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Unformatted text preview: Statics —— 255 PROBLEMS 7.1 For the hoist shown in Fig. P7.l, determine all of the external forces on member CF G as point
D is moved along member AE so that the angle 9 varies
from 0 to 45°. We suggest that you use a spreadsheet in
preparing this solution. Note the angle [3 = 60° and F = 290
N. The dimensions are: CF = 200 mm, FG = 320 mm and .the pulley radius r = 10 mm. Fig. P7.l 7.2 For the hoist shown in Fig. P7.l, determine all of the
external forces on memberCF G as point B is moved along
member AE so that the angle [3 varies from 45 to 75°. We
suggest that you use a spreadsheet in preparing this
solution. Note the angle 0 = 30° and F = 480 N. The
dimensions CF = 200 mm, FG = 320 mm and the pulley
radius r = 10 mm. 7.3 Prepare a FBD for the entire rectangular ﬁ'ame, shown in Fig. P73, if it is subjected to a
concentrated force of 6.20 kN located a distance of 3.0 In F = 6 20 m
from the left end of the horizontal member. ' 5.0 m Fig. P73 7 4.0 m 7.4 Determine the force F required to develop a pressure p = 700 kPa in the cylinder of the pump shown in Fig. P7.4. The piston area for the
pump is 350 m2. Fig. P7.4 254  Chapter 7
Frames and Machines CENTER OF 3200 LB 28in. 60in. 96in. Fig. E7.7b
Step 3: Apply the equilibrium relations and solve for the unknown forces: F Ax, F Ay and FE.
EMA = [FB cos (8)](28) ’— (3,200)(28 + 60) — (1,500)(28 + 60 +96) = 0
FE =20,110 1b , I (a)
ZFX = FAx  FE sin (8°) = 0 FAx = (20,110)(0.1392) = 2,799 lb 1 I (b)
ZFy = FAy + FE cos (8°) _— 3,200 — 1,500 = FAY + (20,110)(0.9903) — 4,700 = 0
FAy=— 15,2141b V ‘ l (c) While the Loadall appears to be a complex machine capable of lifting and moving leads, it is
relatively easy to analyze. The arm is a multiforce member, but if the FBD is prepared
correctly, the solution for the actuator force FE and the forces F Ax and F Ay at the hinge pin is straightforward. 7.5 SUE/EMMY The method of analysis of frames and machines was introduccd. Frames and machines contain one
or more members that have three or more externally applied forces. For these multiforce members,
the internal force does not coincide with the axis of the member. This fact is extremely important!
because it implies that two internal forces (P and V) and an internal moment M must be applied
when making a section cut through a multiforce member. Because we introduce so many unknowns,
section cuts through a multiforce member are usually avoided when analyzing frames and machines.
The approach is to construct FBDs of the individual members of the structure and to apply the law of
action and reaction as well as the equations of equilibrium to each member. Examples for both
ﬂames and machines were presented to demonstrate the method of analysis. Examples of
construction equipment were described to show that complex machines could be analyzed using
these relatively straightforward techniques. 256 —~ Chapter 7
Frames and Machines 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 Determine the reaction force at point G and the mechanical advantage of the toggle mechanism
illustrated in Fig. P7.5. A force F of 250 N
is applied to the lever at point A. The
contact at point G is made with a roller, and
the links are connected with pins inserted at
points B, C, D and E. Fig. P7.5 0.35 m .30 Determine the reaction force at point G and the mechanical advantage of the toggle mechanism
illustrated in Fig. P7.5. The input force F is now 350 N. The contact at point G is made with a
roller and the links are connected with pins inserted at points B, C, D and B. Your manager believes that the dimension (e — d) for the toggle mechanism shown in Fig.
P7.7 is a critical design parameter. She asks you to determine the mechanical advantage of
this mechanism if the dimension d is
ﬁxed and the dimension e is modiﬁed so
that (e — d) varies from 8 mm to 42 mm.
You may consider using a spreadsheet
for this analysis. Fig. P7.7 .30 0.55 m If the spring constant of the block under
displacement of point G in Problem 7.5. point G is 8.0 kN/mm, determine the vertical
If the spring constant of the block under point G is 8.0 kN/mm, determine the work output of
the toggle mechanism for the conditions described in Problem 7.5. If the spring constant of the block under
displacement of point G in Problem 7.6. point G is 10.0 kN/mm, determine the vertical If the spring constant of the block under point G is 10.0 kN/mm, determine the work output of
the toggle mechanism for the conditions described in Problem 7.6. is applied to the toggle mechanism at
point B. Also determine the
mechanical advantage. Fig. P7.12 COMPACTION PRESS Statics — 257 7.13 A pair of pliers clamps a small diameter rubber cylinder as shown in Fig. P7.13. If opposing
forces of 22 1b are applied to the handles of the pliers,
determine the reaction forces acting on the cylinder. Also
determine the work performed if each handle moves though a
distance d = 0.12 in. Finally, determine the amount that the
cylinder is squeezed by the application of the forces. The
dimensions of the pliers are a = 1.2 in. and b = 5.0 in. Fig. P7.13 . a . b
7.14 For the ﬂame, shown in Fig. P7.14, determine the forces and moment at the ﬁxed support at l
A, the forces at pin C and the force in link BD. 12ft Fig. P7.14 7.15 For the frame, illustrated in Fig. P7 .15, determine all the forces acting on member ABCDE. ‘
Also determine the internal force in member
AP. The attached weight W is 6.8 kN and
the pulley radius is 80 mm. The dimensions
in the ﬁgure are given in mm. Fig. P7.15 7.16 For the frame illustrated in Fig. P7.16, determine all the forces acting on member ABCDE.
Also determine the internal force in member AF. The attached weight W is 7.5 kN and the
pulley radius is 90 mm. The dimensions in the ﬁgure are given in mm. 258 — Chapter 7
Frames and Machines Fig. P7.16 7.17 For the arm of the backhoe, shown in Fig. P7.17, determine the force that must be exerted by
the hydraulic actuator AC to maintain the bucket loaded with a weight of 1.8 kN in
equilibrium. Also ﬁnd the forces in links BC and CE and the force acting on pin D. The bucket and the crosshatched appendage are welded together. Fig. 97.17 7.18 For the “Loadall” arm, presented in Fig. P7.18, determine the forces exerted by the hidden
actuator and the Visible actuator BC to maintain equilibrium. Also determine the forces acting
at pins A and D. The arm weighs 1.1 kN and its center of gravity is located 1.8 m to the right
of point A. All of the dimensions are given in meters. A HIDDEN B I, ACTUATOR M o Fig. P7.18 Statics — 259 7.19 Levers are well known machines used for either amplifying or attenuating forces. When used
in scales to weigh heavy objects, the levers are often arranged to compound the attenuation.
Such an arrangement is illustrated in Fig. P7.l9. If the pins are frictionless, show that the
relation between the known scale weight w and the unknown scale weight W is: (a+b+c+dX)(a+b+c)b
aec W=w Fig. P7.19 7.20 Select dimensions a through e if the scale, illustrated in Fig. P7.19, is to measure a weight W =
5.0 kN with a small sliding weight w = 10 N. The value of x = 100 mm is ﬁxed in this design
analysis. 7.21 The horizontal boom of the construction crane, shown in Fig. P721, is counter balanced with
a 18 kip weight that is centered at point B. A cable BF E anchored at points B and E supports
the horizontal boom. The cable is maintained at a constant tension over its length with a small
pulley located at point F. The horizontal boom is attached to the tower with a pin located at
point C. The crane is lifting a load W = 12 kip from a hoist located at point D. Determine all
of the forces acting on the horizontal boom, the cable tension, all of the reactions at point A
and the force acting on the pin 20 ft 30 ft 10 ﬁ ’
at pomt F. The welght of the boom is 6.0 kip and the weight of the tower member is 5.0 kip. ''' COUNTER
WEIGHT Fig. P7.21 ...
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 Force, Fig, FBD, toggle mechanism

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