432_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

432_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 5.6-19 A steel plate (called a cover plate ) having cross-sectional dimensions is welded along the full length of the bottom flange of a wide-flange beam (see figure, which shows the beam cross section). What is the percent increase in the smaller section modulus (as compared to the wide-flange beam alone)? W 12 * 50 6.0 in. * 0.5 in. 426 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.6-19 N UMERICAL PROPERTIES FOR ( FROM T ABEL E-1(a)) F IND CENTROID OF BEAM WITH COVER PLATE ( TAKE 1 ST MOMENTS ABOUT TOP TO FIND ) c 2 ± ( d + 0.5) ² c 1 c 2 ± 5.518 in. c 1 ± A d 2 + (6) (0.5) a d + 0.5 2 b A + (6) (0.5) c 1 ± 7.182 in. c 1 7 c 2 I ± 391 in. 4 S ± 64.2 in. 3 c 1 ± c 2 c 1 ± d 2 A ± 14.6 in. 2 d ± 12.2 in. W 12 * 50 F IND I ABOUT HORIZ . CENTROIDAL AXIS F IND SMALLER SECTION MODULUS % increase in smaller section modulus S top ² S S (100) ± 6.57% ; S top ± I h c 1 S top ± 68.419 in. 3 I h ± 491.411in. 4 + (6) (0.5) a c 2 ² 0.5 2 b 2 I h ± I + A a c 1 ² d 2 b 2 + 1 12 (6) (0.5)
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