- Assignment 1
STRUCTURES ASSIGNMENT 2015
QUESTION 1 (3 MARKS)
Using the indirect tensile stress calculation used with concrete T = , make L, D and P the subject of the pLD formula.
QUESTION 2 (2 MARKS)
If a box has the outside dimensions 1.950 m x 1.50 m and a height of 1360 mm, the thickness of the walls of the box are 55mm all round, what is the capacity of the box in:
(a) Cubic metres (m3)?
(b) Cubic millimetres (mm3)?
QUESTION 3 (4 MARKS)
What is the mass of the following precast reinforced concrete unit (density 2,500kg/m3)?
The precast reinforced concrete unit has a “C” shaped cross-section and is 3.7 m in length. The vertical leg of the unit is 1,500 mm high overall and has a thickness of 260 mm. The horizontal sections have an overall width of 1,250 mm and a thickness of 360 mm (see figure 1).
Figure 1 Cross-section of precast unit
QUESTION 4 (6 MARK)
Draw annotated and dimensioned line diagrams for the following include the forces exerted by the supports:
(a) A beam continuous over 2 equal spans of 2.6 m and with one 1.4 m cantilever to the right of the structure, having point loads of 365 kg at cantilever end and mid points of the spans.
(b) A beam continuous over 3 equal spans of 2.8 m with a uniformly distributed load of 1.6 kN/m over the left and middle spans and point loads of 3.7 kN over each support except for the far left hand support.
(c) A simply supported beam 3.5 m long, with 28 kN point loads located at the third (1/3) of the way from the left hand support as well as the half (1/2) point of the span.
QUESTION 5 (3 MARK)
A reinforced concrete beam 430 mm x 285 mm is 4.3 m long and simply supported at its ends. The beam carries a brickwall along its length that is 3.2 m high and 240 mm thick and has a 4.5 tonne capacity chain block hoist hanging at its mid point. (Density for the concrete 2,500 kg/m3 and the density for the brickwork 1,960 kg/m3)
Analyse the structural condition and describe it fully annotated and dimensioned line diagram.
QUESTION 6 (4 MARK)
From the annotated and dimensioned line diagrams following write a detailed description. Work out the forces exerted by the supports
(a) Case 1 (see figure 2).
Figure 2 First line diagram.
(b) Case 2 (see figure 3).
Figure 3 Second line diagram.
QUESTION 7 (3 MARK)
Find the stress at the base of a 265 mm x 650 mm brick pier 5.2m high due to its own weight. The brickwork has a density of 1960 kg/m3.
If the brick pier is subjected to a force of 1,600 kN how much shorter will the brick work become? (The Young’s modulus for brickwork is 11 x 103 MPa).
QUESTION 8 (2 MARK)
For a square footing of 1.45 m2 and a load of 285 kN what will be the resultant permissible soil pressure?
QUESTION 9 (4 MARKS)
A prestressing wire, 8.4 mm diameter, has a breaking strength (stress) of 1,160 MPa (N/mm2) is used to lift a hopper of fresh cement. The hopper weighs 2.5 tonnes what is the maximum allowable weight in concrete the crane can lift.
If the full capacity of the hopper is 2.4 m3 will the capacity of the hopper be greater than the volume of concrete the hopper can hold without breaking? The answer must be supported; a yes / no response will be marked incorrect without correct working.
The density for the fresh concrete is 2,360 kg/m3 and the Young’s modulus for steel is 2 x 105 N/mm2.
QUESTION 10 (14 MARK)
The following data was obtained from a tension test on a metal specimen:
Diameter of specimen = 10.45 mm
Diameter of specimen at fracture = 6.86 mm
Gauge length = 25.00 mm
Length of specimen at fracture = 35.5 mm
Load at fracture = 27.2 kN
Maximum load recorded = 38.6 kN
The figure below shows a load versus extension curve for this material.
Using the above information and the graph shown in figure 4:
i) the modulus of elasticity, ii) the ultimate tensile strength, iii) the -true- stress at fracture, iv) the modulus of toughness,
v) the modulus of resilience, vi) the upper yield stress, 3
vii) the percentage elongation and the percentage reduction in C.S.A.
Figure 4 Load vs. extension graph.
QUESTION 11 (4 MARKS)
What do Xm and YkN have to equal for the system in figure 5 to be in equilibrium. Show all the logic required to prove the system is in equilibrium.
Figure 5 Equilibrium system.
QUESTION 12 (1 MARK)
What length does a lever arm need to be to exert a moment of 47 kNm if the force applied is 13 kN.