WORLD FOR CIVIL

STATICS / STRENGTH OF MATERIALS - Example

In the structure shown on the right horizontal member ABC is supported by steel member CD, and brass member CE. Member CE has a cross sectional area of .75 in². Member CD has a .5 in² cross sectional area.
The structure is initially unstressed and then experiences a temperature decrease of 50 degrees celsius. For this structure:
A. Draw a Free Body Diagram showing all support forces and loads.
B. Determine the axial stress that develops in member CE.
C. Determine the resulting movement of point B .
E_st = 30 x 10 ⁶ psi; E_br = 15 x 10 ⁶ psi; E_al = 10 x 10 ⁶ psi
a_st = 12 x 10^-6 /^oC; a_br = 20 x 10^-6 /^oC; a_al = 23 x 10^-6 /^oC

Unless otherwise indicated, all joints and support points are assumed to be pinned or hinged joints.

Solution:
Part A: STATICS

STEP 1: Draw a free body diagram showing and labeling all load forces and support (reaction) forces, as well as any needed angles and dimensions.