   # A beam made up all woun equal leg angles is subjected to a bending moment M having its vector .u an angle (i) lo lire axis (see figure paria). (a) For the position shown in lire figure, determine lire orienlalion of lire neulral axis and calculate lire maximum tensile s'av-s ir, and maximum compressive stress (b) The two angles are now inverted and attached back-lo-back lo lorn, a lintel beam that supports two courses of brick facade i see figure part b). Find the new orientation of the neutral axis and calculate the maximum tensile slress r. a::d maximum compressive s'avsrr . in I he beam using 6 = 30° and M = 30 kip-in. ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

#### Solutions

Chapter
Section ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 6, Problem 6.5.5P
Textbook Problem
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## A beam made up all woun equal leg angles is subjected to a bending moment M having its vector .u an angle (i) lo lire axis (see figure paria).(a) For the position shown in lire figure, determine lire orienlalion of lire neulral axis and calculate lire maximum tensile s'av-s ir, and maximum compressive stress (b) The two angles are now inverted and attached back-lo-back lo lorn, a lintel beam that supports two courses of brick facade i see figure part b). Find the new orientation of the neutral axis and calculate the maximum tensile slress r. a::d maximum compressive s'avsrr . in I he beam using 6 = 30° and M = 30 kip-in.  (a)

To determine

Orientation of neutral axis and maximum tensile and compressive stress.

### Explanation of Solution

Given Information:

The following figure is given,

Also, θ=30 and M=30 kip-in.. is given.

The data of L 5×312×12 beam

are as,

Area=4 in.2,width =312 in.,  depth=5 in.c=0.901 in., d=1.65 in.,I1=10 in.4, I2=4.02 in.4.

Neutral axis lies on the zero normal stress line.

The normal stress is given by,

σx=MyzIyMzyIz

Equate it to zero to find the line.

Calculation:

Consider the following figure,

Axis 1 is z -axis and axis 2 is y -axis.

Moments of area of the whole cross section are,

Iz=2I1=20 in4Iy=2[I2+A( c+ 3 8)2]=2[4.02+4( 0.9+ 3 8)2]=21

(b)

To determine

Orientation of neutral axis and maximum tensile and compressive stress.

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