Structural Analysis, 5th Edition
Structural Analysis, 5th Edition
5th Edition
ISBN: 9788131520444
Author: Aslam Kassimali
Publisher: Cengage Learning
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Chapter 5, Problem 61P
To determine

Plot the shear diagram, bending moment diagram, axial force diagram, and the qualitative deflected shape of the frame.

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Explanation of Solution

Write the condition for static instability, determinacy and indeterminacy of plane frames as follows:

3m+r<3j+ecstaticallyunstableframe        (1)

3m+r=3j+ecstaticallydeterminateframe        (2)

3m+r>3j+ecstaticallyindeterminateframe        (3)

Here, number of members is m, number of external reactions is r, the number of joints is j, and the number of elastic hinges is ec.

Find the degree of static indeterminacy (i) using the equation;

i=(3m+r)(3j+ec)        (4)

Refer to the Figure in the question;

The number of members (m) is 2.

The number of external reactions (r) is 3.

The number of joints (j) is 3.

The number of elastic hinges ec is 0.

Substitute the values in Equation (2);

3(2)+3=3(3)+09=9staticallydeterminateframe

Show the free-body diagram of the entire frame as in Figure 1.

Structural Analysis, 5th Edition, Chapter 5, Problem 61P , additional homework tip  1

Refer Figure (1).

Find the distance for the beam AB.

ABsinθ=10AB=10sin63.43°AB=11.18m

Find the horizontal reaction at point C by resolving the horizontal component of forces.

+FX=0Cx+30×11.18×25=0Cx=300kN()

Find the resultant reaction at point C by taking moment about point A.

+MA=0Cy(15)20(10)(102+5)+300(10)30×11.18×11.182=015Cy2,000+3,0001,874.886=0Cy=58.33kN()

Find the vertical reaction at point A by resolving the vertical component of forces.

+FY=0Ay20×1030×11.18×15+Cy=0Ay200149.99+58.33=0Ay=291.66kN()

Consider point A:

Resolve the vertical component of forces.

+FY=0Ay=Ay(15)=291.66(15)=130.4kN

Resolve the horizontal component of forces.

+FX=0Ax=Ay(25)=291.66(25)=260.87kN()

Show the free-body diagram of the members and joints of the entire frame as in Figure 2.

Structural Analysis, 5th Edition, Chapter 5, Problem 61P , additional homework tip  2

Consider point A:

Resolve the vertical component of forces.

+FY=0130.4AYBC=0AYBC=130.4kN

Resolve the horizontal component of forces.

+FX=0260.87AXBC=0AXBC=260.87kN

Consider the member AB:

Resolve the vertical component of forces.

+FY=0AYAB30×11.18+BYAB=0130.43335.4+BYAB=0BYAB=204.97kN

Resolve the horizontal component of forces.

+FX=0BXAB+AXAB=0BXBC+260.87=0BXBC=260.87kN

Take moment about the point B.

+MBAB=0AYAB(11.18)+30×11.18(11.182)MBAB=0130.43(11.18)+450MBAB=0MBAB=416.67kNm

Consider the point C:

Resolve the vertical component of forces.

+FY=058.33CYBC=0CYBC=58.33kN

Resolve the horizontal component of forces.

+FX=0300+CXBC=0CXBC=300kN

Consider the member BC:

Resolve the vertical component of forces.

+FY=0BYBC20×10+CYBC=0BYBC200+58.33=0BYBC=141.67kN

Resolve the horizontal component of forces.

+FX=0BXBCCXBC=0BXBC300=0BXBC=300kN

Take moment about point B:

+MBBC=0CYBC(10)20×10(102)+MBBC=058.33(10)1,000+MBBC=0MBBC=416.7kNm

Plot the moment end forces of the frame as in Figure 3.

Structural Analysis, 5th Edition, Chapter 5, Problem 61P , additional homework tip  3

Refer to the moment end force diagram plot the shear diagram, bending moment diagram, and the axial force diagrams.

Plot the shear force diagram as in Figure 4.

Structural Analysis, 5th Edition, Chapter 5, Problem 61P , additional homework tip  4

The maximum bending moment occurs where the shear force changes sign.

Consider the section ADB, use the similar triangle concept.

130.44x=204.9711.18x1,458.32130.44x=204.97x335.41x=1,458.32x=4.35mfrompoint A

Find the maximum bending at point D.

MD=130.43×4.352=283.68kNm

Consider the section BEC, use the similar triangle concept.

141.67x=58.3310x1,416.7141.67x=58.33x200x=1,416.7x=7.08mfrompoint B

Find the maximum bending at point D.

MD=58.33×(107.08)2=85.1kNm

Plot the bending moment diagram as in Figure 5.

Structural Analysis, 5th Edition, Chapter 5, Problem 61P , additional homework tip  5

Plot the axial force diagram as in Figure 6.

Structural Analysis, 5th Edition, Chapter 5, Problem 61P , additional homework tip  6

Plot the qualitative deflected shape as in Figure 7.

Structural Analysis, 5th Edition, Chapter 5, Problem 61P , additional homework tip  7

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Chapter 5 Solutions

Structural Analysis, 5th Edition

Ch. 5 - Prob. 11PCh. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Prob. 17PCh. 5 - Determine the equations for shear and bending...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - Prob. 25PCh. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - Prob. 27PCh. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - Prob. 34PCh. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - Prob. 36PCh. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - Prob. 44PCh. 5 - Prob. 45PCh. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - Draw the shear and bending moment diagrams for the...Ch. 5 - For the beam shown: (a) determine the distance a...Ch. 5 - For the beam shown: (a) determine the distance a...Ch. 5 - Prob. 55PCh. 5 - Prob. 56PCh. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - Prob. 59PCh. 5 - Prob. 60PCh. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Prob. 63PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - Prob. 66PCh. 5 - Prob. 67PCh. 5 - Prob. 68PCh. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Prob. 71P
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