Mechanics of Materials

To determine the loading on a body Draw a free body diagram indicating – external loads and moments – reaction loads and moments Apply equations of equilibrium – ΣF x = 0 ΣM = 0 – ΣF y = 0 – ΣF z = 0

Reaction Forces and Moments A roller or bearing plate allows only a normal force A pin has a vertical and horizontal force Embedment in concrete has vertical and horizontal forces and a moment.

A B

Class Activity 1 A simply supported beam of length 40 m is pinned at A (left end) and rests on a roller at B (right end). It is loaded by 100 kN downward at 30 m to the right of A. Draw a free body diagram and calculate the reaction forces and moments.

Class Activity 2 A cantilever beam of length 25 ft is embedded in a vertical concrete wall at its left end (A). It is loaded by 10 kips (10,000 lbs) at its free end B. Draw the free body diagram and calculate the reaction forces and moments.

Class Activity 3 A parking lot light of weight 100 lbs is fixed to a horizontal aluminum tube of length 5 feet. The horizontal tube is attached to a vertical aluminum column (tube) of height 40 ft. The base of the vertical tube is embedded in concrete at ground level. Draw a free body diagram of the entire light assembly (light, horizontal tube, and vertical tube).

First neglect the weight of the two tubes. Calculate the reaction forces and moments. Then consider the weight of the two tubes – 50 lbs for the horizontal tube – 400 lbs for the vertical tube. Calculate the reaction forces and moments for the second case.