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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 12, Problem 11P

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 portal method.

FIG. P12.11, P12.19

To determine

Find the approximate axial forces, shears, and moments for all members of the frame using portal 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*

**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 shears in the columns of the frame, pass an imaginary section *aa* through the columns just above the support level.

Draw the free body diagram of the frame portion above section *bb* as in Figure (2).

**Column shears:**

Consider the shear in the interior column *BE* is twice as much as in the exterior columns *AD* and *CF*.

Determine the column shears at the lower end using equilibrium equations.

Substitute 25 k for

The shear force at the lower end of the columns

Determine the shear force at the interior column.

Substitute 10 k for

Draw the free body diagram of frame with the column shear value at the lower end column as in Figure (3).

Draw the free body diagram of the frame portion above section *aa* as in Figure (4).

Consider the shear in the interior column *EH* is twice as much as in the exterior columns *DG* and *FI*.

Determine the column shears at the lower end of the member *DEF* using equilibrium equations.

Substitute 15 k for

The shear force at the end of the columns

Determine the shear force at the interior column.

Substitute 3.75 k for

Draw the free body diagram of frame with the column shear value at the end of the member *DEF* as in Figure (5).

**Column moments:**

Consider upper end column members.

Consider the anticlockwise moment is positive and clockwise moment is negative.

Determine the moment at the column member *DG*.

Substitute 3.75 k for

The moment at the column *DG* is equal to moment at the column *FI*. Therefore, the moment at the column member *DG* and *FI* is

Determine the moment at the column member *EH*.

Substitute –22.5 k-ft for

The moment at the internal hinge of the horizontal member *GH* and *HI* has the equal maginitude and opposite direction of the moment at the vertical column member *DG* and *FI*.

Consider lower end column members.

Consider the anticlockwise moment is positive and clockwise moment is negative.

Determine the moment at the column member *AD*.

Substitute 10 k for

The moment at the column *AD* is equal to moment at the column *CF*. Therefore, the moment at the column member *AD* and *CF* is

Determine the moment at the column member *BE*.

Substitute –60 k-ft for

The moment at the internal hinge of the horizontal member *DE* and *EF* has the equal maginitude and opposite direction of the summazation of moment at the vertical column member (*AD* and *DG*) and(*CF* and *FI*).

Determine the moment at the internal hinge of the horizontal member *DE*.

Substitute 22.5 k-ft for

Determine the moment at the internal hinge of the horizontal member *EF*.

Substitute 60 k-ft for

Draw the free body diagram of frame with the column moments for frame portion *FIH* as in Figure (6).

**Girder axial forces, moments, and shears:**

**Consider girder HI.**

Determine the girder end action at the upper right end joint *I* using the relation.

Substitute 15 k for

Determine the vertical shear at the point *I* using the relation.

Take moment about hinge at the horizontal member *HI*.

Substitute

Determine the vertical shear at point *H* using the relation.

Substitute 3

Structural Analysis

Show all chapter solutions

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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