Example:

Example:

Example:

Example:3 k/ft

4 k/ft

Example:

Example:

Example:

Example:

Area = (2/3)*b*h= 18 kN-m

(+18)

(-18)

Example:

Example:

A B C D E

A B C D E

V- and M- Diagrams for Frames

Procedures:

1. Determine reactions at the frame supports

2. Method of Sections determine axial force, shear force, and bending moment at the ends of each member.

3. Free-Body Diagram with all load components acting parallel and perpendicular to the members axis.

4. M(+) on the compression side and M(-) on the tension side.

Example:

Example:

Example:

Pin Roller

Example:

RollerPin

THE METHOD OF SUPERPOSITION(for M-Diagram)

- Treating each load case separately.

- M-Diagram is divided into series of parts and then combined the results.

- Useful for a structural member under a complicated shape of loadings.

- Advantageous for statically indeterminate beams.