To determine The reactions at the supports A , B , and C . To draw: The shear and moment diagrams. Explanation Given information: The length of the beam is 24 ft. EI is constant. Calculation: Sketch the Free Body Diagram of the beam as shown in Figure 1. Refer to Figure 1. Find the support reactions as shown below. Apply the Equations of Equilibrium as shown below. Summation of forces along horizontal direction is Equal to zero. ∑ F x = 0 C x = 0 Hence, the horizontal reaction at support C is C x = 0 _ . Summation of forces along vertical direction is Equal to zero. ∑ F y = 0 A y + B y + C y − 12 − 36 = 0 A y + B y + C y = 48 (1) Take moment about A is Equal to zero. ∑ M A = 0 B y × 12 + C y × 24 − 12 × 6 − 36 × 18 = 0 B y + 2 C y − 60 = 0 B y + 2 C y = 60 (2) Sketch the elastic curve of the beam as shown in Figure 2. Refer to Figure 2. Find the compatibility condition at B as shown below. v B ′ + v B ′ ′ + v B ′ ′ ′ = 0 (3) Here, v B ′ is the deflection due to the udl, v B ′ ′ is the deflection due to the point load, and v B ′ ′ ′ is the deflection due to the reaction at B . Apply the method of superposition as shown below. Find the deflection v B ′ as shown below. v B ′ = 5 w L 4 768 E I Here, w is the uniformly distributed load, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia. Substitute 3 kip/ft for w and 24 ft for L . v B ′ = 5 × 3 × 24 4 768 E I = 6 , 480 E I Find the deflection v B ′ ′ as shown below. v B ′ ′ = P b x 6 E I L ( L 2 − b 2 − x 2 ) Here, P is the applied load, b is the shortest distance between the load and the support, and x is length of the loaded beam. Substitute 12 kip for P , 6 ft for b , 12 ft for x , and 24 ft for L . v B ′ ′ = 12 × 6 × 12 6 E I × 24 ( 24 2 − 6 2 − 12 2 ) = 2 , 376 E I Find the deflection v B ′ ′ ′ as shown below. v B ′ ′ ′ = P L 3 48 E I Substitute B y for P and 24 ft for L . v B ′ ′ ′ = B y × 24 3 48 E I = 288 B y E I Substitute 6 , 480 E I for v B ′ , 2 , 376 E I for v B ′ ′ , and − 288 B y E I for v B ′ ′ ′ in Equation (3)

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Bending Moment

In general, we can define the bending moment as the reaction induced when a certain amount of load or force is applied to an element which makes it bend.

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Chapter 12.9, Problem 12.119P

To determine

The reactions at the supports A, B, and C.

To draw: The shear and moment diagrams.

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Chapter 12.9, Problem 12.118P

Chapter 12.9, Problem 12.120P

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The reactions at the supports A , B , and C . To draw: The shear and moment diagrams.

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The reactions at the supports A, B, and C.

To draw: The shear and moment diagrams.