   # Draw the shear, bending moment, and axial force diagrams and the qualitative deflected shape for the frame shown.

#### Solutions

Chapter
Section
Chapter 5, Problem 59P
Textbook Problem
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## Draw the shear, bending moment, and axial force diagrams and the qualitative deflected shape for the frame shown. To determine

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

### 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.

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

+MA=0100(1.5)12(5)(52+3)+RC(15)(4)+RC(25)(8)=0150330+4RC5+16RC5=0RC=53.67kN

Consider point C;

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

+FYC=0Cy=RC(25)=53.67(25)=48kN

Consider point C;

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

+FXC=0Cx=RC(15)=53.67(15)=24N

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

Consider point C:

Resolve the vertical component of forces.

+FY=048CYBC=0CYBC=48kN

Resolve the horizontal component of forces.

+FX=0CXBC24=0CXBC=24kN

Consider the member BC:

Resolve the vertical component of forces.

+FY=0BYBC+CYBC12(5)=0BYBC+4860=0BYBC=12kN

Resolve the horizontal component of forces.

+FX=0BXBCCXBC=0BXBC24=0BXBC=24kN

Take moment about the point B

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