Engineering Mechanics Statics - Examples Part 10 ppsx

− 265− 637 Determine the normal force, shear force, and moment acting at a section passing through point C... Determine the largest vertical load P the frame will support and calculate t

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Engineering Mechanics - Statics Chapter 7

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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

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

the two-member frame.

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− 265

− 637

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

Units Used: kip = 103lb

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− ( 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

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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

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V C = − P V C = − kN 8

ΣMC = 0; − M C + P c = 0

M C = P c M C = 6 kN m ⋅

Problem 7-20

The cable will fail when subjected to a tension Tmax Determine the largest vertical load P the frame

will support and calculate the internal normal force, shear force, and moment at a section passing

through point C for this loading.

Units Used:

kN = 103N

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Problem 7-23

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

normal force, shear force, and moment at (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 F2 force.

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Problem 7-24

The jack AB is used to straighten the bent beam DE using the arrangement shown If the axial

compressive force in the jack is P, determine the internal moment developed at point C of the

top beam Neglect the weight of the beams.

The jack AB is used to straighten the bent

beam DE using the arrangement shown If

the axial compressive force in the jack is P,

determine the internal moment developed at

point C of the top beam Assume that each

beam has a uniform weight density γ

Units Used:

kip = 103lb

Given:

P = 5000 lb

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Determine the normal force, shear force, and moment in the beam at sections passing through

points D and E Point E is just to the right of the F load.

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=

B y = 6 kip +

→ Σ Fx = 0; N D = 0

1 2

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

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Problem 7-28

Determine the normal force, shear force, and moment at sections passing through points E and F.

Member BC is pinned at B and there is a smooth slot in it at C The pin at C is fixed to member CD.

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The bolt shank is subjected to a tension F Determine the internal normal force, shear force,

and moment at point C.

Determine the normal force, shear force, and moment acting at sections passing through points B

and C on the curved rod.

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M C = − M A − A x r sin ( ) φ + A y r ( 1 − cos ( ) φ ) M C = − 1.59 kip ft ⋅

Problem 7-31

The cantilevered rack is used to support each end of a smooth pipe that has total weight W.

Determine the normal force, shear force, and moment that act in the arm at its fixed support A along

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This problem requires V C = 0.

Summing forces vertically for the section, we have

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The semicircular arch is subjected to a uniform distributed load along its axis of w0 per unit length Determine the internal normal force, shear force, and moment in the arch at angle θ

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Determine the x, y, z components of internal loading at a section passing through point C in the pipe

assembly Neglect the weight of the pipe.

− 700.00

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M C = − r 1 × F 1 − r 2 × F 2 M C

1400.00 1200.00

− 750.00

Determine the x, y, z components of internal loading at a section passing through point C in the pipe

assembly Neglect the weight of the pipe.

− 200

− 500.00

− 260.00

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− 5

0 0

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− 116.00

− 65.60

− 0.00

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Determine the x, y, z components of internal loading in the rod at point E.

− 5

0 0

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− 116.00

− 65.60

− 26.80

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50510

Draw the shear and moment diagrams

for the beam in terms of the parameters

shown.

Given:

P = 800 lb a = 5 ft L = 12 ft

Solution:

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Problem 7-44

Draw the shear and moment diagrams for the beam (a) in terms of the parameters

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0 1 2 3 4 5 6 7 8 91

0.500.51

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The shear force is zero everywhere in the beam.

The moment is zero in the first third and the last third of the bam.

In the middle section of the beam the moment is M = M 0

Thus the beam will fail when M 0 = M max M 0 = 2.00 kN m ⋅

Problem 7-46

The shaft is supported by a thrust bearing at A and a journal bearing at B Draw the shear and

moment diagrams for the shaft in terms of the parameters shown.

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0 2 4 6 8 105000

05000

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w L

2 − w x − V = 0 V − x w w L

2 +

Draw the shear and moment

diagrams for the beam.

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0 1 2 3 4 50

510

for the beam.

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Problem 7-51

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0 5 10 15 200

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2000200

for the beam.

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Draw the shear and bending-moment

diagrams for beam ABC Note that

there is a pin at B.

Solution:

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Support Reactions: From FBD (b),

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The beam has depth a and is subjected to a uniform distributed loading w which acts at an

angle θ from the vertical as shown Determine the internal normal force, shear force, and

moment in the beam as a function of x Hint:The moment loading is to be determined from a

point along the centerline of the beam (x axis).

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ΣFy = 0; − V 1

2 x w x L

The beam will fail when the maximum shear force is Vmax or the maximum moment is Mmax.

Determine the largest intensity w of the distributed loading it will support.

Solution:

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The beam will fail when the maximum internal moment is Mmax Determine the position x of the

concentrated force P and its smallest magnitude that will cause failure.

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for the beam.

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A y w a

6

M C a

=

A y

2 w x a

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2001000100

Problem 7-60

The cantilevered beam is made of material having a specific weight γ Determine the shear and

moment in the beam as a function of x.

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=

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5000500

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4002000200

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− 2250.00

Determine the normal

force, shear force, and

moment in the curved rod

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The quarter circular rod lies in the horizontal

plane and supports a vertical force P at its

end Determine the magnitudes of the

components of the internal shear force,

moment, and torque acting in the rod as a

function of the angle θ

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200010000

Problem 7-66

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for the beam.

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Problem 7-68

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5051015

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0 0.5 1 1.5 2 2.5 3 3.5 44

202

for the beam.

−

=

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0 2 4 6 8 10 12200

1000100

Problem 7-71

=

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