A suspended walkway in an underground cavern consists of a deck supported by three tie rods placed symmetrically about the centre as shown below:

The rods are each of cross-sectional area 100mm², are made of steel (E = 200GPa) and can be assumed to behave in an elastic-perfectly plastic fashion. The central, longer rod yields at a stress (σ_yc) of 500MPa and the outer, shorter rods yield ( σ_yo) at 250MPa.

The walkway is to be designed so that an alarm is triggered when the first rods yield, but before general yield in the suspension. It is therefore important to now the downward displacement, δ as a function of stress in the rods.

(a) Find the walkway loads and the corresponding downward displacements at which yield first occurs and at which all members have yielded.

(b) Construct the load displacement diagram and select an alarm trigger point.

(c) What is the residual displacement once a load triggering the alarm has been removed.

(d) Determine the residual displacement once a load above general yield has been removed.