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12

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a)
b)

02000ME202052001

Taking into account only the effect of normal stresses, determine the strain energy
of the simply supported beam AB for the loading shown in figure
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ompare bending stresses in a 50 ೫ 50 mm’ Square cross-section bar due to end
moments of 2083 N-m for (i) straight beam and (ii) curved beam of radius 250 mm
(along centroidal curve); moments causing the curve to close.

PART ட்‌
Answer any four full questions, each carries 10marks.
State and explain Maxwell’s reciprocal theorem

A structure has a vertical leg of length ‘L’ with the
bottom part held fixed. It has a semi-circular part

6٦

of radius ‘r’ as shown and applied by load P. Find

deflection at loaded end by Castigliano’s method. 3

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Consider effects due to bending moment alone.

Starting from first principles, demonstrate that the St. Venant’s warping function
(५) should obey the Laplace’s equation, V ५५ = 0.

Explain the principle of minimum potential energy

Using virtual work method, determine the displacement at the end of a cantilever
beam of length ' L’ subjected to a uniformly distributed load of w/L.

Using Prandtl’s stress function method derive the expression for (i) twist per unit
length, (ii) torsional rigidity and (iii) the resultant stress for elliptical cross section
under torsion.

Show that the equilibrium conditions for stresses in a membrane loaded due to
pressure (P) is analogous to the condition that Prandtl’s torsion stress function
should obey. Describe the experimental procedure of finding (i) stresses and (11)

torsional rigidity, using the membrane analogy.

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