Curved Beam - VTU e-Learning
Curved Beam - VTU e-Learning
Curved Beam - VTU e-Learning
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Problem No. 4<br />
<strong>Curved</strong> bar of rectangular section 40x60mm and a mean radius of<br />
100mm is subjected to a bending moment of 2KN 2KN-m m tending to<br />
straighten the bar. Find the position of the Neutral axis and draw a<br />
diagram to show the variation of stress across the section.<br />
Solution<br />
Given data:<br />
b= 40mm h= 60mm<br />
rc=100mm Mb= = 2x10<br />
C1=C2= 30mm<br />
6 N-mm<br />
30mm<br />
rn=<br />
ro= rc+h/2=100+30=130 =130 =(r =(ri+c1+c2)<br />
ri= rc- h/2 = 100 - 30= 70mm (rc-c1)<br />
rn= 96.924mm<br />
Distance of neutral axis to centroidal axis<br />
e = rc - rn= 100-96.924<br />
=3.075mm<br />
Distance of neutral axis to inner radius<br />
ci= rn- ri = (c1-e) = 26.925mm<br />
Distance of neutral axis to outer radius<br />
co=c2+e= (ro-rn) = 33.075mm<br />
Area<br />
A= bxh = 40x60 = 2400 mm 2<br />
e) = 26.925mm<br />
) = 33.075mm<br />
Bending stress at the inner fiber σbi = =<br />
= 104.239 N/mm 2 (compressive)
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