1. If it is known that the center pin A supports one-half of the vertical

loading shown, determine the force in member BF.

DE

DF

BF

AF

I. Cut

Joint A AB AF

Ay=26 kN

DE

DF

BF

AF

Hy=13 kN

Hy=13 kN

I. Cut

2. Determine the forces acting in members DE, DI, JK,AJ.

J K

A

L

M

D C B

I

E F

G

H 20 kN

37o

4 m 4 m 4 m

3 m

3 m

6 m

3. Determine the force acting in member JI.

4 m

A B

D

C H G F

E

K J I L

N M P

4 m 4 m 4 m

3 m

3 m

3 m

20 kN

3 kN

5 kN

10 kN 5 kN

4 kN

3 kN

4. Determine the forces in members DE, EI, FI and HI.

Gx

Ay

I. Cut

Gy

II. Cut

5. Compute the force in link AB of the lifting tongs which cross without touching.

6. The design of a hoisting

mechanism for the dump truck is

shown in the enlarged view.

Determine the compression P in

the hydraulic cylinder BE and the

magnitude of the force supported

by the pin at A for the particular

position shown, where BA is

perpendicular to OAE and link DC

is perpendicular to AC. The dump

and its load together have a mass

of 9 Mg with center of gravity at G.

All dimensions for the indicated

geometry are given on the figure.

F

7. The pruning mechanism of a pole saw is shown as it cuts a branch S. For the

particular position drawn, the actuating cord is parallel to the pole and carries a

tension of 120 N. Determine the shearing force P applied to the branch by the cutter

and the total force supported by the pin at E. The force exerted by the light return

spring at C is small and may be neglected.

F Two-force member: CD

FBD of member EDF

8. A pneumatic cylinder pivoted at F operates the lever AB of the quick-acting toggle

clamp, which holds the workpiece in position while it is machined. For an air pressure of

400 kPa against the 50 mm diameter piston, determine the clamping force at G for the

position α=10o. For this position the piston rod is perpendicular to AB.

9. A small trailer-mounted dumper is shown. All connections are pinned and member EF is

horizontal. The hydraulic cylinder simultaneously tilts the dumper and opens the gate FG. The

pin at D can slide freely in the slot at the dumper and point E does not contact the dumper.

Determine the force supported by hydraulic cylinder AE. State whether it works in Tension /

Compression.

10. The mechanism in the figure is used to raise the bucket of a bulldozer. The bucket and its contents

weigh 10 kN and have a center of gravity at H. Arm ABCD has a weight of 2 kN and a center of gravity

at B, arm DEFG has a weight of 1 kN and a center of gravity at E. The weights of the hydraulic cylinders

can be neglected. Determine the forces in the hydraulic cylinders CJ, BF and EI and also determine all

the forces acting at arm DEFG.

Two-force members: CJ, BF, EI.

FBD of bucket

FEI

Gx

Gy

10 kN

( ) ( )

kNGGFkN.GFGFkN.Fcos.F.M

yyy

xEIxx

EIEIG

100100882008820302130100

==−⇒=

==−⇒===−⇒=

∑∑∑

FBD of hydraulic cylinder EI

FEI FEI I E

FBD of DEFG

( ) ( ) ( ) ( )

( )

( )

kN.DsinFDGFkN.DFcosFDGF

kN.F

sin.Gcos.Gsin.cosFcos.sinFsin.cos.FM

yBFyyy

xEIBFxxx

BF

y.

xBFBF.EI

D

617019108590190

4210

0308130813021713021713060130600

10882882

==−−+−⇒=

−==−−+⇒=

−=

=+++++−⇒=

∑∑

∑

30o

Gx Gy

1 kN

FEI

Dx

Dy

FBF

30o 30o

19o

G

F

E

D

D

B

F

( )( )oo ,

sin.

sin.

sin.

m.BFcos....BF

794160

591812159160218122181 222

==⇒==

=⇒−+=

βαβα

α

β

FBD of entire system

( ) ( ) ( ) ( )

kNAAFkNAAFF

kNFsin.sin.sin.sin.sin..sin.F

M

yyy

xxCJx

CJ

CJ

A

130101201800

180309023072306013072308130106081

0

==−−−⇒=

==+−⇒=

≅=++++++−

⇒=

∑∑

∑

Ax

10 kN

P=FCJ

Ay 1 kN

2 kN

11. The figure shows a special rig

designed to erect vertical sections of a

construction tower. The assembly A has

a weight of 15 kN and is elevated by the

platform B, which itself has a weight of

20 kN. The platform is guided up the

fixed vertical column by rollers and is

activated by the hydraulic cylinder CD

and links EDF and FH. For the

particular position shown, calculate the

force exerted by the hydraulic cylinder

at D and the magnitude of the force

supported by the pin at E.

15 kN

20 kN

15 kN

20 kN

FBD of HF

FHF

Two-force members: CD, HF.

(FHF) y=35 kN

(FHF) x

1.25 m

3 m

α

kN.F.F

.

FHFH

o

91637253335

61922

=⇒=

=α

E

FBD of EDF

1 m

3 m

kN.F,. FHo 9163761922 ==α

Ey

Ex

β

FHF α

FCD

β

0.75

m

D

C o.

.sin 4318

1631

=⇒= ββ

( ) ( ) ( ) ( )

kN.EcosFcosFEFkN.EsinFsinFEF

kN.F.sinFcosF.sinFcosFM

yCDFHyy

xCDFHxx

CDFHFHCDCD

E

742200833300

87600252375010

−==+−⇒=

−==++⇒=

==−+−−⇒=

∑∑

∑

βα

βα

ααββ

12. The lever AB is welded to the bent rod BCD which is supported by bearing E and cable

DG. Assuming that the bearing can exert an axial thrust and couples about axes parallel to

the x and z axes, determine the tension in cable DG and the reaction at E under the action

of the 220 N force. The mass of ABCD is neglected.

220 N

240 mm

60 mm

250 mm

225 mm

160 mm

120 mm

G D

C

E

B

y

z

x

A

13. The bent rod is supported by a ball-and-socket joint at O, a cable at B, and a

radial bearing at D. Neglecting the weight of the rod, calculate the tension in

the cable BE and the reactions at D and O. Assume that the radial bearing does

not support any moments.