Explanation Given information: The yield strength ( σ y ) of the steel beam is 240 MPa . Assume the steel beam as elastoplastic. Calculation: Calculate the total area ( A ) of the cross-section of the beam as follows: A = A t o t a l − A h o l l o w = 50 × 90 − 30 × 30 = 4 , 500 − 900 = 3600 mm 2 Show the forces on cross-section of the beam as shown in Figure 1. Refer Figure 1. Calculate the value of x using the relation: b x = A 2 x = A 2 b (1) Substitute 3600 mm 2 for A and 50 mm for b in Equation (1). x = 3600 2 × 50 = 36 mm Calculate the area of the rectangles 1, 2, 3, and 4 as follows: Consider the width and depth of the rectangles are denoted by b and h . A 1 = b 1 h 1 = 50 × 36 = 1800 mm 2 A 2 = b 2 h 2 = 50 × ( 50 − 36 ) = 50 × ( 50 − 36 ) = 700 mm 2 A 3 = 2 b 3 h 3 = 2 × 10 × 30 = 600 mm 2 A 4 = b 4 h 4 = 50 × 10 = 500 mm 2 Consider the distance between the neutral axis and the centroid of rectangle 1, 2, 3, and 4 are denoted by y ¯ 1 , y ¯ 2 , y ¯ 3 , y ¯ 4 respectively. Calculate the value of y ¯ 1 as follows: y ¯ 1 = x 2 Substitute 36 mm for x . y ¯ 1 = 36 2 = 18 mm Calculate the value of y ¯ 2 as follows: y ¯ 2 = h 2 2 Substitute 14 mm for h 2 . y ¯ 2 = 14 2 = 7 mm Calculate the value of y ¯ 3 as follows: y ¯ 3 = h 3 2 + h 2 Substitute 14 mm for h 2 and 30 mm for h 3 . y ¯ 3 = 30 2 + 14 = 29 mm Calculate the value of y ¯ 4 as follows: y ¯ 4 = h 4 2 + h 2 + h 3 Substitute 14 mm for h 2 , 30 mm for h 3 , and 10 mm for h 4

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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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 4.6, Problem 82P

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Find the plastic moment Mp of the steel beam.

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Chapter 4.6, Problem 81P

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Mechanics of Materials, 7th Edition

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