A rectangular beam with two notches (with radius r = 2.5 mm) is shown in Figure 1.1. The beam has dimensions w = 55 mm and d = 50 mm. The beam is subjected to a bending moment of M = 1.3 kNm and the maximum allowable bending stress in the material is 400 MPa. Determine the smallest thickness, tmin, in mm that this beam should be designed for. Stress concentration graph is provided in Figure 1.2.

Draw free body diagram without writing shear and moment equation of beam shown in Figure 2.19. Give numerical values at all change of loading positions and at all points of zero shear.

Find the max shear stress in bending in the cross section below if Vmax = 10 kips. 10" Flange 2" Web 2" 8" Flange 2" 10" • Identify where in the cross section the max shear will occur. Determine the thickness of the cross-section at the location you wish to find shear stress. • Calculate the Ix for the shape (assume bending in the x with most basic beams). • Calculate Q by dividing the section into two pieces at the point you want shear stress. Select one of the pieces (either will work), I picked the top piece. Use the Shear Stress equation to determine the requested stress. Compare you answer: Max shear stress = at the center of the cross section.

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