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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 12, Problem 17P

Textbook Problem

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Determine the approximate axial forces, shears, and moments for all the members of the frames shown in Figs. P12.6 through P12.13 by using the cantilever method.

FIG. P12.9, P12.17

To determine

Find the approximate axial forces, shears, and moments for the all members of the frames using cantilever method.

**Given information:**

The axial force acting at point *I*

The axial force acting at point *F*

The vertical distance of the member *AD*, *BE*, and *CF*

The vertical distance of the member *DG*, *EH*, and *FI*

The horizontal distance of the members *AB*, *DE*, and *GH*

The horizontal distance of the members *BC*, *EF*, and *HI*

Take the counterclockwise moment is positive and clockwise moment is negative.

The axial force in horizontal direction, towards right is positive and towards left side is negative.

The axial force in vertical direction, towards upward is positive and towards downward is negative.

**Calculation:**

Insert the internal hinges at the midpoints of all the members of the given frame to obtain the simplified frame for approximate analysis.

Draw the simplified frame as in Figure (1).

For the calculation of column axial forces of story of the frame, pass an imaginary section *aa* through the internal hinges at the midheights of columns *AD*,* BE*, and *CF*.

Draw the free body diagram of the frame portion with the passed imaginary lines as in Figure (2).

**Column axial forces:**

**Above section aa:**

Draw the free body diagram of the frame portion above the section *aa* as in Figure (3).

Determine the location of the centroid using the relation.

Substitute 0 ft for

The given lateral load is acting on the frame to the left, therefore the axial force in column *DG* located to the left of the centroid, must be compressive, whereas the axial force in column *FI* placed to the right of the centroid, must be tensile.

Determine the axial force in the column members *DG* and *FI* using equilibrium conditions.

Take moment about point *J*.

Substitute 24 ft for

The axial force at the column member *DG* and *FI* is

Draw the free body diagram of the frame portion above the section *aa* with the axial forces in the column members as in Figure (4).

Draw the free body diagram of the frame portion above the section *bb* as in Figure (5).

Determine the location of the centroid using the relation.

Substitute 0 ft for

The given lateral load is acting on the frame to the left, therefore the axial force in column *AD* located to the left of the centroid, must be compressive, whereas the axial force in column *CF* placed to the right of the centroid, must be tensile.

Determine the axial force in the column members *AD* and *CF* using equilibrium conditions.

Take moment about point *K*.

Substitute 24 ft for

The axial force at the column member *AD* and *CF* is

Draw the free body diagram of the frame portion above the section *bb* with the axial forces in the column members as in Figure (6).

**Girder shear and moments:**

**Consider girder GH**.

Determine the shear at upper left end joint *G* using equilibrium equation.

Substitute 3.33 k for

Determine the shear at upper right end joint *H* using equilibrium equation.

Substitute 3.33 k for

Determine the moment at left end of the girder *GH* using equilibrium equations.

Substitute 3.33 k for

Determine the moment at right end of the girder *GH* using equilibrium equations.

Take moment about point *G*.

Substitute

**Consider girder HI.**

Determine the shear at left end joint *H* using equilibrium equation.

Substitute 3.33 k for

Determine the shear at right end joint *I* using equilibrium equation.

Substitute 3.33 k for

The sheare at the joint *I* is

Determine the moment at left end of the girder *HI* using equilibrium equations.

Substitute 3.33 k for

Determine the moment at right end of the girder *HI* using equilibrium equations.

Take moment about point *H*.

Substitute

**Consider girder DE**.

Determine the shear at upper left end joint *D* using equilibrium equation.

Substitute 3.33 k for

Determine the shear at right end joint *E* using equilibrium equation.

Substitute 13.33 k for

Determine the moment at left end of the girder *DE* using equilibrium equations.

Substitute 13.33 k for

Determine the moment at right end of the girder *DE* using equilibrium equations.

Take moment about point *D*.

Substitute

**Consider girder EF.**

Determine the shear at left end joint *E* using equilibrium equation.

Substitute 13.33 k for

Determine the shear at right end joint *F* using equilibrium equation.

Substitute 13.33 k for

The sheare at the joint *F* is

Determine the moment at left end of the girder *EF* using equilibrium equations.

Substitute 13.33 k for

Determine the moment at right end of the girder *EF* using equilibrium equations.

Take moment about point *E*.

Substitute

**Column moments and shears:**

**Column moment for member DG, EH, and FI:**

Determine the moment at the column member *DG* using moment equilibrium of joints.

Apply the moment equilibrium of joints at *G*.

Substitute

The moment at the column member *GD* is

Determine the moment at the column member *EH*.

Apply the moment equilibrium of joints at *H*.

Substitute

Structural Analysis

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Ch. 12 - 12.1 through 12.5 Draw the approximate shear and...Ch. 12 - 12.1 through 12.5 Draw the approximate shear and...Ch. 12 - 12.1 through 12.5 Draw the approximate shear and...Ch. 12 - 12.1 through 12.5 Draw the approximate shear and...Ch. 12 - 12.1 through 12.5 Draw the approximate shear and...Ch. 12 - Determine the approximate axial forces, shears,...Ch. 12 - Determine the approximate axial forces, shears,...Ch. 12 - Determine the approximate axial forces, shears,...Ch. 12 - Determine the approximate axial forces, shears,...Ch. 12 - Determine the approximate axial forces, shears,...

Ch. 12 - Determine the approximate axial forces, shears,...Ch. 12 - 12.6 through 12.13 Determine the approximate axial...Ch. 12 - 12.6 through 12.13 Determine the approximate axial...Ch. 12 - 12.14 through 12.21 Determine the approximate...Ch. 12 - 12.6 through 12.13 Determine the approximate axial...Ch. 12 - Determine the approximate axial forces, shears,...Ch. 12 - Determine the approximate axial forces, shears,...Ch. 12 - Determine the approximate axial forces, shears,...Ch. 12 - Determine the approximate axial forces, shears,...Ch. 12 - Determine the approximate axial forces, shears,...Ch. 12 - Determine the approximate axial forces, shears,...

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