Engineering Mechanics - Statics Episode 1 Part 9 pdf

⎝ ⎞⎟ ⎠ 2 + Determine the length b of the triangular load and its position a on the beam such that the equivalent resultant force is zero and the resultant couple moment is M clockwise...

⎝ ⎞⎟ ⎠

2 +

Determine the length b of the triangular load and its position a on the beam such that the

equivalent resultant force is zero and the resultant couple moment is M clockwise.

2 w 1 b a

2b

3 +

Replace the distributed loading by an equivalent resultant force and specify its location,

measured from point A.

⎛⎜

⎝ ⎞⎟ ⎠

2 +

⎛⎜

⎝ ⎞⎟ ⎠

2 +

The distribution of soil loading on the bottom of a building slab is shown Replace this loading

by an equivalent resultant force and specify its location, measured from point O.

Units Used:

⎝ ⎞⎟ ⎠

2 +

6F R

Problem 4-150

The beam is subjected to the distributed

loading Determine the length b of the

uniform load and its position a on the beam

such that the resultant force and couple

moment acting on the beam are zero.

⎝ ⎞⎟ ⎠ w 1 b a b

2 +

Replace the loading by an equivalent resultant force and specify its location on the beam,

measured from point B.

=

x

1 2

F R

( to the right of B )

Problem 4-152

Replace the distributed loading by an equivalent resultant force and specify where its line of action

intersects member AB, measured from A.

Given

Replace the distributed loading by an equivalent resultant force and specify where its line of

action intersects member BC, measured from C.

Units Used:

kN = 10 3 N

Determine the equivalent resultant force

and couple moment at point O.

Determine the equivalent resultant force acting on the bottom of the wing due to air pressure and

specify where it acts, measured from point A.

y g y p j y

alleviate this problem, an automobile seat restraint has been developed that provides additional

pressure contact with the cranium During dynamic tests the distribution of load on the cranium

has been plotted and shown to be parabolic Determine the equivalent resultant force and its

location, measured from point A.

Determine the coordinate direction angles of F, which is applied to the end A of the pipe

assembly, so that the moment of F about O is zero.

Determine the moment of the force F about

point O The force has coordinate direction

angles α, β, γ Express the result as a Cartesian

Replace the force at A by an equivalent resultant force and couple moment at point P Express

the results in Cartesian vector form.

Units Used:

− 0.6

A force F1 acts vertically downward on the Z-bracket Determine the moment of this force

about the bolt axis (z axis), which is directed at angle θ from the vertical.

The horizontal force F acts on the handle of the wrench What is the magnitude of the moment

of this force about the z axis?

− 0

M z = ( r OA × F v ) k M z = − 4.03 N m ⋅

Problem 4-169

The horizontal force F acts on the

handle of the wrench Determine the

moment of this force about point O.

Specify the coordinate direction

angles α , β , γ of the moment axis.

− 0

If the resultant couple moment of the three couples acting on the triangular block is to be zero,

determine the magnitudes of forces F and P.

Problem 5-1

Draw the free-body diagram of the sphere of weight W resting between the smooth inclined

planes Explain the significance of each force on the diagram.

NA, NB force of plane on sphere.

W force of gravity on sphere.

Problem 5-3

Draw the free-body diagram of the beam supported at A by a fixed support and at B by a roller.

Explain the significance of each force on the diagram.

Ax, Ay, MA effect of wall on beam.

NB force of roller on beam.

Draw the free-body diagram of the

C-bracket supported at A, B, and C by

rollers Explain the significance of each

forcce on the diagram.

NA , NB , NC force of rollers on beam.

Problem 5-6

Draw the free-body diagram of the smooth

rod of mass M which rests inside the

glass Explain the significance of each

force on the diagram.

Ax , Ay , NB force of glass on rod.

M(g) N force of gravity on rod.

Problem 5-7

Draw the free-body diagram of the “spanner wrench” subjected to the force F The support at

A can be considered a pin, and the surface of contact at B is smooth Explain the significance of

p p g each force on the diagram.

Draw the free-body diagram of the automobile, which is being towed at constant velocity up the

incline using the cable at C The automobile has a mass M and center of mass at G The tires are

free to roll Explain the significance of each force on the diagram.

NA, NB force of road on car.

F force of cable on car.

Mg force of gravity on car.

Problem 5-9

Draw the free-body diagram of the uniform bar, which has mass M and center of mass at G The

supports A, B, and C are smooth.

Draw the free-body diagram of the beam, which is pin-connected at A and rocker-supported at B.

T he sphere of weight W rests between the smooth

inclined planes Determine the reaactions at the

N A = 1 lb N B = 1 lb

Given

N B cos ( θ 1 − 90 deg ) − N A cos ( ) θ 2 = 0

N A sin ( ) θ 2 − N B sin ( θ 1 − 90 deg ) − W = 0

Problem 5-14

T he smooth rod of mass M rests inside the

glass Determine the reactions on the rod.

T he “spanner wrench” is subjected to the force F The support at A can be considered a pin,

and the surface of contact at B is smooth Determine the reactions on the spanner wrench.

T he automobile is being towed at constant velocity up the incline using the cable at C The

automobile has a mass M and center of mass at G The tires are free to roll Determine the

reactions on both wheels at A and B and the tension in the cable at C.

Units Used:

Mg = 10 3 kg kN = 10 3 N

The uniform bar has mass M and

center of mass at G The supports

A, B, and C are smooth Determine

the reactions at the points of contact

Determine the reactions at the pin A

and at the roller at B.

Given:

F = 500 N

M = 800 N m ⋅

a = 8 m

⎝ ⎞⎟ ⎠

When holding the stone of weight W in equilibrium, the humerus H, assumed to be smooth, exerts

normal forces FC and FA on the radius C and ulna A as shown Determine these forces and the

force FB that the biceps B exerts on the radius for equilibrium The stone has a center of mass at

G Neglect the weight of the arm.

F B W + F A

sin ( ) θ

=

F B = 36.2 lb +

→ Σ Fx = 0; F C − F B cos ( ) θ = 0

F C = F B cos ( ) θ

F C = 9.378 lb

Problem 5-22

The uniform door has a weight W and a center of gravity at G Determine the reactions at the

hinges if the hinge at A supports only a horizontal reaction on the door, whereas the hinge at B

exerts both horizontal and vertical reactions.

The ramp of a ship has weight W and center of gravity at G Determine the cable force in CD

needed to just start lifting the ramp, (i.e., so the reaction at B becomes zero) Also, determine the

horizontal and vertical components of force at the hinge (pin) at A.

A y = W − F CD cos ( ) θ A y = 31.2 lb

Problem 5-24

The drainpipe of mass M is held in the tines of the fork lift Determine the normal forces at A

and B as functions of the blade angle θ and plot the results of force (ordinate) versus θ (abscissa) for 0 ≤ θ ≤ 90 deg

While slowly walking, a man having a total mass M places all his weight on one foot Assuming

that the normal force NC of the ground acts on his foot at C, determine the resultant vertical

compressive force FB which the tibia T exerts on the astragalus B, and the vertical tension FA in

the achilles tendon A at the instant shown.

The platform assembly has weight W1 and center of gravity at G1 If it is intended to support a

maximum load W2 placed at point G2,,determine the smallest counterweight W that should be

placed at B in order to prevent the platform from tipping over.

Given:

W 1 = 250 lb a = 1 ft c = 1 ft e = 6 ft

W 2 = 400 lb b = 6 ft d = 8 ft f = 2 ft

Given: