Engineering Mechanics - Statics Episode 2 Part 6 pot

Determine the x,y, z components of reaction at B and the tension in member ED... If the pin at G will fail when the resultant force there is Fmax, determine the largest vertical force P

The three-member frame is connected at its ends using ball-and-socket joints Determine the x,

y, z components of reaction at B and the tension in member ED The force acting at D is F

Given:

F

135 200 180

d = 6 ft g = 2 ft

c = g + f

Solution:

AC and DE are two-force members.

Define some vectors

− 0

− 0

− 0

− 3.039 × 10 − 12

The four-member "A" frame is supported at A and E by smooth collars and at G by a pin All

the other joints are ball-and-sockets If the pin at G will fail when the resultant force there is

Fmax, determine the largest vertical force P that can be supported by the frame Also, what

are the x, y, z force components which member BD exerts on members EDC and ABC? The

collars at A and E and the pon at G only exert force components on the frame

g pp y

D and a pole that fits in a smooth snug circular hole at E Determine the x, y, z components of

reaction at E and the tension in cable AB.

d b

c + d b

The structure is subjected to the loadings shown.Member AB is supported by a ball-and-socket

at A and smooth collar at B Member CD is supported by a pin at C Determine the x, y, z

components of reaction at A and C.

MBx MBy

− 0 47.3 61.9

− 125

⎜⎝ ⎞⎟ ⎟⎠

350 1531

The mechanism consists of identical meshed gears A and B and arms which are fixed to the

gears The spring attached to the ends of the arms has an unstretched length δ and a stiffness

k If a torque M is applied to gear A, determine the angle θ through which each arm rotates.

The gears are each pinned to fixed supports at their centers.

FDF FCF sin + ( ) θ − F2 = 0

FDE

− cos ( ) θ − FEF = 0

− 13.13

− 9.37

− 3.13

− 12.50 15.62

− 9.37

The spring has an unstretched length δ Determine the angle θ for equilibrium if the uniform

links each have a mass mlink.

The spring has an unstretched length δ Determine the mass mlink of each uniform link if the

angle for equilibrium is θ

Given:

δ = 0.3 m

Determine the force in each member of the truss and

indicate whether the members are in tension or

Determine the force in each

member of the truss and state if

the members are in tension or

− 333 0 667 667 471 943

− 667

Determine the force in members AB, AD, and AC of the space truss and state if the members are

in tension or compression The force F is vertical.

− 0

Given FAB AB AB + FAC AC AC + FAD AD AD

0 0

− 2.474

Problem 7-1

The column is fixed to the floor and is subjected to the loads shown Determine the internal normal

force, shear force, and moment at points A and B.

Free body Diagram: The support reaction need not be computed in this case.

Internal Forces: Applying equations of equillibrium to the top segment sectioned through

The shaft is supported by smooth bearings at A and B and subjected to the torques shown.

Determine the internal torque at points C, D, and E.

Given:

M 1 = 400 N m ⋅

M 2 = 150 N m ⋅

The shaft is supported by a journal bearing at A and a thrust bearing at B Determine the normal

force, shear force, and moment at a section passing through (a) point C, which is just to the

right of the bearing at A, and (b) point D, which is just to the left of the force F2.

Determine the normal force, shear force, and moment at a section passing through point

C Assume the support at A can be approximated by a pin and B as a roller.

The beam AB will fail if the maximum internal moment at D reaches Mmax or the normal force in

member BC becomes Pmax Determine the largest load w it can support.

⎝ ⎞⎟ ⎠ a

Problem 7-12

The boom DF of the jib crane and the

column DE have a uniform weight density

γ If the hoist and load have weight W,

determine the normal force, shear force,

and moment in the crane at sections

passing through points A, B, and C Treat

the boom tip, beyond the hoist, as

Determine the normal force, shear force, and moment at a section passing through point D of

the two-member frame.

Determine the normal force, shear force, and moment acting at a section passing through point C.

Units Used: kip = 103lb

− ( a + b ) − F 2 ( a + b + c ) cos ( ) θ − F 3 cos ( ) θ ( a + b + c + d + e ) cos ( ) θ

F 3 sin ( ) θ f sin ( ) θ + B y2 ( a + b + c ) cos ( ) θ +

Determine the normal force, shear force, and moment acting at a section passing through point D.

Units Used: kip = 103lb

V D sin ( ) θ − N D cos ( ) θ − F 3 sin ( ) θ = 0

B y + V D cos ( ) θ + N D sin ( ) θ − F 3 cos ( ) θ = 0

− ( a + b ) − F 2 ( a + b + c ) cos ( ) θ − F 3 cos ( ) θ ( a + b + c + d + e ) cos ( ) θ

F 3 sin ( ) θ f sin ( ) θ + B y2 ( a + b + c ) cos ( ) θ