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Structural Analysis

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

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BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 8, Problem 15P
Textbook Problem
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Draw the influence lines for the shear and bending moment at point D of the beam shown in Fig. P8.13.

FIG. P8.13, P8.14, P8.15

Chapter 8, Problem 15P, Draw the influence lines for the shear and bending moment at point D of the beam shown in Fig.

To determine

Draw the influence lines for the shear and bending moment at point D.

Explanation of Solution

Calculation:

Use Muller-Breslau's principle.

Influence line ordinate for the shear at point D.

Sketch the deflected shape of the released structure when cut the beam at D as shown in Figure 1.

To obtain the deflected shape of the released structure by cut the beam at D and then applied a small displacement of Δ. The portion ED can neither translate nor rotate because of the fixed support at D. The general shape of the influence line is the same as the deflected shape of the released structure.

Sketch the free body diagram of D when 1 kN load placed at D as shown in Figure 2.

Place a 1 kN load placed just left of D and right D.

Refer Figure 2.

Find the shear at D just left of D.

Apply force equilibrium equation along vertical.

Consider upward force as positive and downward force as negative.

ΣFy=0Ay1SD=001SD=0SD=1kN

Thus, the influence line ordinate at just left of D is 1kN/kN.

Find the shear at D just right of D.

The portion ED is a rigid portion. Hence, the influence line ordinate at just right of D is 0.

The influence line ordinate at A is zero.

Sketch the influence line for the shear at point D as shown in Figure 3.

Influence line ordinate for the bending moment at point D.

Sketch the deflected shape of the released structure when an internal hinge is inserted at point D as shown in Figure 4.

To obtain the deflected shape of the released structure by an internal hinge is placed at D and then applied a small rotation θ at point D. The portion ED can neither translate nor rotate because of the fixed support at E. The general shape of the influence line is the same as the deflected shape of the released structure.

Find the influence-line ordinate at C.

Sketch the free body diagram when 1 kN load is applied on point D as shown in Figure 5.

Refer Figure 5.

Consider section DE

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Chapter 8 Solutions

Structural Analysis
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Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical reaction...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - Draw the influence lines for the reaction moments...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - 8.35 and 8.36 Draw the influence lines for the...Ch. 8 - 8.35 and 8.36 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear in panel CD...Ch. 8 - Draw the influence lines for the shear in panel DE...Ch. 8 - Draw the influence lines for the shear in panel BC...Ch. 8 - Draw the influence lines for the shear in panel BC...Ch. 8 - Draw the influence line for the shear in panel CD...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.45 through 8.52 Draw the influence lines for the...Ch. 8 - 8.45 through 8.52 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - Draw the influence line for the vertical...Ch. 8 - 8.59 and 8.60 Draw the influence line for the...Ch. 8 - 8.59 and 8.60 Draw the influence line for the...Ch. 8 - Draw the influence line for the vertical...

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