Explanation Given information: The simply supported beam is made of A-36 steel. The moment of inertia of the beam is I = 0.1457 × 10 − 3 m 4 . Calculation: The Modulus of elasticity of A-36 steel is E = 200 GPa . Sketch the Elastic curve of the beam as shown in Figure 1. Refer to Figure 1. Apply the method of superposition as shown below. Find the deflection of the beam at C as shown below. Δ C = ( Δ C ) 1 + ( Δ C ) 2 (1) Here, ( Δ C ) 1 is the deflection due to the applied distributed load and ( Δ C ) 2 is the deflection due to the applied point load. Find the deflection ( Δ C ) 1 as shown below. ( Δ C ) 1 = 5 w L 4 768 E I Here, w is the applied distributed load, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia. Substitute 4 kN / m for w , 10 m for L , 0.1457 × 10 − 3 m 4 for I , and 200 GPa for E . ( Δ C ) 1 = 5 × ( 4 kN / m × 1 , 000 N 1 kN ) × ( 10 m ) 4 768 × ( 200 GPa × 10 9 N / m 1 GPa ) × ( 0.1457 × 10 − 3 m 4 ) = 200 × 10 6 2

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 12.5, Problem 12.91P

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The deflection at point C.

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Chapter 12.5, Problem 12.90P

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