430_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

430_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 05Ch05.qxd 9/24/08 424 4:59 AM Page 424 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.6-16 NUMERICAL DATA h 152 mm ratio of top to bottom stresses b 55 mm 1 11385 take 1st moments to find distances c1 & c2 1st moments about base c2 c1 c2 c1 c1 2bt + t (h b J b 2t) (t) + 2bt a b 2 t (h 2 2t) 2 t (152 2 t (152 2 2.55t + t (152 55 2t) (t) + 2.55 t a t (152 2 2 a 11385 7a 2t) 55 2t) (t) + 2.55t a b 2 2.55t + t(152 1 11385 c3 c 55 b 2 186 t + t 131 + t t2 2t) t 2 11092 Problem 5.6-17 Determine the ratios of the weights of three beams that have the same length, are made of the same material, are subjected to the same maximum bending moment, and have the same maximum bending stress if their cross sections are (1) a rectangle with height equal to twice the width, (2) a square, and (3) a circle (see figures). 7/3 t2 b d 186 t 76 t 3025 b d t2 K 2 t) 3025 109 t + 1298 109 55 b 2 186 t + t22 111385 76 t + t2 2t) (t) + 2.55t a 7/3 186 t + t2 131 + t 2.55 t + t (152 c2 c1/c2 0 0 4 (1298) t 2 ; 13.61 mm h = 2b a b a d Solution 5.6-17 Ratio of weights of three beams Beam 1: Rectangle (h 2b) Beam 2: Square (a side dimension) Beam 3: Circle (d diameter) L, g, Mmax, and smax are the same in all three beams. M S section modulus S s Since M and s are the same, the section moduli must be the same. (1) RECTANGLE: S bh2 6 2b3 3 A1 2b2 2a b 3S 2/3 b 2 (2) SQUARE: S a3 6 A2 a2 (3) CIRCLE: S 3S 1/3 ab 2 2.6207S2/3 A3 pd 3 32 pd 2 4 (6S)1/3 a (6S)2/3 a d 3.3019 S2/3 32S 1/3 b p p 32S 2/3 a b 4p 3.6905 S2/3 Weights are proportional to the cross-sectional areas (since L and g are the same in all 3 cases). W1 : W2 : W3 A1 : A2 : A3 W1 : W2 : W3 A1 : A2 : A3 2.6207 : 3.3019 : 3.6905 1 : 1.260 : 1.408 ; ...
View Full Document

This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

Ask a homework question - tutors are online