Engineering Mechanics - Statics Episode 1 Part 8 docx

Engineering Mechanics - Statics Chapter 4Replace the loading on the frame by a single resultant force.. Replace the loading system acting onthe beam by an equivalent resultant force and

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⎝ ⎞⎟ ⎠

=

α β γ

Express the moment of the couple acting on the pipe in Cartesian vector form What is the magnitude

of the couple moment?

− 0

If the couple moment acting on the pipe has a magnitude M, determine the magnitude F of the

forces applied to the wrenches.

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Engineering Mechanics - Statics Chapter 4

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F v F

sin ( ) θ

cos ( ) θ

− 0

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d b

=

M O

0 0 480

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M P

0 0 921

Replace the force system by an equivalent

force and couple moment at point O.

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− 0

0 0 4.609

− 0

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− 0

0 0 5.476

− 0

=

M O

0 0 100

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− 0

0

a

− 0

=

M P

0 0 124

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− 0

0

d

− 0

=

M O

0 0 10.615

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− 0

b

−

d

− 0

=

M P

0 0 16.838

Replace the force system by a single force resultant and specify its point of application, measured

along the x axis from point O.

Given:

F 1 = 125 lb

F 2 = 350 lb

F 3 = 850 lb

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Replace the force system by a single force resultant and specify its point of application, measured

along the x axis from point P.

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The forces and couple moments which are exerted on the toe and heel plates of a snow ski are

Ft, Mt, and Fh, Mh, respectively Replace this system by an equivalent force and couple moment

acting at point O Express the results in Cartesian vector form.

The forces and couple moments which are exerted on the toe and heel plates of a snow ski are

Ft, Mt, and Fh, Mh, respectively Replace this system by an equivalent force and couple moment

Problem 4-110

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acting at point P Express the results in Cartesian vector form.

a + b

0 0

26

− 357.4 126.6

Replace the three forces acting on the shaft by a single resultant force Specify where the force

acts, measured from end B.

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− 0

a + b + c

0 0

− 0

x

− 0 0

Replace the three forces acting on the shaft by a single resultant force Specify where the force

acts, measured from end B.

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− 0

d

− 0 0

− 0

x

− 0 0

Replace the loading on the frame by a single resultant force Specify where its line of action

intersects member AB, measured from A.

F Rx = − F 4 F Rx = − 200 lb

F Ry = − F 1 − F 2 − F 3 F Ry = − 900 lb

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Replace the loading on the frame by a single resultant force Specify where the force acts ,

measured from end A.

Replace the loading on the frame by a single resultant force Specify where the force acts ,

measured from end B.

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Replace the loading system acting on

the beam by an equivalent resultant

force and couple moment at point O.

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θ = 30 deg

Solution:

F R F 1

0 1 0

− 0

Determine the magnitude and direction θ

of force F and its placement d on the

beam so that the loading system is

equivalent to a resultant force FR acting

vertically downward at point A and a

clockwise couple moment M.

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Determine the magnitude and direction θ of force F and its placement d on the beam so that the

loading system is equivalent to a resultant force FR acting vertically downward at point A and a

clockwise couple moment M.

Initial guesses: F = 1 kN θ = 30 deg d = 1 m

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intersects member AB, measured from A.

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intersects member CD, measured from end C.

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Replace the force system acting on the frame

by an equivalent resultant force and specify

where the resultant's line of action intersects

member AB, measured from point A.

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Replace the force system acting on the frame by an equivalent resultant force and specify where the

resultant's line of action intersects member BC, measured from point B.

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Replace the force and couple-moment system by an equivalent resultant force and couple

moment at point O Express the results in Cartesian vector form.

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− 20

8 6 8

moment at point P Express the results in Cartesian vector form.

− 20

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8 6 8

moment at point Q Express the results in Cartesian vector form.

− 20

8 6 8

− 20

The belt passing over the pulley is subjected to forces F1 and F2 F1 acts in the k − direction.

Replace these forces by an equivalent force and couple moment at point A Express the result in

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− sin ( ) θ

− 40

− 12

The belt passing over the pulley is subjected to forces F1 and F2 F1 acts in the k − direction.

Replace these forces by an equivalent force and couple moment at point A Express the result in

Cartesian vector form

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− sin ( ) θ

− 68.28

− 8.49

Replace this system by an equivalent resultant force and couple moment acting at O Express the

results in Cartesian vector form.

Given:

F 1 = 50 N

F 2 = 80 N

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0 0

15

− 225 0

Handle forces F1 and F2 are applied to the electric drill Replace this system by an equivalent

resultant force and couple moment acting at point O Express the results in Cartesian vector

− 10

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Solution:

6 1

− 14

1.3 3.3 0.45

A biomechanical model of the lumbar region of the human trunk is shown The forces acting in

the four muscle groups consist of FR for the rectus, FO for the oblique, FL for the lumbar

latissimus dorsi, and FE for the erector spinae These loadings are symmetric with respect to the

y - z plane Replace this system of parallel forces by an equivalent force and couple moment

acting at the spine, point O Express the results in Cartesian vector form.

The building slab is subjected to four parallel column loadings.Determine the equivalent resultant

force and specify its location (x, y) on the slab.

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The building slab is subjected to four parallel column loadings Determine the equivalent resultant

force and specify its location (x, y) on the slab.

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The pipe assembly is subjected to the action of a wrench at B and a couple at A Determine the

magnitude F of the couple forces so that the system can be simplified to a wrench acting at

point C.

Given:

a = 0.6 m

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The three forces acting on the block each have a magnitude F1 = F2 = F3 Replace this system

by a wrench and specify the point where the wrench intersects the z axis, measured from

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F 1v

F 1

b 2 + a 2

b a

− 0

Replace the three forces acting on the plate by a wrench Specify the magnitude of the force

and couple moment for the wrench and the point P(x, y) where its line of action intersects the

plate.

Units Used:

kN = 10 3 N

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b a

Replace the three forces acting on the

plate by a wrench Specify the magnitude

of the force and couple moment for the

wrench and the point P(y, z) where its

line of action intersects the plate.

Given:

F A = 80 lb a = 12 ft

F B = 60 lb b = 12 ft

F C = 40 lb

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The loading on the bookshelf is distributed as shown Determine the magnitude of the equivalent

resultant location, measured from point O.

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Replace the loading by an equivalent resultant force and couple moment acting at point A.

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Replace the loading by a single resultant force, and specify the location of the force on the beam

measured from point O.

The column is used to support the floor which exerts a force P on the top of the column.

The effect of soil pressure along its side is distributed as shown Replace this loading by an

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p g p g y equivalent resultant force and specify where it acts along the column, measured from its

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Problem 4-145

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

beam, measured from the pin at C.

The beam supports the distributed load caused by the sandbags Determine the resultant force

on the beam and specify its location measured from point A.

Tiêu đề	Statics Chapter 4
Trường học	Hanoi University of Science and Technology
Chuyên ngành	Engineering Mechanics
Thể loại	lecture notes

Định dạng
Số trang	40
Dung lượng	390,51 KB