GATE CE 2014 Set 1 — Question 42
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Structural Engineering → Determinate Structures & Energy Methods → Unit Load Method
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Question
For the truss shown below, the member PQ is short by . The magnitude of vertical displacement of joint R (in mm) is _______________
Correct answer
1 to 2.5
Solution
Using the unit load method, the vertical displacement at joint R is given by:where is the force in the members due to a unit vertical load applied at joint R, and is the change in length of the members.Only member PQ has a specified change in length: (since it is short).Step 1: Apply a unit vertical load at joint R.
By symmetry, the vertical reactions at supports P and Q are .Step 2: Find the force in member PQ ().
Let be the angle member PR makes with the horizontal. From the geometry:At joint P:So, .Step 3: Calculate displacement.
By symmetry, the vertical reactions at supports P and Q are .Step 2: Find the force in member PQ ().
Let be the angle member PR makes with the horizontal. From the geometry:At joint P:So, .Step 3: Calculate displacement.
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