cameroon gce advanced level 2025 building construction applied mechanics 2

As before, due to the watermarks and quality of the images, some text may be difficult to read. I will transcribe the content to the best of my ability.

 

Question 1

Figure 1 below represents a metallic roof truss of a residential building to be mounted by your company. As a site foreman, you were asked to carry out certain calculation related to the dimensioning of the roof truss.

Figure 1

Diagram of a truss with applied loads and dimensions.

a) Calculate the reactions at A and B

b) Calculate the efforts in the bar b1 and g1 using; the force method or Cullman’s method while stating their nature

c) Determine all the efforts in the bars using Cremona’s method, consider 10KN = 1cm. SEE APPENDIX 1

d) Determine the section and choice of I.P.E Profile to be used for member b1; given that its effort is 60KN and the admissible direct stress of IPE σ is 240MPa. SEE APPENDIX 2

Question 2

Figure 2 below is the most loaded reinforced concrete pillar of an upper solid floor, for a storey building to be realised by your enterprise. As the second chief in command heading the structural engineering department, you were asked to do some necessary calculation to reinforce this pillar. Considering the density of reinforced concrete as 25KN/m³ and that of live load as 3KN/m².

Diagram of a reinforced concrete pillar with dimensions.

Transversal cross section

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Document 2 (image_4ed584.jpg)

 

Some preliminary calculations/formulas are visible at the top of the page, but are cut off or incomplete.

I=3.20m

If=0.7L

i=12I​​

λ=iIf​

fc=400MPa,fs=1.15

α=1+0.2(100λ​)20.85​; if λ≤50

α=0.6+λ20​; if 50<λ≤100

Ast≥(α⋅σs​N​)⋅Bs⋅fy⋅2.5Br⋅fc⋅20​

Asm​in=Max(1000.25​⋅B⋅L,1000.28​)

fc28=20MPa and γb​=1.5

a) Calculate the surface of influence for the floor slab

b) Evaluate the dead and live loads in KN at the bottom of the pillar including itself weight

c) Evaluate the loads at ULS and SLS in KN

d) Considering that Pu​=142KN; Calculate and choose a suitable cross sectional area of reinforcement needed for the pillar.

Question 3

Figure 3 represents a pre-stress concrete beam spanning over a multipurpose hall to be realised by your company. In order to limit excessive stressing of the materials during pre-stressing, you were assigned by the main structural engineer to do certain preliminary calculations. Consider the live load applied on the beam as 5KN/m and self weight of concrete as 25KN/m³.

Figure 3

Diagram of a pre-stressed concrete beam with loads and cross-section details.

SECTION A-A

a) Evaluate the loads at service limit in KN/m

b) Deduce the maximum bending moment at the span in KNM.

c) Deduce the centre of gravity along yc and its moment of inertia Ixx about the centre of gravity along x-x axis for (section A-A) in m and m² respectively.

d) Determine the bending stress at the most compressive and tensile fibre of the beam in MPa and draw its diagram.

e) Determine the compressive force P to be applied at the lowest middle third of the beam to obtain a zero tensile stress at the most tensile fibre.

Question 4

Figure 4 below is an isolated purlin resting on two rafters to be realised by your company carpenters. After the evaluation of loads, by the main structural engineer, you were assigned to complete the following calculations.