The structure shown below is a truss which is
pinned to the floor at point D, and supported by a roller at
point A. 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 in member GC by method of joints.
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 Fx = Dx = 0
Sum Fy = Ay + Dy - 10,000 lbs -
12,000 lbs = 0
Sum TA = Dy(12 ft) - (12,000 lbs)(8 ft) -
(10,000 lbs)(4 ft) = 0
Solving for the unknowns:
Dy = 11,300 lbs; Ay = 10,700 lbs
PART C - Now find internal force in member GC by method of joints.
JOINT A:
STEP 1: Draw a free body diagram of the joint.
STEP 2: Resolve all forces into x and y components (see diagram).
STEP 3: Apply equilibrium conditions:
Sum Fx = AB - AG cos (56.3o) = 0
Sum Fy = 10,700 lbs - AG sin (56.3o) = 0
Solving for the unknowns: AG = 12,900 lbs (c); AB = 7,140 lbs (t)
JOINT B:
STEP 1: Draw a free body diagram of the joint.
STEP 2: Resolve all forces into x and y components (see diagram).
STEP 3: Apply equilibrium conditions:
Sum Fx = -7,140lbs + BC = 0
Sum Fy = BG = 0
Solving for the unknowns: BG = 0 lbs ; BC = 7,140 lbs (t)
JOINT D:
STEP 1: Draw a free body diagram of the joint.
STEP 2: Resolve all forces into x and y
components (see diagram).
STEP 3: Apply equilibrium conditions:
Sum Fx = -CD +ED cos (56.3o) = 0
Sum Fy = 11,300 lbs - ED sin (56.3o) = 0
Solving for the unknowns: CD = 7,560 lbs (t); ED = 13,600 lbs (c)
JOINT C:
STEP 1: Draw a free body diagram of the joint.
STEP 2: Resolve all forces into x and y
components (see diagram).
STEP 3: Apply equilibrium conditions:
Sum Fx = 7,560 lbs - 7,140 lbs - GC cos (56.3o)
= 0
Sum Fy = CE - 12,000 lbs - GC sin (56.3o) =
0
Solving for the unknowns: CE = 11,400 lbs (t); GC = 730 lbs (t)
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