Unit 1 Engineering Physics

1.11. UNIFORM BENDING AND NONUNIFORM BENDING

l

Load

Pin

Load

a a

A B

C E D

F

Figure 1.28:Uniform bending - experimental set up

a a

l

A B

C E D

F

W W

W W

Figure 1.29: Uniform bending - forces acting on the neutral filament

Since for a given loadW, the values ofa,Y andIgare constants,Ris also a constant
so that the beam is bent uniformly into an arc of a circle of radiusRas shown in Figure
1.30.

Now,CD=landyis the elevation of the midpoint E of the beam so thaty=EF.
From Pythagoras theorem we have,

CE^2 =OC^2 ≠ OE^2. Or

A

l

2

B 2

=R^2 ≠(R≠y)^2 =2Ry≠y^2

That is,

A

l

2

B 2

=2Ry≠y^2

Since the radius of curvatureRis usually very large compared to the elevationy, the term
y^2 is negligible compared to 2 Ry.

)

A

l

2

B 2

¥ 2 Ry

Hence
1
R

=

8 y

l^2

(1.37)

Substituting for ( 1 /R)from(1.37) in equation (1.36), we arrive at:

Wa=YIg

(^38) y
l^2
4

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