Explanation The Young’s modulus ( E ) is 200 GPa. The moment of inertia ( I ) is 262 × 10 6 mm 4 . Calculation: Consider elastic modulus E of the beam is constant. Show the free body diagram of the given beam as in Figure (1). Refer Figure (1), Consider upward is positive and downward is negative. Consider clockwise is negative and counterclowise is positive. Determine the support reaction at A using the Equation of equilibrium; ∑ M C = 0 R A × 10 − ( 120 × 3 ) = 0 R A = 360 10 R A = 36 kN Determine the reaction at support C using the relation; ∑ V = 0 R A + R C − 120 = 0 R C = 120 − 36 R C = 84 kN Show the reactions of the given beam as in Figure (2). Refer Figure (2), Determine the bending moment at A ; M A = ( 84 × 10 ) − ( 120 × 7 ) = 840 − 840 = 0 Determine the bending moment at B ; M B = ( 36 × 7 ) = 252 kN ⋅ m Determine the bending moment at C ; M C = − 36 ( 10 ) + ( 120 × 3 ) = − 360 + 360 = 0 Show the M / E I diagram for the given beam as in Figure (3). Show the M / E I diagram for the conjugate-beam as in Figure (4). Consider counterclockwise is positive and clockwise is negative. Take moment about C : Determine the support reaction at A using the Equation of equilibrium; R A ( 10 ) − 1 2 ( 252 E I ) ( 7 ) ( 3 + 1 3 × 7 ) − 1 2 ( 252 E I ) ( 3 ) ( 2 3 × 3 ) = 0 R A = 5 , 460 kN ⋅ m 3 10 E I R A = 546 kN ⋅ m 2 E I Determine the shear force at D using the relation; S D = − R A + ( 1 2 × b 1 × h 1 ) Here, b is the width and h is the height of the triangle. Substitute 546 kN ⋅ m 2 E I for R A , 10 m for b 1 , and ( 252 E I ) for h 1 . S D = − 546 kN ⋅ m 2 E I + ( 1 2 × 10 × 252 E I ) = 714 kN ⋅ m 2 E I Determine the slope at D using the relation; θ D = 714 kN ⋅ m 2 E I Substitute 200 GPa for E and 262 × 10 6 mm 4 for I

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ISBN: 9781337630931

Author: KASSIMALI, Aslam.

Publisher: Cengage,

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Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe be…

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Chapter 6, Problem 57P

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Find the slope θD and deflection ΔD at point D of the given beam using the conjugate-beam method.

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Structural Analysis

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Find the slope θ D and deflection Δ D at point D of the given beam using the conjugate-beam method.

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Find the slope θD and deflection ΔD at point D of the given beam using the conjugate-beam method.

Chapter 6 Solutions