Lec-6.Torsion and Sf Bm Compatibility Mode

8/12/2019 Lec-6.Torsion and Sf Bm Compatibility Mode

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Consider a bar to be rigidly attached at one end and twisted at the other endby a torque or twisting moment T equivalent to F d, which is appliedperpendicular to the axis of the bar, as shown in the figure. Such a bar issa o e n ors on.

TORSIONAL SHEARING STRESS,For a solid or hollow circular shaft subject to a twisting moment T, thetorsional shearing stress at a distance from the center of the shaft is

where J is the polar moment of inertia of the section and r is the outer radius.


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ANGLE OF TWIST

The angle through which the bar length L will twist iswhere T is the torque in Nmm, L is the length of shaft in mm, G is shearmodulus in MPa J is the olar moment of inertia in mm4 D and d are

diameter in mm, and r is the radius in mm.

POWER TRANSMITTED BY THE SHAFTA shaft rotating with a constant angular velocity(in radians per second)

is being acted by a twisting moment T. The power transmitted by the shaftis

where T is the torque in Nm, f is the number of revolutions per second,and P is the power in watts.


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304 A 3 4 . 15 . D . G = 12 106 .


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3 6 12 ? ? G = 83 G.


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A 14 . 18 5000 189 . I G = 12 106 , .


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A 2 240 . I 12 , .


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A 4.5 3 H

50 1 26 . C G = 83 G.


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15/16 .


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A F. 316.

D : = 83 , = 55 , 6. F , G = 83 G , G = 28 G.


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A 50

F. 311. G = 28 G, D A.


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A F. 316.D : = 83 , = 55 , 6. F , G = 83 G , G = 28 G


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A 3 . 2 . 2 . . . F , G = 6 106 , ,G = 12 106 .

8000 12 ?

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DEFIII F A BEA A

. A , .

. .


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I , . I , .

. I , 1, 2, ( = 0

;F = 0) , (3 2 = 1).


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( ), , , . .


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The vertical shear at C in the figure shown in previous section is taken aswhere R1 = R2 = wL/2

If we differentiate M with respect to x:

Thus, the rate of change of the bending moment with respect to x is equal tothe shearing force, or the slope of the moment diagram at the given point isthe shear at that point. Thus

Thus, the rate of change of the bending moment with respect to x is equal tothe shearing force, or the slope of the moment diagram at the given point isthe shear at that point.Differentiate V with respect to x givesThus, the rate of change of the shearing force with respect to x is equal to theload or the slope of the shear diagram at a given point equals the load atthat oint.


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:

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. 2, ( ) , .

, .

, .


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A . A .

A

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B F. 425.


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C F. 426.


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B F. 428.


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B F. 444


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B F. 446.


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F. 273

. A = 50 60F. C 120F. A = 6.5 106 /(F) 12.8 106 /(F) .

A F . 16.

D : = 83 , = 55 , 6. F , G = 83 G , G = 28 G.

B F. 417

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Lec-6.Torsion and Sf Bm Compatibility Mode