Explanation Given information: The Young’s modulus is 200 GPa. Calculation: Consider flexural rigidity EI of the beam is constant. Show the given beam as in Figure (1). Consider upward is positive and downward is negative. Consider clockwise is negative and counterclockwise is positive. Since support A is a free end there will be no reaction. Therefore, the reaction at support A is automatically zero. Determine the support reaction at C using the Equation of equilibrium; ∑ V = 0 R C = 50 + 100 R C = 150 kN Determine the moment at point A ; M A = 400 kN ⋅ m Determine the moment at point B ; M B = 400 + ( 50 × 6 ) = 700 kN ⋅ m Determine the moment at support A ; M C = 400 + ( 50 × 12 ) + ( 100 × 6 ) = 400 + 1 , 200 = 1 , 600 kN ⋅ m Show the M / E I diagram of the given beam as in Figure (2). Show the deflected shape of the given beam as in Figure (3). Express the deflection at A using the second moment-area theorem as follows: Δ A = Δ A C = Moment of the area of the M / E I diagram between A and C about C Divide the M / E I into triangle and rectangle to evaluate the deflection. Δ A = Δ A C = [ M E I ( Area of rectangle ) + M E I ( Area of triangle ) + M E I ( Area of rectangle ) + M E I ( Area of triangle ) ] Δ A = Δ A C = [ 400 E I ( 6

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Author: KASSIMALI, Aslam.

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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 18P

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Find the smallest moment of inertia (I) required for the beam if the deflection does not exceed the limit of l/360 of the span length by using moment-area method.

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Chapter 6 Solutions

Structural Analysis

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Find the smallest moment of inertia ( I ) required for the beam if the deflection does not exceed the limit of l / 360 of the span length by using moment-area method.

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Find the smallest moment of inertia (I) required for the beam if the deflection does not exceed the limit of l/360 of the span length by using moment-area method.

Chapter 6 Solutions