Explanation Given information: The width ( b ) and depth ( d ) of the cross-section of the beam are 0.6 in . and 0.6 in . The yield stress ( σ y ) for beam is 48 ksi . Consider the Young’s modulus ( E ) of steel is 29 × 10 6 psi . Calculation: Calculate the moment of inertia ( I ) of the cross section of the beam using the relation: I = 1 12 b d 3 (1) Here, b and d are the cross sectional width and depth of the beam. Substitute 0.6 in . for b and 0.6 in . for d in Equation (1). I = 1 12 × 0.6 × 0.6 3 = 0.0108 in . 4 Consider the distance between the neutral axis and the extreme outer fiber is denoted by c . Calculate the distance c using the relation: c = d 2 (2) Substitute 0.6 in . for d in Equation (2). c = 0.6 2 = 0.3 in . Calculate the maximum elastic moment M y in the square solid rod using the relation: M y = σ y I c (3) Here, σ y is the yield stress. Substitute 48 ksi for σ y , 0.3 in . for c, and 0.0108 in . 4 for I in Equation (3). M y = 48 × 0.0108 0.3 = 0.5184 0.3 = 1.728 kip ⋅ in . × 1 , 000 lb ⋅ in . 1 kip ⋅ in . = 1728 lb ⋅ in . The radius of curvature ( ρ ) is 3 ft . Calculate the maximum strain ( ε max ) using the relation: ε max = c ρ (4) Substitute 0.3 in . for c and 3 ft for ρ in Equation (4). ε max = 0.3 in . 3 ft × 12 in . 1 ft = 0.3 in . 36 in

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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When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 4.6, Problem 70P

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The moment M applied on the square rod such that the radius of curvature is 3 ft.

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Chapter 4.6, Problem 69P

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The moment M applied on the square rod such that the radius of curvature is 3 ft .

Solution Summary: The author calculates the moment of inertia of the cross-section of a beam using the relation: I=112bd3.

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The moment M applied on the square rod such that the radius of curvature is 3 ft.

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