An extruded polymer beam is subjected to a bending moment M. The length of the beam is L = 500 mm. The cross-sectional dimensions of the beam are bị = 35 mm, d1 = 115 mm, b2 = 21 mm, d2 = 21 mm, and a = 7 mm. For this material, the allowable tensil bending stress is 15 MPa, and the allowable compressive bending stress is 14 MPa. Determine the largest moment M that can be applied as shown to the beam. b2 |ak a M. d2 d1 | A В z- L b1

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. K₁ M 3.0 2.6 2.2 1.8 1.4 16 1.0 0 1.10 1.05 1.02 0.05 wld = ∞ W 1.5 0.10 Figure 1.1. 0.15 rld Figure 1.2. Inom 0.20 6M td² 0.25 M M 0.30

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An extruded polymer beam is subjected to a bending moment M. The length of the beam is L = 600 mm. The cross-sectional dimensions of the beam are b₁ = 36 mm, d₁ = 112 mm, b₂ = 22 mm, d₂ = 22 mm, and a = 7 mm. For this material, the allowable tensile bending stress is 15 MPa, and the allowable compressive bending stress is 9 MPa. Determine the largest moment M that can be applied as shown to the beam. b₂ ak ak ✓ a M B L A Answer: M = i N•m d₂

The beam is acted upon by force F = 17 kN as shown in the figure.    What is the shear force in section C in kN.  Find the moment of area of the fiber 30 mm above the bottom of the beam about the neutral axis in mm3.  find the shear stress in MPa at a point 30 mm above the bottom of the beam at section C.

Example 1 The bar is subjected to a moment of M = 17.5 N.m. If r = 5 mm, determine the maximum bending stress in the material. 80 mm 7 mm 20 mm M M

The beam shown in Figure 2 is loaded in the xy and xz planes.(a) Find the y and z components of the reactions at the supports.(b) Plot the shear and bending moment diagrams.

Determine the maximum shear stress acting in the fiberglass beam at the section where the internal shears force is maximum. (t1=15 mm, t2=20 mm, h=150 mm, b=50mm)

consider a beam with two 60-inch-long rods. The rods have a cross section area of 0.50 in 2 . Find the axial stress in each rod, draw the shear and moment diagrams for the beam, and find the maximum stress in the beam.

X w MB w = 3 kN/m L = 4 m 2.4 What is the value of the bending moment at x = 2.5 m?