Problem Graphics

Double Hanging Bookcase Diagram

A new set of shelves were built in a college dorm room by a first year engineering student. The bottom shelf is held by two pieces of copper wire of different lengths, while the upper shelf is held by two steel wires of the same length. All of the wires have the same cross sectional area of 0.02 in². The copper wire has a Young's modulus of 8,600 ksi and the steel wire has a Young's modulus of 28,000 ksi.

The top shelf holds a 50 lb globe at its midpoint. The bottom shelf holds a set of books equivalent to an evenly distributed 280 lb. Both shelves were horizontal before the globe and books were placed on them.

Parameters:

A = 0.02 in²
L_AB = 7 ft
L_CD = 2 ft
L_EF = L_HG = 5 ft
E_c = 8,600 ksi
E_s = 28,000 ksi
W_g = 50 lb
W_b = 280 lb

How much does the lower shelf rotate (if any) after the globe and books are placed on the shelves?

• Using static equilibrium equations, determine the load in each wire.
• Calculate the strain and deflection for each wire.
• From the deflection, find the angle of rotation for the loaded shelves.