WORLD FOR CIVIL

Statics - Review/Summary/Problem Sheet

I Equilibrium Conditions 3-dimensions

Translational: S F = 0 or S F_x = 0, S F_y = 0, S F_z = 0
Rotational S t = 0 or S t_x = 0 (right hand rule +), S t_y = 0 (right hand rule +), S t_z = 0 (right hand rule +)
where t = R x F or (t = force x perpendicular distance to pivot point)

II Equilibrium Conditions 2-dimensions

Translational: S F = 0 or S F_x = 0, S F_y = 0
Rotational S t = 0 or S t_p = 0 (ccw = +), where t = R x F or (t = force x perpendicular distance to pivot point)

Example 1

A simply supported 40 foot, 4000 lb bridge, shown above, has a 5 ton truck parked 10 feet from the left end of the bridge. We would like to determine the compressional force in each support. The weight of the bridge may be considered to act at its center.

1. Free body diagram is shown above.
2. All forces are in x or y direction
3. Eq. Cond: S Fx = 0 (no external x forces acting on structure.)
S Fy = + Fa + Fb - 10,000 lb - 4,000 lb = 0
S ta = -10,000 lb x 10 ft - 4,000 lb x 20 ft + Fb x 40 ft = 0
Solving: Fa = 9500 lb, Fb = 4500 lb

III Statics Problems: Techniques

1. Draw Free Body Diagram of entire structure, showing and labeling all external forces, including support forces and loads. Choose an appropriate coordinate system. Determine needed dimensions and angles.
2. Resolve all forces into their x and y components.
3. Apply the equilibrium conditions and solve for unknown external forces and torques as completely as possible.

Often we wish to know the internal forces (tension & compression) in each member of the structure in addition to the external support forces. To do this (with non-truss problems) we continue the procedure above, but with members of the structure, not the entire structure.

4. Draw Free Body Diagram of a member (s) of the structure of interest. Show and label all external forces and loads acting on the selected member. Choose an appropriate coordinate system. Determine needed dimensions and angles.
5. Resolve all forces into their x and y components.
6. Apply the equilibrium conditions and solve for unknown external forces and torques acting on the member as completely as possible.

In certain problems, the equilibrium equations for both the entire structure and for its members may have to be written and solved simultaneously before all the forces on the structure and in its members can be determined.

Problem #1. A beam is supporting two painters as shown below. Each painter weighs 180 lbs. Determine the tension in each rope (AB & FE). (Neglect the weight of the beam.) (210 lb., 150 lb.)

Probem #2. Rework problem #1. Assume that the plank weighs 100 pounds and that this weight may be considered to act at the center of the span.(260 lb., 200 lb.)

Problem #3. A 160 lb person is standing at the end of a diving board as shown below. The diving board weighs 140 lbs, and this weight may be considered to act at the center of the board. Calculate the vertical forces acting at each support, A & B. (Include the directions of the forces) (-390 lb., 690 lb.)

Problem #4. A 500 pound sign is supported by a beam and cable as shown below. The beam is attached to a wall by a hinge, and has a uniformly distributed weight of 100 lbs. Determine the tension in the cable and the forces acting at the hinge. (BC=917 lb., Ax = 733 lb., Ay = 50lb.)