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HW 8 - 3 98 CHAPTER 6 Stresses in Beams(Advanced Topics...

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398 CHAPTER 6 Stresses in Beams (Advanced Topics) Bending Df Unsymmetric Beams When solving the problems for Section 6.5, be sure to draw a sketch of the cross section showing the orientation of the neutral axis and the locations of the points where the stresses are being found. Problem 6.5-1 A beam of channel section is subjected to a M bending moment M having its vector at an angle 0 to the z axis (see figure). Determine the orientati on of the neutral axis and calculate the c maximum tensile stress u, and maximum compressive stress U in c the beam. Use the following data: C 8 X 11.5 section, M = 20 k-in., tan 0 = 1/3. (Note: See Table E-3 of Appendix E for the dimensions and properties of the channel section.) Probs. 6.5-1 and 6.5-2 Solution 6.5-1 Channel section n MAXIMUM TENSILE STRESS (POINT A) (EQ. 6-38) ZA = C = 0.571 in. Y A = -dl2 = -4.00 in. (M sin O)ZA (M cos ti)YA U, = UA = 1 y I, = 5060 psi - z --L----L-~R MAXIMUM COMPRESSIVE STRESS (POINT B) (EQ. 6-38) ZB = -(b - c) = -(2.260 - 0.571) = -1.689 in. c---+ Y, = dl2 = 4.00 in. (M sin O)zs (M cos O)Ys 1- A n U c = Us = 1 y ( M = 20 k-in. C 8 X 11.5 c = 0.571 in. d = 8.00 in. tan 0 = 1/3 1 = 1.32 in. 4 y b = 2.260 in. (j = 18.435° t = 32.6 in. 4 = -10,420 psi - NEUTRAL AXIS nn (EQ. 6-40) tan (3 = 1, - tan 0 = 1 y 32.6 -- (1/3) 1.32 = 8.2323 {3 = 83.07° - Problem 6.5-2 Solve the preceding problem for a C 6 X 13 channel section with M = 5.0 k-in. and 0 = ISO.
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SECTION 6.5 Bending of Unsymmetric Beams 399 Problem 6.5-3 An angle section with equal legs is subjected to 2 a bending moment M having its vector directed along the 1-1 axis, as shown in the figure.
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