A wood beam reinforced using two channels is subjected to a positive bending moment M_ = 25 kip-ft. Calculate the largest tensile and compressive stresses in the wood and steel if E w = 1500 ksi and £ s = 30,000 ksi. | bartleby

Mechanics of Materials (MindTap Co...

9th Edition

Barry J. Goodno + 1 other

Publisher: Cengage Learning

ISBN: 9781337093347

Chapter 6, Problem 6.3.17P

Textbook Problem

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A wood beam reinforced using two channels is subjected to a positive bending moment M_ = 25 kip-ft. Calculate the largest tensile and compressive stresses in the wood and steel if E_w = 1500 ksi and £_s = 30,000 ksi.

To determine

The largest tensile and compressive stress of the wood and steel.

Explanation of Solution

Given: .

AreaAc=3.37in2..

Moment of InertiaI11=32.5in4..

Depthhc=8in..

Es =30000 ksi..

Ew=1500 ksi..

Calculation: .

The ratio of moduli

n=EsEw.

n=300001500n=20.

The area of cross section of wood is,

Aw=nAc.

Substitute the value n=20n,Ac =3.37 in.

Aw=20×2.27Aw=67.4in2.

h1=(2Aw)hc2+bhh22Aw+bh.

h for 6 in , b for 4in,hcfor 8in,Aw for 67.4in

h1={(2×67.4)82}+{(4×6)62}(2×67.4)+(4×6)h1=3.349in.

The location of neutral axis from other end,

h2=hc−h1h2=8−3.849h2=4.151in.

IT=bh312+bh(h1−h2)2+2nI11+2Aw(h1−hc2)2.

IT=4×6312+{(4×6)(3.849−62)2}+{2×20×32.5}+{2×67.4((3.849−82)2)}.

IT=72+17.299+1300+3.0736IT=1.392×103in4.

The allowable normal stress in the top part of the wood section is calculated as,

σwTop=−MZh1IT.

MZfor 25 kip,h1for 3.849 in andITfor1.392×103 , h for 6 in and n=20..

σwTop=−MZh1IT.

σwTop=−(25×12)×3.8491.392×103σwTop=−1154

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