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Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

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Chapter
Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 7, Problem 23P
Textbook Problem
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7.22 and 7.23 Determine the deflection at point B of the beam shown in Figs. P7.20 and P7.21 by the virtual work method. Use the graphical procedure (Table 7.6) to evaluate the virtual work integrals.

Chapter 7, Problem 23P, 7.22 and 7.23 Determine the deflection at point B of the beam shown in Figs. P7.20 and P7.21 by the

FIG. P7.21, P7.23, P7.58

To determine

Find the deflection at point B of the beam using virtual work method.

Explanation of Solution

Given information:

The beam is given in the Figure.

The value of E is 70 GPa and I is 164(106)mm4.

Apply the sign conventions for calculating reactions, forces, and moments using the three equations of equilibrium as shown below.

  • For summation of forces along x-direction is equal to zero (Fx=0), consider the forces acting towards right side as positive (+) and the forces acting towards left side as negative ().
  • For summation of forces along y-direction is equal to zero (Fy=0), consider the upward force as positive (+) and the downward force as negative ().
  • For summation of moment about a point is equal to zero (Matapoint=0), consider the clockwise moment as negative and the counter clockwise moment as positive.

Calculation:

Consider the real system.

Sketch the real system of the beam as shown in Figure 1.

Refer to Figure 1.

Find moment at A.

Summation of moments about A is equal to 0.

MA=0MA50=0MA=50kNm

Sketch the moment diagram of the real system M as shown in Figure 2.

Consider the virtual system.

Remove all the real loads and apply unit load where the point to find the deflection.

Let the bending moment due to virtual load be Mv.

Sketch the virtual system of the beam with unit load at point B as shown in Figure 3.

Refer to Figure 1.

Find the reaction and moment at A.

Summation of forces along y-direction is equal to 0.

+Fy=0Ay1=0Ay=1

Summation of moments about A is equal to 0.

MA=0MA1(4)=0MA=4kNm

Sketch the moment diagram of the virtual system Mv as shown in Figure 4.

Find the deflection at B using the virtual work expression:

1(ΔB)=0LMvMEIdx (1)

Refer Table 7.6, “Integrals 0LMvMdx for moment diagrams of simple geometric shapes” in the textbook.

For the moment diagram in Figure 2 and Figure 4, the value of 0LMvMdx is 12Mv1M1L

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Chapter 7 Solutions

Structural Analysis
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Ch. 7 - Determine the smallest cross-sectional area A...Ch. 7 - Determine the smallest cross-sectional area A...Ch. 7 - 7.13 through 7.15 Determine the smallest...Ch. 7 - 7.13 through 7.15 Determine the smallest...Ch. 7 - 7.13 through 7.15 Determine the smallest...Ch. 7 - Determine the horizontal deflection at joint E of...Ch. 7 - Determine the vertical deflection at joint G of...Ch. 7 - Determine the horizontal deflection at joint E of...Ch. 7 - Determine the vertical deflection at joint G of...Ch. 7 - 7.20 and 7.21 Use the virtual work method to...Ch. 7 - 7.20 and 7.21 Use the virtual work method to...Ch. 7 - 7.22 and 7.23 Determine the deflection at point B...Ch. 7 - 7.22 and 7.23 Determine the deflection at point B...Ch. 7 - 7.24 through 7.27 Use the virtual work method to...Ch. 7 - 7.24 through 7.27 Use the virtual work method to...Ch. 7 - 7.24 through 7.27 Use the virtual work method to...Ch. 7 - 7.24 through 7.27 Use the virtual work method to...Ch. 7 - 7.28 through 7.30 Determine the deflection at...Ch. 7 - 7.28 through 7.30 Determine the deflection at...Ch. 7 - 7.28 through 7.30 Determine the deflection at...Ch. 7 - 7.31 through 7.33 Determine the smallest moment of...Ch. 7 - 7.31 through 7.33 Determine the smallest moment of...Ch. 7 - 7.31 through 7.33 Determine the smallest moment of...Ch. 7 - 7.34 and 7.35 Use the virtual work method to...Ch. 7 - 7.34 and 7.35 Use the virtual work method to...Ch. 7 - 7.36 and 7.37 Use the virtual work method to...Ch. 7 - 7.36 and 7.37 Use the virtual work method to...Ch. 7 - Use the virtual work method to determine the...Ch. 7 - Use the virtual work method to determine the...Ch. 7 - Use the virtual work method to determine the...Ch. 7 - Use the virtual work method to determine the...Ch. 7 - Use the virtual work method to determine the...Ch. 7 - Use the virtual work method to determine the...Ch. 7 - Determine the rotation of joint D of the frame...Ch. 7 - 7.45 and 7.46 Use the virtual work method to...Ch. 7 - 7.45 and 7.46 Use the virtual work method to...Ch. 7 - 7.47 and 7.48 Determine the smallest moment of...Ch. 7 - 7.47 and 7.48 Determine the smallest moment of...Ch. 7 - Use the virtual work method to determine the...Ch. 7 - Using the method of virtual work, determine the...Ch. 7 - 7.51 through 7.55 Use Castiglianos second theorem...Ch. 7 - 7.51 through 7.55 Use Castiglianos second theorem...Ch. 7 - 7.51 through 7.55 Use Castiglianos second theorem...Ch. 7 - 7.51 through 7.55 Use Castiglianos second theorem...Ch. 7 - 7.51 through 7.55 Use Castiglianos second theorem...Ch. 7 - Use Castiglianos second theorem to determine the...Ch. 7 - 7.57 and 7.58 Use Castiglianos second theorem to...Ch. 7 - 7.57 and 7.58 Use Castiglianos second theorem to...Ch. 7 - 7.59 through 7.62 Use Castiglianos second theorem...Ch. 7 - 7.59 through 7.62 Use Castiglianos second theorem...Ch. 7 - 7.59 through 7.62 Use Castiglianos second theorem...Ch. 7 - 7.59 through 7.62 Use Castiglianos second theorem...Ch. 7 - 7.63 and 7.64 Use Castiglianos second theorem to...Ch. 7 - 7.63 and 7.64 Use Castiglianos second theorem to...Ch. 7 - Use Castiglianos second theorem to determine the...Ch. 7 - Use Castiglianos second theorem to determine the...Ch. 7 - Use Castiglianos second theorem to determine the...Ch. 7 - 7.68 and 7.69 Use Castiglianos second theorem to...Ch. 7 - Use Castiglianos second theorem to determine the...

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