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Strategy to Solve Statically Indeterminate Problems

Steps in Strategy:

Step 1

Construct a free body diagram of the entire structure and perhaps each part

of the structure.

Remember you are isolating the structure and each part of the structure.

This first step is essential. By doing so you are identifying all forces and

all couples that act on the structure including both magnitude and direction.

Incorrect FBD's will always result in incorrect equations of equilibrium

since you are writing the equations of equilibrium based on your FBD's.

Step 2

Write the equations of equilibrium for the entire structure and for each part

of the structure. For systems in the x˗y plane the equations of equilibrium are:

→∑ Fx = 0, ↑∑ Fy = 0, and ccw ∑ M_A = 0 where point A is any

convenient point to sum moments about. ccw refers to counterclockwise

although you could take clockwise as positive

Step 3

Identify the unknowns in the equations of equilibrium. They may include

forces, couples, angles, and lengths. There will always be more unknowns

than equations of equilibrium for statically indeterminate problems.

Step 4

Additional information to supplement the equations of equilibrium comes

from load˗deflection relations and geometrical constraints. Use this

information to supplement that from the equations of equilibrium.

Step 5

Once you have the same total number of unknowns as total number of

independent equations you can proceed to solve for the unknowns.

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