Explanation Given information: The bending moment of wood beam is M = 5 kN ⋅ m . The young’s modulus of wood ( E w ) is 11 GPa . The young’s modulus of steel ( E st ) is 200 GPa . Calculation: Show the beam section as shown in Figure 1. Find the value of transformation factor ( n ) as follows: n = E st E w (1) Substitute 200 Gpa for E st and 11 Gpa for E w in Equation (1). n = 200 11 = 18.182 Refer to Figure 1: The width and depth of the rectangle section ABCD as b = 3 , 636.36 mm and d = 340 mm . The width and depth of the rectangle 1 are b 1 = 1718.18 mm and d 1 = 300 mm . Calculate the moment of inertia ( I ) using the relation as follows: I = b d 3 12 − 2 b 1 d 1 3 12 (2) Substitute 3 , 636.36 mm for b , 340 mm for d , 1 , 718.18 mm for b 1 , and 300 mm for d 1 in Equation (2). I = ( 3 , 636.63 × 340 3 ) 12 − 2 ( 1 , 718.18 × 300 3 ) 12 = 3 , 636.63 × 39 , 304 , 000 12 − 3 , 436.36 × 27 , 000 , 000 12 = 1.191175 × 10 10 − 7 , 731 , 810 , 000 = 4 , 179 , 940 , 000 mm 4 ( 1 m 4 10 12 mm 4 ) = 4.1799 × 10 − 3 m 4 Calculate the maximum stress in steel ( σ st ) max using relation as follows: ( σ st ) max = n M c 1 I (3) Here, n is the transformed section, M is the bending moment, I is the moment of inertia, c 1 is the centroid distance. Substitute 18.182 for n , 5 kN ⋅ m for M , 0.17 m for c 1 , and 4.1799 × 10 − 3 m 4 for I in Equation (3). ( σ st ) max = 18

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 6.9, Problem 6.129P

To determine

The maximum bending stress (σst)max developed in steel.

The maximum bending stress (σwood)max developed in wood.

To sketch:

The stress distribution acting over the cross section.

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Chapter 6.9, Problem 6.128P

Chapter 6.9, Problem 6.130P

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The maximum bending stress ( σ st ) max developed in steel. The maximum bending stress ( σ wood ) max developed in wood. To sketch: The stress distribution acting over the cross section.

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The maximum bending stress (σst)max developed in steel. The maximum bending stress (σwood)max developed in wood. To sketch: The stress distribution acting over the cross section.

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The maximum bending stress (σst)max developed in steel.

The maximum bending stress (σwood)max developed in wood.

To sketch:

The stress distribution acting over the cross section.