torque diagrams

8/11/2019 Torque Diagrams

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I nternal F orces

ENGR 221

March 17, 2003http://www.drshokuhi.com
http://www.drshokuhi.com/http://www.drshokuhi.com/


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What use are the I nternal L oads?

In terms of the grand scheme of things, why do weneed to find the internal loads?

Stresses are determined by the bendingmoment and shear stresses are determined

by the maximum shear force and the

maximum torsional moments. NOT ALL MAXIMUM FORCES OCCUR AT THSUPPORTS!


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General Solution Scheme

The general scheme for finding the internal set offorces is

a) Draw the free-body diagram

b) Determine the support reactions

c) Apply the equations of equilibrium

x y z

x y z

0 0 0

0 0 0

F F F

M M M


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Simplest form Solution Scheme

Axial Forces and Torque in bars and shafts

Internal force act along the axis

Torque acts along the axis of symmetry

From the internal forces we can obtain axialforce diagram and from the torques we canobtain a torque diagram along the axis ofsymmetry.


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F orce Diagrams

Force diagrams show the all of the internalforces acting in the member.

1) Axial Force Diagram

2) Torque Diagram

3) Shear Diagram4) Moment Diagram


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Example Axial L oad Problem

Determine the axial forces transmitted by transversecross sections in intervals AB, BC, and CD of the bar.

Draw an axial force diagram for the bar .


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Determine the axial forces at point A,

x A

A

80 kips 50 kips 10 kips

20 kips

F F

F


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Determine the axial forces at point B,

x BC

BC

50 kips 10 kips

60 kips

F F

F


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Determine the axial forces at point C,

x CD

CD

10 kips

10 kips

F F

F


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Draw the axial forcediagram, all of the

forces are in tension.


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Class Axial L oad Problem

Determine the axialforces transmitted by

transverse cross sectionsat points A, B, and C ofthe bar. Draw an axialforce diagram for the

bar .


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Torque

Torque is a moment acting about the central axis of the body. For a shaft

The double arrow represents the moment at a point

M

M


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Torque

Solve the torque using equilibrium to find all of themoments.

Cut a section at a transition point (torque is applied)and solve the internal moment at the point bring thesystem back to equilibrium and this is the torque at the

point.

Using this information to draw the torque diagram.


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Example Torque Problem

Determine the moment T from equilibrium.

10 k-ft 17 k-ft 60 k-ft 25 k-ft 12 k-ft

54 k-ft

M T

T


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Determine the moment at point moving from left tothe right at point A.

A

A

10 k-ft

10 k-ft

M M

M


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Determine the moment at point B.

B

B

10 k-ft 17 k-ft

7 k-ft

M M

M


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Determine the moment at point C

C

C

10 k-ft 17 k-ft 54 k-ft

47 k-ft

M M

M


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Determine the moment at point E

E

E

10 k-ft 17 k-ft 54 k-ft 60 k-ft 25 k-ft

12 k-ft

M M

M


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Class Torque Problem

For the steel shaft, determine the maximum torquetransmitted by any transverse cross section of the

shaft. Draw a torque diagram for the shaft .


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I nternal F orces and Bending

Moment Three internal force act in members frames and beams,axial load, F, shear force, V, and bending moment, M.

The axial load, F, is in either compression or tension andacts along the centroid of the member.

The shear force, V, acts perpendicular to the surface of the

cut or section.The bending moment, M, acts about the axis coming outof the surface.


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Moment Three internal force act in members frames and beams,axial load, F, shear force, V, and bending moment, M.


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Moment The bending moment, M.


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Moment The shear force, V.


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Example I nternal F orces in a

F rame Problem Determine the internal forces in member EFG at

point J .


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F rame Problem Draw the free body diagram

x x x

y y y

y y

D x

x

x

0

0 60 lb.

60 lb

0 2 ft. 60 lb 3 ft.

90 lb

90 lb

F D G

F D G

D G

M G

G

D


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F rame Problem Do a cut at point J and draw a free-body diagram anduse equilibrium.

x Jx

Jx

y Jy

Jy

J J

J

0 90 lb90 lb.

0 40 lb.

40 lb.

0 40 lb 1.5 ft.

60 lb-ft

F F

F

F F

F

M M

M


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Class I nternal F orces in a

F rame Problem Determine the internal forces in member BE at

point F.


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H omework (Due 3/24/03)

Problems:

8-1, 8-6, 8-10, 8-12, 8-14

torque diagrams

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