   # A beam is constructed of two angle sections, each L5 x 3 x 1/2, that reinforce a 2 x g (actual dimensions) wood plank (see the cross section shown in the figure). The modulus of elasticity for the wood is £ w = L2 X 10 6 psi and for the steel is E s = 30 x 10 6 psi. Find the allowable bending moment M 3 ] [ c m for the beam if the allowable stress in the wood is tr v = 1100 psi and in the steel is 3 = 12,000 psi. Note: Disregard the weight of the beam, and see Table F-5(a) of Appendix F for the dimensions and properties of the angles. ### 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 6.3.11P
Textbook Problem
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## A beam is constructed of two angle sections, each L5 x 3 x 1/2, that reinforce a 2 x g (actual dimensions) wood plank (see the cross section shown in the figure). The modulus of elasticity for the wood is £w = L2 X 106 psi and for the steel is Es= 30 x 106 psi.Find the allowable bending moment M3][cmfor the beam if the allowable stress in the wood is trv= 1100 psi and in the steel is 3 = 12,000 psi. Note: Disregard the weight of the beam, and see Table F-5(a) of Appendix F for the dimensions and properties of the angles. To determine

The allowable bending momentumMallowfor the beam

### Explanation of Solution

Given: .

IZ=9.43in.4AS=3.75in.2d=1.74in..

ES=30×106psi..

EW=1.2×106psi..

Calculation: .

The modular ratio is,n=ESEW.

n=30×1061.2×106=25.

The centroidal distances is,

y1¯=(h1b2)=(h122)=(h11).

y2¯=h1(b+d)=h1(2+1.74)=h13.74.

Ay¯=A1y1¯+2nASy2¯.

Substitute 0 forAy¯ ,(2×8)in2.forA1 ,3.75in2.forAS ,(h11)fory1¯ , and(h13.74)fory2¯..

0=(2×8)(h11)+2(25)(3.75)(h13.74)h1=3.5246.

The transformed moment of inertia is,

Ir=[b3h12+bh(h1b2)2]+2n[IZ+AS{h1(b+d)}2].

Substitute h, 3.5246 in. forh1 , 25 for n,9.43in4

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