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Unformatted text preview: 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 ofthe cross section showing the orientation of the neutral axis and the locations ofthe points where the stresses are being found. Problem 6.51 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 kin., tan 0 = 1/3. (Note: See Table E3 of Appendix E for the dimensions and properties of the channel section.) Probs. 6.51 and 6.52 Solution 6.51 Channel section n MAXIMUM TENSILE STRESS (POINT A) (EQ. 638) 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 LL~R MAXIMUM COMPRESSIVE STRESS (POINT B) (EQ. 638) 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 kin. 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. 640) tan (3 = 1,  tan 0 = 1 y 32.6  (1/3) 1.32 = 8.2323 {3 = 83.07  Problem 6.52 Solve the preceding problem for a C 6 X 13 channel section with M = 5.0 kin. and 0 = ISO. SECTION 6.5 Bending of Unsymmetric Beams 399 Problem 6.53 An angle section with equal legs is subjected to 2 a bending moment M having its vector directed along the 11 axis, as shown in the figure. Determine the orientation of the neutral axis and calculate the maximum tensile stress u and maximum compressive stress t u e if the angle is an L 6 X 6 X 3/4 section and M = 20 kin....
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This note was uploaded on 11/14/2011 for the course ECIV 310 taught by Professor Huckelbridge during the Spring '11 term at Case Western.
 Spring '11
 huckelbridge

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