WORLD FOR CIVIL

STATICS / STRENGTH OF MATERIALS - Example

In the structure shown below members ABC , BDE and CD are assumed to be solid rigid members. The structure is pinned at A and supported by a roller at E. For this structure:
A. Draw a Free Body Diagram showing all support forces and loads.
B. Determine the value of all the support forces acting on the structure.
C. Determine the force (tension or compression) in member CD.
Unless otherwise indicated, all joints and support points are assumed to be pinned or hinged joints.

Solution:
PARTS A & B:
STEP 1: Draw a free body diagram showing and labeling all load forces and support(reaction) forces, as well as any needed angles and dimensions.
STEP 2: Break any forces not already in x and y direction into their x and y components.
STEP 3: Apply the equilibrium conditions.
Sum F_x = A_x = 0
Sum F_y = A_y + E_y - 8,000 lbs - 4,000 lbs = 0
Sum T_A = (-8,000 lbs)(3 ft) - (4,000 lbs)(6.5 ft) + E_y(8.5 ft) = 0
Solving for the unknowns:
E_y = 5,880 lbs; A_y = 6,120 lbs

PART C - Now find internal force in member CD.
STEP 1: Draw a free body diagram of a member that CD acts on - member BDE.
STEP 2: Resolve all forces into x and y components (see diagram).
STEP 3: Apply the equilibrium conditions:
Sum F_x = -B_x + CD cos (60^o) = 0
Sum F_y = B_y - CD sin (60^o) - 4,000 lbs + 5,880 lbs = 0
Sum T_B = -CD sin (60^o)(3 ft) - (4,000 lbs)(5 ft) + (5,880 lbs)(7 ft) = 0
Solving for the unknowns:
CD = 8,140 lbs; B_x = 4,070 lbs; B_y = 5,170 lbs
These are the external forces acting on member BDE.
The force in CD is 8,140 lbs (c).