Question 1:
a. Sketch a 2D pin-jointed structure model of the crane. You are allowed to make simplifications on the structure of the crane as you cannot be expected to figure out all the structural details from the photograph. You do not need to model the individual braces in the jib structure.
b. Indicate on your sketch the type of forces (e.g. tension or compression) that each member is subjected to when the crane is carrying a load.
c. Apply a statical determinacy test on your model. If it is not a determinate system, discuss what alterations can be done to make it statically determinate.
Question 2
a. Explain briefly why this structure in Figure 2 can be modelled as a pin-jointed structure (PJS) for the purpose of determining the axial forces in the members.
b. Show that the structure is statically determinate.
c. Determine the reaction forces at supports A and B.
d. Using the method of joints determine the axial forces in members AC and AF.
e. Using the method of sections, determine the force in member GH.
Question 3
Figure 3 shows a vertical structural member, with a rectangular cross-sectional area, made of an aluminium alloy. The member, which is fixed at its upper end with its lower end unconstrained, is intended to bear a maximum vertical tensile load of F = 20 kN at the centre of its free end. The design specification for the member also indicates that the nominally ‘vertical' load may be inclined to the vertical by up to 3° in any direction.
a.
i. Calculate the longitudinal stress in the member when it is subject to the purely vertical maximum design load.
ii. Write down the two-dimensional stress tensor for stresses in the x-y plane. What is the stress state in the member when loaded purely vertically?
b. Determine the resolved horizontal and vertical forces at the free end of the member when the 20 kN load is inclined at 3° to the vertical.
c. Calculate the maximum longitudinal tensile stress in the member when the 20 kN load is inclined at 3° to the vertical such that bending occurs about the z-axis only.
Recall, from Block 1 Part 6, that you will need to treat the member as a cantilever beam and sum the longitudinal stress due to the axial load with the longitudinal bending stress.
d. Repeat the calculation in (c), this time for the case where the 20 kN load is inclined at 3° to the vertical such that bending occurs about the y-axis only.
e. If the same member was subjected to a purely vertical compressive force of 20 kN at the centre of its free end, determine whether buckling failure would be likely to occur. Assume E = 70 GPa for the aluminium alloy.