Explanation Given information: The modulus of elasticity in tension is E t . The modulus of elasticity in compression is E c . Calculation: Consider E t as the reference modulus of elasticity. Calculate the modular ratio ( n ) as shown below. n = E c E t Calculate the moment of inertia ( I ) of the beam as shown below. I = b h 3 12 Here, b is the width of cross section and h is the height of the cross section. Sketch the transformed cross section as shown in Figure 1. Refer to Figure 1. Calculate the location of neutral axis ( x ) as shown below. n × b x × x 2 − 1 × b ( h − x ) × h − x 2 = 0 n b x 2 2 − 1 2 b ( h − x ) 2 = 0 n x 2 = ( h − x ) 2 x = 1 n ( h − x ) x = h n − x n x ( 1 + 1 n ) = h n x ( n + 1 n ) = h n x = h n + 1 Calculate the value of ( h − x ) as shown below: h − x = h − h n + 1 = h ( n + 1 − 1 n + 1 ) = h n n + 1 Calculate the moment of inertia ( I trans ) for the transformed section as shown below. I trans = n 1 × 1 3 b x 3 + n 2 × 1 3 b ( h − x ) 3 Substitute n for n 1 , h n + 1 for x , 1 for n 2 , and h n n + 1 for h

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Chapter 4.5, Problem 60P

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The curvature of the beam in pure bending is 1ρ=MErI, where Er=4EtEc(Ec+Et)2

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Chapter 4.5, Problem 59P

Chapter 4.5, Problem 61P

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The curvature of the beam in pure bending is 1 ρ = M E r I , where E r = 4 E t E c ( E c + E t ) 2

Solution Summary: The author explains the curvature of the beam in pure bending. The modulus of elasticity in tension is E_t.

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The curvature of the beam in pure bending is 1ρ=MErI, where Er=4EtEc(Ec+Et)2

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Chapter 4 Solutions