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**Q.1 A simply supported beam is subjected to a uniformly distributed load. Which one of the following statements is true? [2017 : 1 Mark, Set-I](a) Maximum or minimum shear force occurs where the curvature is zero.(b) Maximum or minimum bending moment occurs where the shear force is zero.(c) Maximum or minimum bending moment occurs where the curvature is zero.(d) Maximum bending moment and maximum shear force occur at the same section.Ans.** (B)

Given that the modulus of elasticity, E is 2.5 x 10

(a) S

(b) S

(c) S

(d) S

Ans.

Hence correct option is (c).

**Q.3 A rigid member ACB is shown in the figure. The member is supported at A and B by pinned and guided roller supports, respectively. A force Pacts at Cas shown. Let R _{Ah} and R_{Bh} be the horizontal reactions at supports A and B, respectively, and R_{Av} be the vertical reaction at support A. Selfweight of the member may be ignored.** (D)

Which one of the following sets gives the correct magnitudes of R_{Av}, R_{Bh} and R_{Av}? [2016 : 2 Marks, Set-I]

Ans.

I. The slope of the bending moment diagram is equal to the shear force.

II. The slope of the shear force diagram is equal to the load intensity.

III. The slope of the curvature is equal to the fiexural rotation.

IV. The second derivative of the deflection is equal to the curvature.

The only FALSE statement is [2012 : 1 Mark]

(a) I

(b) II

(c) III

(d) IV

Ans.

We know that,

(a) The portion RS has a constant twisting moment with a value of 2WL.

(b) The portion QR has a varying twisting moment with a maximum value of WL.

(c) The portion PQ has a varying bending moment with a maximum value of WL.

(d) The portion PQ has no twisting moment,

Ans.

Bending moment at a distance x from P, M

Now moment WL will act as a twisting moment for the member QR. Portion QPhas varying BM with a maximum value of 2WL at R.

Now moment 2 Wl will act as a twisting moment for portion RS which is constant in nature.

(a) Zero

(b) M

(c) ML

(d) M/L

Ans.

Let the reaction at the right hand support be V

V

Thus, the reaction at the left hand support V

∴ Moment at the mid-span

Infact the bending moment through out the beam is zero.

(a) WL/8

(b) WL/16

(c) WL/32

(d) zero

Ans.

The plank will be balanced by the buoyant force acting under its bottom. Let the intensity of buoyant force be w.

For equilibrium, w x L = W + W

⇒

Thus, the bending moment at the centre of the plank will be,

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