Beams of Uniform Strength

Q. A simply supported beam of span L carries a concentrated load W at its mid-span. If the width b of the beam is constant throughout the span, then, with permissible bending stress as $\sigma$, the depth of the beam at mid-span will be

1. $\frac{3WL}{2b\sigma }$
2. $\sqrt{\frac{3WL}{2b\sigma }}$
3. $\frac{6WL}{b\sigma }$
4. $\sqrt{\frac{6WL}{b\sigma }}$

Q. A rectangular timber beam is cut out of a cylindrical log of diameter D. The depth of the strongest timber beam will be

1. $\sqrt{\frac{1}{2}}D$
2. $\sqrt{\frac{2}{3}}D$
3. $\sqrt{\frac{5}{8}}D$
4. $\sqrt{\frac{3}{4}}D$

Q. A simply supported beam of span L carries a concentrated load W at mid-span. If the width 'b' of the beam is constant and its depth is varying throughout the span , then what should be its mid-span depth , when design stress is 'f' ?

1. $\sqrt{\frac{6WL}{bf}}$
2. $\frac{6WL}{bf}$
3. $\sqrt{\frac{3WL}{2bf}}$
4. $\frac{3WL}{2bf}$

Q. A simply supported beam of constant width and varying depth and uniform strength is subjected to a cental concentrated load. The depth of the beam ${}^{\prime }{d}_x^{\prime }$ at a distance 'x' from one of the supports is proportional to

1. $x^{1/2}$
2. $x^{1/3}$
3. x
4. $x^2$

Q. A cantilever of constant depth carries a uniformly distributed load on the whole span. To make the maximum stress at all sections the same, the breadth of the section at a distance x from the free end should proportional to

1. x
2. $\sqrt{x}$
3. $x^2$
4. $x^3$

Q. A simply supported beam of span L carries a point load W at midspan. The breadth 'b' of the beam along the entire span is constant. Given, f = permissible stress is bending, for a beam of uniform strength, the depth of the beam at any cross-section at a distance 'x' from the support would be

1. $\frac{6Wx}{fb}$
2. $\sqrt{\frac{6Wx}{fb}}$
3. $\frac{3Wx}{fb}$
4. $\sqrt{\frac{3Wx}{fb}}$

Q. A beam is made of two identical metal flats soldered together. What is the ratio of stiffness of this beam to the stiffness of a beam in which the two flats are not soldered and which acts independently?

1. 2
2. 4
3. 6
4. 8