VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
11th Edition
ISBN: 9781259633133
Author: BEER
Publisher: MCG
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Chapter 10.1, Problem 10.53P
To determine

Find the force representing the reaction at A using the virtual work method.

Find the couple representing the reaction at A using the virtual work method.

Expert Solution & Answer
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Answer to Problem 10.53P

The force representing the reaction at A is 250N()_.

The couple representing the reaction at A is 450Nm(Counterclockwise)_.

Explanation of Solution

Find the force at A;

Show the free-body diagram of the continuous beam as in Figure 1.

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 10.1, Problem 10.53P , additional homework tip  1

Consider the member AB is horizontal.

The vertical displacement at point A is δyA.

Find the vertical displacement (δyA) at A with respect to vertical displacement (δyB) at B as follows;

δyA=δyB

Find the vertical displacement (δyC) at C with respect to vertical displacement (δyB) at B as follows;

δyB2.4=δyC1.5δyC=1.52.4δyB=58δyB

Find the vertical displacement (δyE) at E with respect to vertical displacement (δyB) at B as follows;

δyB2.4=δyE1.2δyE=1.22.4δyB=δyB2

Find the vertical displacement (δyF) at F with respect to vertical displacement (δyB) at B as follows;

δyE1.8=δyF1.5δyF=1.51.8δyE=56(δyB2)=512δyB

Use the concept of virtual work;

δU=0;AδyA+800δyC600δyF=0

Substitute δyB for δyA, 58δyB for δyC, and 512δyB for δyF.

AδyB+800(58δyB)600(512δyB)=0A+500250=0A=250N()

Therefore, the force representing the reaction at A is 250N()_.

Find the couple at A;

Show the free-body diagram of the continuous beam as in Figure 2.

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 10.1, Problem 10.53P , additional homework tip  2

Rotate the member AB in the beam through δθ at the point A.

Find the vertical reaction (δyB) at point B as follows;

δθ=δyB1.8δyB=1.8δθ

Find the vertical displacement (δyC) at C with respect to vertical displacement (δyB) at B as follows;

δyB2.4=δyC1.5δyC=1.52.4δyB=58(1.8δθ)=1.125δθ

Find the vertical displacement (δyE) at E with respect to vertical displacement (δyB) at B as follows;

δyB2.4=δyE1.2δyE=1.22.4δyB=12(1.8δθ)=0.9δθ

Find the vertical displacement (δyF) at F with respect to vertical displacement (δyB) at B as follows;

δyE1.8=δyF1.5δyF=1.51.8δyE=56(0.9δθ)=0.75δθ

Use the concept of virtual work;

δU=0;MAδθ+800δyC600δyF=0

Substitute 1.125δθ for δyC and 0.75δθ for δyF.

MAδθ+800(1.125δθ)600(0.75δθ)=0MA+900450=0MA=450Nm(Anticlockwise)

Therefore, the couple representing the reaction at A is 450Nm(Counterclockwise)_.

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Chapter 10 Solutions

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS

Ch. 10.1 - Prob. 10.11PCh. 10.1 - Prob. 10.12PCh. 10.1 - Prob. 10.13PCh. 10.1 - Prob. 10.14PCh. 10.1 - Prob. 10.15PCh. 10.1 - Prob. 10.16PCh. 10.1 - Prob. 10.17PCh. 10.1 - Prob. 10.18PCh. 10.1 - Prob. 10.19PCh. 10.1 - Prob. 10.20PCh. 10.1 - Prob. 10.21PCh. 10.1 - A couple M with a magnitude of 100 Nm isapplied as...Ch. 10.1 - Rod AB is attached to a block at A that can...Ch. 10.1 - Solve Prob. 10.23, assuming that the 800-N force...Ch. 10.1 - Prob. 10.25PCh. 10.1 - Prob. 10.26PCh. 10.1 - Prob. 10.27PCh. 10.1 - Prob. 10.28PCh. 10.1 - Prob. 10.29PCh. 10.1 - Two rods AC and CE are connected by a pin at Cand...Ch. 10.1 - Solve Prob. 10.30 assuming that force P is movedto...Ch. 10.1 - Prob. 10.32PCh. 10.1 - Prob. 10.33PCh. 10.1 - Prob. 10.34PCh. 10.1 - Prob. 10.35PCh. 10.1 - Prob. 10.36PCh. 10.1 - Prob. 10.37PCh. 10.1 - Prob. 10.38PCh. 10.1 - Prob. 10.39PCh. 10.1 - Prob. 10.40PCh. 10.1 - Prob. 10.41PCh. 10.1 - The position of boom ABC is controlled by...Ch. 10.1 - Prob. 10.43PCh. 10.1 - Prob. 10.44PCh. 10.1 - Prob. 10.45PCh. 10.1 - Prob. 10.46PCh. 10.1 - Denoting the coefficient of static friction...Ch. 10.1 - Prob. 10.48PCh. 10.1 - Prob. 10.49PCh. 10.1 - Prob. 10.50PCh. 10.1 - Prob. 10.51PCh. 10.1 - Prob. 10.52PCh. 10.1 - Prob. 10.53PCh. 10.1 - Prob. 10.54PCh. 10.1 - Prob. 10.55PCh. 10.1 - Prob. 10.56PCh. 10.1 - Prob. 10.57PCh. 10.1 - Prob. 10.58PCh. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.29....Ch. 10.2 - Prob. 10.60PCh. 10.2 - Prob. 10.61PCh. 10.2 - Prob. 10.62PCh. 10.2 - Prob. 10.63PCh. 10.2 - Prob. 10.64PCh. 10.2 - Prob. 10.65PCh. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.38....Ch. 10.2 - Prob. 10.67PCh. 10.2 - Prob. 10.68PCh. 10.2 - Prob. 10.69PCh. 10.2 - Prob. 10.70PCh. 10.2 - Prob. 10.71PCh. 10.2 - Prob. 10.72PCh. 10.2 - Prob. 10.73PCh. 10.2 - Prob. 10.74PCh. 10.2 - Prob. 10.75PCh. 10.2 - Prob. 10.76PCh. 10.2 - Prob. 10.77PCh. 10.2 - Prob. 10.78PCh. 10.2 - Prob. 10.79PCh. 10.2 - Prob. 10.80PCh. 10.2 - Prob. 10.81PCh. 10.2 - A spring AB of constant k is attached to two...Ch. 10.2 - Prob. 10.83PCh. 10.2 - Prob. 10.84PCh. 10.2 - Prob. 10.85PCh. 10.2 - Prob. 10.86PCh. 10.2 - Prob. 10.87PCh. 10.2 - Prob. 10.88PCh. 10.2 - Prob. 10.89PCh. 10.2 - Prob. 10.90PCh. 10.2 - Prob. 10.91PCh. 10.2 - Prob. 10.92PCh. 10.2 - Prob. 10.93PCh. 10.2 - Prob. 10.94PCh. 10.2 - Prob. 10.95PCh. 10.2 - Prob. 10.96PCh. 10.2 - Bars AB and BC, each with a length l and of...Ch. 10.2 - Prob. 10.98PCh. 10.2 - Prob. 10.99PCh. 10.2 - Prob. 10.100PCh. 10 - Determine the vertical force P that must be...Ch. 10 - Determine the couple M that must be applied...Ch. 10 - Prob. 10.103RPCh. 10 - Prob. 10.104RPCh. 10 - Prob. 10.105RPCh. 10 - Prob. 10.106RPCh. 10 - Prob. 10.107RPCh. 10 - Prob. 10.108RPCh. 10 - Prob. 10.109RPCh. 10 - Prob. 10.110RPCh. 10 - Prob. 10.111RPCh. 10 - Prob. 10.112RP
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