   # A canti lever beam A B of a n isosceles t rapezoi-dal cross section has a length L = 0.8 m, dimensions b x = 80 mm and b 2 = 90 mm, and height h = 110 mm (see figure). The beam is made of brass weighing 85 kN/m 3 . Determine the maximum tensile stress a s and maximum compressive stress &amp; t _ due to the beam's own weight. If the width b x is doubled, what happens to the stresses? If the height h is doubled, what happens to the stresses? ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 5, Problem 5.5.20P
Textbook Problem
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## A canti lever beam A B of a n isosceles t rapezoi-dal cross section has a length L = 0.8 m, dimensions bx= 80 mm and b2= 90 mm, and height h = 110 mm (see figure). The beam is made of brass weighing 85 kN/m3. Determine the maximum tensile stress asand maximum compressive stress &t_ due to the beam's own weight. If the width bxis doubled, what happens to the stresses?If the height h is doubled, what happens to the stresses? a.

To determine

The maximum tensile and compressive stress.

### Explanation of Solution

Given:

L = 0.8m.h = 110mm, b1 = 80mm, b2= 90mm, ? = 85KN/m3.

Concept Used:

The problem is carried out by using pure bending equation. When the bending stress is developed along the axis of the material, the stress and strain can be calculated based on this equation

ER=MI=σyccR=σyE=εmax

E = young’s modulus, R = radius of gyration, M = Bending moment, I = moment of inertia, σy= normal stress, c = distance from the center to maximum stress.

Calculation:

Area of cross-section, A=(b1+b22)×h=(80+902)×110 = 9.35*1000 mm2 =

Self-weight is treated as uniformly distributed load, q = ?A = 85* (9.35*1000) = 794.75N/m

Maximum bending moment, M=qL22=794.75×0.822 =254.32 N.m

yc=h(2b1b2)3(b1b2)=110(2×8090)3(8090) = 53

b.

To determine

The maximum tensile and compressive stress if ‘b1’ is doubled.

c.

To determine

The maximum tensile and compressive stress if ‘h’ is doubled

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