Bending Stress 1 For simply supported beams with

Bending Stress 1

For simply supported beams with downward-acting loads (i. e. , with gravity loads), the beam is stretched on the bottom (tension) and shortened on the top (compression) as shown in Figure below:

For cantilevered beams fi xed at one end, with downward-acting loads, the beam is stretched on the top and shortened on the bottom as shown in Figure below:

For continuous beams spanning over several supports, the changing curvature causes the position of tension and compression zones to reverse a number of times over the length of the beam, as illustrated in Figure

Stress due to axial loading Stress due to bending

4 2 m 3 200 k. N A steel beam with a tensile strength of 700 MPA is loaded as shown. Assuming that the beam is made from hollow square tubing with the dimensions shown 0. 01 m will the loading in the x direction exceed the failure stress? 0. 02 m

Step 1: Free body diagram 4 2 m 240 k. N. m 120 N 160 k. N 3 200 k. N 160 k. N 120 k. N

Step 2: Calculate moment of inertia I=1/12 x (0. 024)- 1/12 x (0. 014) m 4 =1. 25 x 10 -8 m 4 A=0. 022 -0. 012 m 2 =0. 0003 m 2 0. 01 m 0. 02 m

Step 3: Shear and moment diagrams 4 V 3 2 m 120 200 k. N x M x -240

Step 4: Calculation of maximum tensile stress • Stress due to axial loading • Stress due to bending Total stress greater than failure stress therefore failure will occur