follows;
Volume of mould = 1000 cm3 = 0.001 m3 Number of blows = 10 Number of soil layers = 5 Weight of rammer = 4.5 kg Height of fall = 0.4575 m
Therefore, the compaction energy (compactive effort) of WAS using BS Mould is given as follows; Compactive effort = (9.81 x 10 x 5 x 4.5 x 0.4575)/0.001 = 1009816.875 N.m/m3 = 1009.816 kN.m/m3.
The details of the West African Standard compaction test using the CBR Mould are as follows;
Volume of mould = 2305 cm3 = 0.002305 m3 Number of blows = 25 Number of soil layers = 5 Weight of rammer = 4.5 kg Height of fall = 0.4575 m
Compactive effort using CBR mould = (9.81 x 25 x 5 x 4.5 x 0.4575)/0.002305 = 1094.527 kN.m/m3.
It can be observed that WAS compaction test an intermediate compaction energy when compared with BS Light (605.49 kN.m/m3) and BS Heavy (2726.5 kN.m/m3).
Applications of WAS compaction in Nigeria (1) Laboratory compaction of sub-base course according to Federal Ministry of Works Specification (1997) (2) Soaked CBR test of base course (clause 6200) (3) Soaked CBR test of sub-base course Type 2 (clause 6200)
Landing a good job soon after graduation is the dream of many young civil engineering students. On the other hand, as a professional engineer grows on the job, there might come a time when he will want to switch from one civil/structural engineering job to another. This can happen for a lot of reasons which may be personal or professional. The process of finding a new job often involves passing through interviews during which the employers will try to know as much as possible about the person interested in working for them.
The questions asked during interviews are usually related to the ideals of the organisation, and the requirements of the position they are seeking to fill. All civil engineering firms do not offer the same services. As a result, it is important to research properly on the company, know what they do, and what they stand for. Employers will also try to take a look at you, and at how your attitude and appearance will reflect their brand. Once again, it strongly depends on the area that the company will be needing your services.
Having said that, let us look at what you should expect during interviews for graduate trainee/internship roles in various civil engineering companies.
Consultancy firms Consultancy firms are usually involved in civil engineering designs, drawings, supervision, and project management. For beginner roles, they will likely be more interested in your basic knowledge of civil engineering structures, analyses, design, and drawings. They will expect the candidate to be sound, smart, and trainable. Having a basic knowledge of AUTOCAD, and other civil engineering software will be added advantage.
Small and medium scale consultancy firms usually conduct in-house interviews, and will be more interested in your technical capacity and how well you will fit into their team. For such job assessments, you might be given simple beams and slabs to analyse and design, and asked questions on the behaviour of some construction materials such as concrete. A hands-on test on AUTOCAD and other civil engineering software might be done.
On the other hand, bigger/multinational firms who have distinguished Human Resources Department might wish to conduct a larger scale interview, or might outsource the recruitment process to external consultants. In this case, the interview questions will usually extend to leadership and competency-based questions. For such bigger firms, the interview panel might consist of only one engineer and other members who might have studied sociology or business administration.
In such cases, therefore, you should widen your scope and present yourself as a general problem solver, as it will excite them more. Your ability to analyse and design complex frame structures might not really excite them as much as when you tell them how you solved a complex social problem during a volunteering activity. Apart from your technical capacity, they are very much interested in your leadership, emotional, and social credentials. Smaller design firms may not pay much attention to those aspects.
You should note that in both cases, the organisation and the interviewers understand that you are a fresh graduate with no experience, hence, they are simply looking out for a few basic things during the interview. Your ability to communicate, answer questions smartly, coordinate yourself properly, and present yourself as a quick learner will earn you serious consideration.
If you have made any significant achievement such as publications, verifiable unique designs, significant contributions, or possession of a unique skill, you should try and talk about them so that they can take you seriously from the onset. It simply gives the impression that you are an achiever. What might distinguish you from another civil engineering graduate may be your ability to write computer programs or codes, and in this digital age, any serious organisation will likely give you preferential treatment.
In summary, find the right time to talk about your special skills and experience during interviews. An organisation might wish to hire you because you did your student internship with a company they rate highly, or perhaps because you have participated in the construction of a green building, which is an area they might be interested in.
Generally, from the way you present yourself and answer questions, they will decide whether to hire you or not. As hinted earlier, your technical ability and academic records will excite smaller firms than bigger firms. This is because when an interview is done in-house, you are going to be interviewed by engineers and other technical people who will eventually become your direct colleagues. But in bigger firms, the requirements often appear broader as they seem to focus more on ‘general problem solving’ skill than specialised technical ability. Therefore, it is important to understand your interviewers based on the kind of questions they ask, and know how to answer accordingly.
Note that consultants often go to site visitation, supervision, and meeting with clients or contractors. As a result, you will be representing your firm on many occasions as an image of the organisation. Therefore, your ability to dress properly and communicate effectively is of paramount importance. It will be observed during the interview, and if your communication skills are poor, it might limit your chances.
Construction firms There are some companies that are mainly builders/contractors and rarely do designs. Interviews for civil engineering jobs with such companies are usually not focused on designs and theory of structures but on site practices. You might be asked questions like:
How do you set out a building? How do you establish levels? What concrete mix ratio will give you grade 25 concrete? How can you calculate the quantity of tiles needed to tile an area? Describe the process of constructing a flexible pavement? What is the minimum gauge of aluminium roof required to roof a steel roof building? How do you prepare bar bending schedule? etc
As you can see, these are more of practical site questions, because the firm knows that they will be sending you to a construction site. However, they know you are a fresh graduate with limited or no site experience, but you still need to impress with knowledge of basic site practices.
Bigger firms might also be interested in other things such as your knowledge of HSE, project management tools/techniques, and ability to manage people. However, for many trainee positions, most organisations will rather train you in their own way provided you are trainable.
It is important to know that highway/road construction companies will typically ask you highway-related questions, while water resources engineering companies will ask you water-related questions. But it is generally important that you exhibit good competency and knowledge of civil engineering, to the extent required of a fresh graduate.
In our previous article, we were able to evaluate the effects of temperature difference on rectangular tanks. In this article, we are going to evaluate the same effect on a cylindrical tank of the same volume, in order to obtain the internal stresses and displacements in the tank due to temperature differences. This article will serve as a comparison between the response of a rectangular and cylindrical tank to temperature actions.
In our last article, the dimensions of the rectangular tank was observed to be 3m (L) x 3m (B) x 2.5m (H), thereby giving a volume of 22.5 m3. To model an equivalent cylindrical tank of the same height of 2.5 m, the diameter of the tank was obtained as 3.38 m. The other details of the tank are as follows;
Dimensions of columns = 300 mm diameter circular column Dimension of beams = 300 x 500 mm Height of column above ground level = 3 m Diameter of tank = 3.38 m (centre to centre) Height of tank = 2.5 m (centre to centre) Thickness of tank walls and base = 250 mm Support condition = Fixed Temperature inside the tank = 120 oC Temperature outside the tank = 25 oC Maximum hydrostatic pressure from the liquid stored = 25 kPa Modulus of elasticity of concrete = 2.8 x 107 kN/m2 Coefficient of expansion of concrete = 1.0 x 10-5 /oC
Temperature change for axial elongation = Average temperature = (25 + 120)/2 = 72.5 oC Temperature difference = 25 – 120 = -95 oC
When modelled on Staad Pro using the procedure described in the video above, the configuration and results below were obtained.
Fig 1: 3D model of cylindrical water tank
Fig 2: Radial bending moment on the tank shell due to temperature load
Fig 3: Longitudinal bending moment on the tank shell due to temperature load
Fig 4: Twisting bending moment on the tank shell due to temperature load
Fig 5: Radial shear on the tank shell due to temperature load
Fig 6: Longitudinal shear on the tank shell due to temperature load
Fig 7: Hoop tension (membrane) on the tank shell due to temperature load
Fig 8: Longitudinal tension on the tank shell due to temperature load
The differences in internal stresses induced in cylindrical tanks of equal volume and height with the rectangular tank are shown in Table 1.
Table 1: Internal stresses in rectangular and cylindrical tanks due to temperature load
In some factories and industries, tanks are used for the storage of hot liquids which are used in production. In such scenarios, the temperature inside the tank and the temperature in the surrounding may not be the same. It is well known that internal forces are induced in statically indeterminate structures when there is temperature difference as the elements undergo differential thermal expansion/contraction. For simple frames, the internal forces due to temperature difference can be easily obtained using the force method of structural analysis. But for more complex structures like combination of beams and plates, software like Staad Pro can be used for evaluation of temperature difference.
For example, let us consider the reinforced concrete tank with the dimensions shown in Figure 1;
Fig 1: Structural scheme of water tank subjected to temperature difference
Dimensions of columns = 300 x 300 mm Dimension of beams = 300 x 500 mm Height of column above ground level = 3 m Length of tank = Width of tank = 3 m (centre to centre) Height of tank = 2.5 m (centre to centre) Thickness of tank walls and base = 250 mm Support condition = Fixed Temperature inside the tank = 120 oC Temperature outside the tank = 25 oC Maximum hydrostatic pressure from the liquid stored = 25 kPa Modulus of elasticity of concrete = 2.8 x 107 kN/m2 Coefficient of expansion of concrete = 1.0 x 10-5 /oC
The tank has been modelled on Staad Pro (see Figure 2) using the parameters defined above.
Fig 2: Modelling of the tank on Staad Pro
The walls of the tank were subjected to a triangular hydrostatic pressure distribution of 25 kPa. You can check how apply hydrostatic loads on Staad Pro here. The temperature difference action applied to the the tank is shown below.
Temperature change for axial elongation = Average temperature = (25 + 120)/2 = 72.5 oC Temperature difference = 25 – 120 = -95 oC
The application on Staad Pro is shown in Figure 3.
Fig 3: Application of temperature load on Staad Pro
When analysed on Staad Pro, the results shown in Figures 4-8 were obtained for the tank shells at SLS.
Fig 4: Bending moment on the tank shell due to water pressure
Fig 5: Shear stress on the tank shells due to water pressure
Fig 6: Bending moment on the tank shell due to temperature difference
Fig 7: Shear stress on the tank shell due to temperature difference
Fig 8: Displacement of tank shell and frame due to temperature difference
The internal stresses induced in the tank shell due to temperature difference is quite serious and requires detailed attention during design.
The aftermath of any building collapse is usually horrendous, and the experience is an ugly one for everybody concerned. Human lives might be lost, many might be injured, people will be traumatized, properties will be destroyed, and the environment will become a mess. The media usually responds to such events in a manner that will escalate the woes of the stakeholders involved in the construction of the building. That is why professionals must strive to get it right from start to finish.
From a technical point of view, if the recommended/standard process has been followed in construction, a lotof things will need to go wrong before a building will collapse. There are prominent issues that have been identified as the reasons for building collapse such as inadequate design, poor detailing, faulty construction, use of substandard materials, engaging non-professionals etc. In this article, we are going to focus on a special aspect of design called ‘partial factors of safety’.
The procedures for the design of buildings evolved through the years as researchers gained better understanding of the behaviour of structures and materials. This has particularly led to reductions in the factors of safety applied in the design of buildings, thereby leading to more economical designs. As a matter of fact, it is expected that the factors of safety applied in designs will continue to reduce as we gain better understanding of the behaviour of materials that we are dealing with. These factors of safety are simply associated with the fact of not being ‘so sure’. At one point in time in your life, you must have gone an extra mile in doing something, ‘just in case the worst happens’. This is exactly what the factors of safety in modern codes of practice for design offer us, but they also give us guidance on the extent of extra mile we should go, so that we would not spend too much money unnecessarily. The factors of safety were arrived at after rigourous statistical evaluations.
I have seen a cantilever roof parapet collapse due to poor placement of the reinforcement. That could have been a detailing or construction error but it has nothing to do with factor of safety which is the main topic of discussion here. Before we proceed, let us briefly look at some design principles with emphasis on factors of safety.
Design philosophies The first generally accepted principle in the design of structures is the permissible stress method. In this method;
σmax < σper ————— (1)
where σper is given by σcrit/k. In this method, the coefficient k is assessed with regard to uncertainties in the determination of local load effect σmax and of resistance σper. Therefore, the value of k may ensure with an appropriate level of security, the reliability of the structure. The main insufficiency of this method is perhaps the local verification of reliability (in the elastic range) and the impossibility to consider separately the uncertainties of basic quantities and the uncertainties of computational models for the assessment of action effects and structural resistance. In this method, the probability of failure is controlled by one quantity only, the coefficient k (Holicky, 2009).
The second widely-accepted method of structural design is the method of global safety factor. It is based on the condition;
Xresistance/Xaction > S0 ————— (2)
Accordingly, the calculated safety factor s must be greater than its specified value s0. It is a method which attempts mainly to give a truer picture of the behaviour of elements and their cross-sections, in particular through the aggregate quantities of structural resistance Xresistance and action effect Xaction. As in the case of the permissible stresses method the main insufficiency of this method remains the impossibility to consider the uncertainties of particular basic quantities and theoretical models (Holicky, 2009). The probability of failure can, again, be controlled by one quantity only, i.e. by the global safety factor s.
The last on this list is the partial factor method of design (also called the limit state method), and is currently the most advanced operational method of structural design. Partial factor method of structural design is generally characterized by the inequality shown in Equation (3);
Ed(Fd, fd, ad, θd) < Rd(Fd, fd, ad, θd) ———– (3)
This design concept is deemed satisfactory when the effects of actions Ed are less than or equal to the structural resistance Rd. The basic variables involved in modelling the relationship are the actions (Fd = ψγFFk), material properties (fd = fk/γm), dimensions (ad + Δa) and model uncertainties (θd). The reduction factors (ψ) and partial factors for actions and materials (γF and γm) are used to describe the reliability of the structure.
What defines the safety of a building? According to Section 2 of EN 1990, a structure shall be designed and executed in such a way that it will during its intended life, with appropriate degrees of reliability, and in an economic way,
– sustain all actions and influences likely to occur during execution and use; – remain fit for the use for which it is required.
The last two sentences above generally define what is referred to as ultimate limit state (ULS) and serviceability limit state (SLS), and the two key words to look out for in achieving them are ‘reliability’ and ‘economy’. Ultimate limit states are associated with collapse or other similar forms of structural failure. Serviceability limit states correspond to conditions of normal use (deflections, vibration, cracks, etc.). In general the design should include both safety and serviceability, including durability in both cases. The nature of ultimate limit states is essentially different from the nature of serviceability limit states and should be taken into account in reliability verification. ISO 2394 defined reliability as the ability of a structure to comply with given requirements under specified conditions during the intended life for which it was designed.
Can you exhaust your factors of safety? To keep what we showed in equation (3) simple, let us consider BS 8110-1:1997 code of practice (which has been withdrawn), where we normally apply partial factors of safety to loads and materials. At ultimate limit state, we factor the design loads on a building as follows;
P= 1.4gk + 1.6qk ————- (4)
Where gk and qk are the dead load (permanent actions) and imposed loads (variable actions) respectively. A little observation of Equation (4) will show that we are actually increasing the value of the dead load in the building by 40%, and the value of the live load by 60%. If we sum both actions up, we can say that we are designing the building to sustain loads that are almost in excess of 60% of what we anticipate that it will carry in its design life – which is like the collapse load.
In the Eurocodes, the design action of a building at ultimate limit state is given by;
P= 1.35gk + 1.5qk ————- (5)
As can be seen from equations (4) and (5), the partial factors of safety for loads (actions) reduced in the Eurocodes, but the partial factors for materials remained almost the same. For characteristic strength of concrete, the partial factor γc remained 1.5 in both codes of practice, while for steel, the partial factor of 1.15 was also maintained. We should note that the later releases of BS 8110 prior to its withdrawal reduced factor of safety for steel reinforcements from 1.15 (0.87fy) to 1.05 (0.95fy) after it was discovered that the reinforcements manufactured and tested in the laboratories in the UK rarely fell below the minimum strength.
Having taken note of all these partial factors, is it possible for a structure to fail due to actions and materials? The answer still remains yes. In Nigeria, most local contractors do not pay attention to the quality of materials used in construction, and some property owners may misuse the building by overloading it. The most popular design code in Nigeria is still BS 8110, which is widely applied and accepted by the government and other institutions. Let us use the standard to show how the factors of safety can be squandered.
Concrete We have seen cases where the 28 day characteristic strength of concrete used in construction was observed to be about 13 MPa. If grade 25 concrete was used in the design, and partial factor of 1.5 applied, the conservative design strength will be (25/1.5 = 16.67 MPa). In this case, the factor of safety for the concrete is gone.
Steel In most published works available online, we have seen cases where the average characteristic yield strength of reinforcements falls below 400 MPa. If the yield strength of 460 Mpa was used in the design (0.95fy = 0.95 x 460 = 437 MPa), we will discover that the factor of safety for steel is also gone.
Loads The imposed load used in the design of most residential buildings is 1.5 kPa. Sometimes, the usage of a buildings can be abused by say for example, converting a residential building to a place of worship/gathering, or storage house. If a building designed as residential building is used to stack four bags of cement spread all over the floor, we can assume that the slab has been subjected to an imposed load of about 6 kPa. At ultimate limit state, the building was designed to take imposed load of (1.6qk = 1.6 x 1.5 = 2.4 kPa), and with imposed load of 6 kPa, there will be ‘real fire on the mountain’.
Therefore we can see that through poor materials and misuse of building through overloading, the factors of safety used in a design can be exhausted, thereby placing the structure on the risk of imminent collapse. All hands must be on deck to make building collapse a thing of the past in Nigeria.
References Holicky M. (2009): Reliability Analysis for Structural Design (1st Edition). Sun Media Press Stellenbosch
