2.114 A horizontal circular plate weighing 60 lb is suspended as shown from three wires that are
attached to a support at D and from 30 angles with the vertical. Determine the tension in each wire.
(a)
(b)
(c)
SOLUTION I
Free Body Diagram. Consider the jo
3.80 Shaft A and B connect the gear box to the wheel assemblies of a tractor, and shaft C
connects it to the engine. Shafts A and B lie in the vertical yz plane, while shaft C is
directed along the x axis. Replaces the couples applied to the shafts with a
4.95 A 200-mm lever and a 240-mm-diameter pulley are welded to the axle BE that is supported by
bearings at C and D. If a 720-N vertical load is applied at A when the lever is horizontal, determine
(a) the tension in the cord, (b) the reactions at C and D
4.115 A 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by
cable DCE that passes over a frictionless hook at C. Assuming that the tension is the same in both
parts of the cable, determine (a) the tension in the ca
5.37 Determine by direct integration the centroid of the area shown.
SOLUTION
= 2b/[3(4-)]
Or use the vertical differential element in the textbook:
The results are the same as in the double-integral approach.
= 2a/[3(4-)]
5.22 The horizontal x axis is drawn through the centroid C of the
area shown, and it divides the area into two component
areas A1 and A2 . Determine the first moment of each
component area with respect to the x axis, and explain the
results obtained.
SOLU
4.67 Determine the reactions at B and D when b = 120 mm.
SOLUTION
Free Body Diagram. Consider ABC as a free body. Since CD is a two-force member, the line of
action of reaction at D must pass through C and D. Therefore, RD must be at 45 as shown. The pinn
4.71 One end of rod AB rests in the corner A and the other end is attached to cord BD. If the rod supports
a 40-lb load at its midpoint C, find the reaction at A and the tension in the cord.
SOLUTION
Free Body Diagram. Consider ACB as a free body. It is e
4.50 Determine the range of allowable values of the tension in wire BD if the magnitude of the couple at
the fixed support C is not to exceed 100 N m.
SOLUTION
Select the frame as a free body. The reactions at the fixed support at C have two force compone
4.38
Determine the tension in each cable and the reaction at D.
SOLUTION
Free Body Diagram. Select the bar ABCD as a free body. The wall at the roller D provides one
support force, RD, perpendicular to the surface, as shown. Each of the cable provides a t
4.22 For the frame and loading shown, determine the reactions at A and E when (a) =30 , (b)
= 45.
SOLUTION
Free Body Diagram. Select the frame ABCDE as a free body. The reactions at the fixed support at
A have two force components, as shown, and the slop
4.18 Determine the maximum tension that can be developed in cable AB if the maximum allowable value
of the reaction at C is 250 lb.
SOLUTION
Free Body Diagram. Select the frame DCB as a free body. The reactions at the fixed support at C
have two force com
5.35 Determine by direct integration the centroid of the area shown.
Express your answer in terms of a and h.
SOLUTION
The values of k and m are determined by substituting x = a and y = h into the equations of the two curves.
We have h = ma and h = ka2. T
ENGR 213 A: Statics
Fall 2010
Homework Set # 13
DUE: Wednesday 12/08/2010
7.31, 7.39, 7.46, 7.x1, 7.x2
7.x
For the beam and loading shown, ( a) draw the shear and
bending-moment diagrams, (b) determine the maximum
absolute values of the shear and bending
7.x
Draw the shear and bending-moment
diagrams for the beam and loading shown.
SOLUTION
Reactions. From the equilibrium of the entire beam,
Internal Forces. It is seen that there are three segments, AC, CD and
DB, in which the applied loads are continuous
6.63 Determine the force in members EH and GI of the truss shown. (Hint: Use section aa.)
SOLUTION
Reaction Forces. Consider the entire truss as a free body to determine the unknown reactions.
RP = 24 kips
RAx = 0 kips
RAy = 12 kips
Member Forces. Pass th
Assuming the upward reaction of the ground on beam AB to be uniformly distributed, (a)
draw the shear and bending-moment diagrams, ( b) determine the maximum absolute
values of the shear and bending moment.
SOLUTION
Reactions. Consider the entire beam as
7.x
For the beam and loading shown, ( a) draw the shear and bending moment diagrams, ( b)
determine the maximum absolute values of the shear and bending moment.
SOLUTION
Reactions. Consider the entire beam as a free body.
RB = 64 kN
RA = 46 kN
Internal Fo
6.99 For the frame and loading shown, determine the components of the forces acting on member CFE
at C and F.
SOLUTION
Free Body: Entire Frame. There are three unknown reactions from the supports.
RA = 52 lb
RDx = 52 lb
RDx = 40 lb
Free Body: Member ABF.
6.51 A Howe scissors roof truss is loaded as shown. Determine the force in members DF, DG, and EG.
SOLUTION
Reaction Forces. Consider the entire truss as a free body to determine the unknown reactions.
Because of symmetry of loading,
RAx = 0 kips
Member F
7.x
For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b)
determine the maximum absolute values of the shear and bending moment.
SOLUTION
Reactions. Consider the entire beam as a free body. By symmetry, we have
Internal Force
6.110 For the frame and loading shown, determine (a) the reaction at C, (b) the force in member AD.
FAD
FBE
3
5
4
RCy
RCx
RFy
RFx
FBD of the entire frame
RCy
RCx
FBD of ABC
SOLUTION
Free Body: Entire Frame. There are four unknown reactions from the suppor
6.14 Determine the force in each member of the roof truss shown. State whether each member is in
tension or compression.
SOLUTION
Reaction Forces. Consider the entire truss as a free body. Because of symmetry of loading,
RAx = 0 kN
In the following calcul
5.41 Determine by direct integration the centroid of the area shown. Express your answer in terms of a
and
b.
SOLUTION
The
and y = b
b = k2a4.
values of k1 and k2 are determined by substituting x = a
into the equations of the two curves. We have b = k1a2
3.59 A regular tetrahedron has six edges of length a. A force P is directed as shown along
edge BC. Determine the moment of P about edge OA.
SOLUTION
By definition,
It is easy to see that
Determining OA is a little tedious. From OBC, we have
Since
or
we h
3.55 The frame ACD is hinged at A and D
and is supported by a cable that passes
through a ring at B and is attached to
hooks at G and H. Knowing that the
tension in the cable is 450 N, determine
the moment about the diagonal AD of
the force exerted on the