Force Vectors

Equilibrium of Forces

Moments from Forces (I)

Moments from Forces (II)

Illustrations for Forces and Moments

Force Couples

Transmissibility of Forces

Force/Moment Resultants

Equivalent Loading (I)

Equivalent Loading (II)

Practical Examples

Typical 2-D Supports (I)

Typical 2-D Supports (II)

Free Body Diagram (I)

Free Body Diagram (II)

Free Body Diagram (III)

Free Body Diagram (IV)

Two/Three Force Members

When a member is subject to no couple moments and the applied forces can be combined to be resultants at only two points, the member is called a Two-Force Member.

If a member is subject to three forces, then it is necessary for them to be either concurrent or parallel when this member is in equilibrium. Such a member is called a Three-Force Member.

Application of Two/Three Force Members

Redundant Constraints

Statically Indeterminate Structure

Ax = 0, Ay + Cy = 500 N --------- (2)

Cy * 5 m + MA = 500 N * 4 m ----------- (3)

Ay * 5 m - MA = 500 N * (5 - 4) m ----- (4)

5 m

4 m

{(3) + (4) (2)

Cannot solve for all unknowns !!!

Tricky Problems

Truss Structures

Truss Analysis

Joint Method (I)

Joint Method (II)

Zero-Force Members

(a)

(b)

(a)

(b)

Exercise Example

Internal Forces/Moments

Section Method (I)

Section Method (II)