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Standards for Highway Materials in Nigeria

Earth materials are extensively utilised for highway construction in Nigeria. It has been recognised that high quality lateritic soils which are abundant in Nigeria can be used as fill, sub-base, and base course materials in highway construction. In this article, we are going to show the recommended standards for highway materials based on Federal Ministry of Works Specifications for Roads and Bridges (1997).

Generally, the material to be used for highway construction shall not be excavated from swamps, marshes or bogs. Furthermore, they shall be free from peat, logs, stumps, roots, and other perishable or combustible materials. Top soils and highly organic clays and silt shall not to be used for constructiont. All clays having liquid limit exceeding 80% or plasticity index exceeding 55 should be rejected.

earthworks

The basic recommendations given for base course materials are for crushed stone base in clauses 6250, 6251, and 6252. Therefore, the recommendations for sub-base course materials shall be deemed to apply to base course earth materials too. Recommendations for crushed stone base will not be covered in this this article.

List of Tests for selection of highway earth materials
The lists of test that shall be conducted for highway materials are;

(1) Plasticity tests
(2) Grading tests
(3) Compaction tests
(4) Laboratory CBR tests

CBR testing machine 1

Materials for sub-base course (Type 1) – Heavy Traffic
(1) The percent by weight passing No 75μm sieve shall not be greater than 35%
(2) The material passing 425μm sieve shall have a liquid limit not more than 35% and plasticity index of nit more than 12%
(3) The material shall have unsoaked CBR value of 80% using Modified AASHTO or West African Standard Compaction and minimum CBR of 30% after 24 hours soaking.

Materials for sub-base course (Type 2) – Light Traffic
(1) The percent by weight passing No 75μm sieve shall not be greater than 35%
(2) The material passing 425μm sieve shall have a liquid limit not more than 35% and plasticity index of nit more than 12%
(3) The material shall have unsoaked CBR value of 80% using Modified AASHTO or West African Standard Compaction and minimum CBR of 20% after 24 hours soaking.

Materials for sub-base course (Type 3) – Substandard materials
When the site engineer recognises that suitable materials are not available for use, and the materials slightly fall short of the required standard, the following measures can be adopted;

(1) Compacting the material to a lesser density at the wet side of the optimum to contain the tendency of the material to shrink or swell.
(2) Mechanical stabilisation of the material with sand (if available) to reduce the fines content

Inclusion of women in construction industry

Growing up as a Nigerian from one of the least developed communities, I have identified that our continent Africa and Nigeria in particular has a problem in infrastructure that is yet to be addressed.

Engineering as a discipline is male dominated both globally and locally. For us to retain the women we have, we need to create more opportunities for them whether as colleagues, wives, sisters or friends.

Inclusion of women in construction

In the construction industry generally, it is perceived that only men work on site. Everyday at work, I hear a lot of people say things like, “this is my first time of seeing a female engineer on site”. What this literarily means is that we have left the work for men alone, allowing them to decide a significant part of our lives – building homes.

intersectionality 1

There is need for us to begin to rethink the way we build infrastructure and who builds them. This will begin from design to procurement, construction, finishes, and even commissioning. On the long run, this will help us to recognize talent inclusively, bridge the gender gap, increase the retention of women, and also work towards achieving global goals.

For example, on a construction site, you will discover that most safety wears, boots and signs are designed to be more compatible with men. Some read – ‘Men at Work’. Some are with visual signals that denotes men.

162 1628253 gender equality feminism gender symbol social equality women

As a starting point to inclusion on construction sites, access to construction areas including walk-ways, stairs, and temporary platforms should include women in the design. Also, initial site planning and management should include restrooms for women as well as men.

While some women are working hard and pushing to be outstanding in the profession whether as technical leaders, engineers and project managers, there are some reasons why many people feel women should not be on site.

Firstly engineering and construction is male oriented, as workers on site are already used to taking instructions from men, which has been a norm for centuries.

20190130192656 GettyImages 552721707 1

Secondly women are believed to have poor leadership skills and as such receive bais from both the society and those above them who ought to be an excellent support to enhance their productivity and performance.

Thirdly women are believed to be too sensitive amidst a few others which are not true. Perhaps on site when they delegate responsibilities and follow up to ensure that it gets done, managers may conclude that those are small things. One way to help is by constructively critising them when necessary, evaluating their performance for the sole purpose of providing useful feedback that could lead to self-improvement.

NAWIC image 4

Overall, we recognize that over 90% of workers in construction are men. There is need for managers, leaders, engineers and decision makers to begin to shape the future through inclusion, shared opportunities, equity and promoting a culture of respect and empathy.

Modelling and Analysis of Spherical LPG Tanks (Horton Sphere)

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.

LPG TANK
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.

LPG TANK FARM UNDER CONSTRUCTION 1
Fig 2: LPG Tank farm under construction in Lagos, Nigeria
TANK FARM CONSTRUCTION
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

LPG TANK MODEL ON STAAD PRO
Fig 4: Spherical LPG model on Staad Pro
3D RENDERING OF LPG SPHERE TANK
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.

Bending moment on LPG Tank Shell
Fig 6: Lateral bending moment on the tank shell due to gas pressure
MY 1
Fig 7: Longitudinal bending moment on the tank shell due to gas pressure
MXY
Fig 8: Twisting moment on the tank shell due to gas pressure
SQX
Fig 9: Lateral shear stress on the tank shell due to gas pressure
SQY
Fig 10: Longitudinal shear stress on the tank shell due to gas pressure
SX
Fig 11: Lateral axial tension on the tank shell due to gas pressure
SY
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 .

How to price/quote for concrete works

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.

concrete slab

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.

Bidding war


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

Build up of rates

(a) Materials
Mix ratio = 1:2.5:3.5
Cement = 7 bags/m3
Sand = 1088.99 kg/m3
Aggregate = 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 the cost of producing one cubic metre of grade 25 concrete is ₦64,388

The West African Standard Compaction Test

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)

Tips for Civil Engineering Job Interviews

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.

Interview

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.

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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.

best interview

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.

Effects of Temperature Difference on Circular Tanks

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.

cylindrical water tank
Fig 1: 3D model of cylindrical water tank
Bending moment radial 1
Fig 2: Radial bending moment on the tank shell due to temperature load
Longitudinal bending moment due to temperature difference
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
Radial shear
Fig 5: Radial shear on the tank shell due to temperature load
Logitudinal shear
Fig 6: Longitudinal shear on the tank shell due to temperature load
Hoop membrane forces
Fig 7: Hoop tension (membrane) on the tank shell due to temperature load
Vertical axial tension
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

Evaluation of effects of temperature difference in storage tanks using Staad Pro

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;

Tank storing hot liquid
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.

Water tank modelled on Staad
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.

Temperature load on Staad Pro
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.

Bending moment due to water pressure 1
Fig 4: Bending moment on the tank shell due to water pressure
Shear force due to water pressure 1
Fig 5: Shear stress on the tank shells due to water pressure
Bending moment due to temperature difference 1
Fig 6: Bending moment on the tank shell due to temperature difference
Shear stress due to temperature difference
Fig 7: Shear stress on the tank shell due to temperature difference
Displacement due to temperature difference 1
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.

Can you identify the cause of failure of this building?

Structural failure is real, and it is the duty of structural engineers to identify all possible modes of failure in a structure, and design against them with appropriate factor of safety. When a building fails, we can identify the most probable cause of the failure by looking at the crack patterns and their location.

building failure 1

By looking at the image above, can you identify the cause of failure of the building? Let us know your answer in the comment section. Thank you very much.

Modelling and Analysis of Imperfections in Portal Frames

Equivalent horizontal forces (EHF) are not strictly actions, but are forces that are applied to a frame in combination with other actions to model the effect of frame imperfections. Another alternative of doing this is to model the frame out of plumb. According to clause 5.3.2(6) of Eurocode 3, if a frame is sensitive to second order effects, member imperfection must be modelled in the analysis if the member has a moment resisting joint. In this post, we are going to show how to model the effects of imperfection for gravity actions in portal frames.

Determination of EHF
According to clause 5.3.2(3) of EC3, for frames sensitive to buckling in a sway mode the effect of imperfections should be allowed for in frame analysis by means of an equivalent imperfection in the form of an initial sway imperfection and individual bow imperfections of members. The imperfections may be determined from:

ϕ = ϕ0 αh αm

Where ϕ0 = 1/200
αh = 2/√h (h is the height of the structure in metres)
αm = √[0.5(1+ 1/m)] (where m is the number of columns in the row)

Solved Example
Model the effect of imperfection in the frame shown in Figure 1 using the equivalent horizontal force approach
Columns – UB 610 x 229 x 125
Rafters – UB 533 x 210 x 92

portal frame 1
Fig 1: Portal frame subjected to gravity action

When analysed under the gravity action shown above, the following reactive forces and bending moment diagram was obtained.

Portal frame bending moment diagram
Fig 2: Bending moment and support reaction of portal frame under gravity load

For the example above;
αh = 2/√h = 2/√7 = 0.755 (h is the height of the structure in metres)
αm = √[0.5(1 + 1/m)] (where m is the number of columns in the row)
αm = √[0.5(1 + 1/2)]= 0.8660
Therefore;
ϕ = (1/200) × 0.755 × 0.8660 = 0.0032

The equivalent horizontal forces are calculated as:

HEHF = ϕVEd

However, sway imperfections may be ignored where HEd ≥ 0.15VEd

Choosing to incorporate the effect of imperfection in our analysis, the equivalent horizontal force is given by;
HEHF = 0.0032 × 114.27 = 0.366 kN

We will now model and analyse the frame for load combination 1 with the effects of imperfection included. The analysis will be done with the base pinned.

Equivalent horizontal forces on portal frames
Fig 3: Portal frame with equivalent horizontal force

The resulting bending moment diagram with the effect of imperfection is given below;

effect of imperfection
Fig 4: Bending moment and support reaction with the effect of imperfection

A little consideration of the above results will show that the effects of imperfection can be safely ignored in the design of the structure. Thank you for visiting Structville today.