Strength of Materials - Stresses in Beams

1. Section modulus(Z) of a beam is given by
(a) M/I
(b) σ/y
(c) I/y
(d) none of these

2. Section modulus has a unit
(a) mm³
(b) m³
(c) either (a) or (b)
(d) neither (a) nor (b)

3. Section modulus represents
(a) toughness of beam
(b) strength of beam
(c) weight of beam
(d) ductility of beam

4. Section modulus({Z_{xx}}) of rectangular beam section is
(a) \frac{1}{6}b{d^3}
(b) \frac{1}{6}b{d^2}
(c) \frac{1}{{12}}b{d^3}
(d) \frac{1}{{12}}b{d^2}
where b is breadth and d is depth.

5. Section modulus({Z_{xx}}) of a hollow rectangular section will be
(a) \frac{{B{D^3} - b{d^3}}}{6}
(b) {B{D^3} - b{d^3}}
(c) \frac{{B{D^3} - b{d^3}}}{{6D}}
(d) none of these
where external dimension is B x D and internal dimension is b x d.

6. {Z_{xx}} for circular section is
(a) \frac{{\pi {d^2}}}{{64}}  
(b) \frac{{\pi {d^3}}}{{32}}
(c) \frac{{\pi {d^2}}}{{32}}  
(d) none of these

7. A rectangular timber beam is cut out of a cylindrical log of diameter D. The depth of strongest timber beam will be
(a) \frac{1}{2}D  
(b) \frac{{\sqrt 2 }}{3}D
(c) \frac{{\sqrt 5 }}{8}D  
(d) \frac{{\sqrt 3 }}{4}D (IES 1998)

8. The maximum bending moment existing in a steel beam is 75 kNm, if a commercial section is to be selected, and the maximum working stress in tension or compression is 150 MPa, the required section modulus is
(a) 5 x 105 mm³
(b) 5 x 104 mm³
(c) 5 x 102 mm³
(d) none of these

9. A timber joist of 6 m span has to carry a load of 15 kN/metre. The depth of joist is twice the width. If maximum permissible stress is limited to 8 N/mm² then depth of joist will be
(a) 233 mm
(b) 466 mm
(c) 133 mm
(d) 266 mm

10. The ratio of moment carrying capacity of a circular beam of diameter D and square beam of size D is
(a) 𝜋/4
(b) 3𝜋/8
(c) 𝜋/3
(d) 3𝜋/16 (IES 1995)

Answers

    1. (a)    2. (c)    3. (b)    4. (b)    5. (c)
    6. (b)    7. (b)    8. (a)    9. (b)    10. (d)

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