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**Q.1 For a channel section subjected to a downward vertical shear force at its centroid, which one of the following represents the correct distribution of shear stress in flange and web? [2019 : 1 Mark, Set-ll](a)(b)(c)(d)Ans. **(C)

Shear flow distribution for channel.

**Q.2 Cross section of a built-up wooden beam as shown in figure (not drawn to scale) is subjected to a vertical shear force of 8 kN. The beam is symmetrical about the neutral axis (NA), shown, and the moment of inertia about N.A. is 1.5 x 10 ^{9} mm^{4}. Considering that the nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each of the nails at P will be subjected to the shear force of [2019 : 2 Marks, Set-I]** (A)

(a) 240 N

(b) 480 N

(c) 60 N

(d) 120 N

Ans.

Shear Flow,

Distance between two nails l = 60 mm

∴ S.F. resisted by each nail = q x l = 240 N

Given: D= 500 mm

⇒

⇒

= 1*10^{-6}

**Q.4 An 8 m long simply-supported elastic beam of rectangular cross-section (100 mm x 200 mm) is subjected to a uniformly distributed load of 10kN/m over its entire span. The maximum principal stress (in MPa, up to two decimal places) at a point located at the extreme compression edge of a cross-section and at 2 m from the support is ______ . [2018 : 2 Marks, Set-II] Solution:**

[Due to symmetry]

M

= 60 kNm

σ = My/I

Direct shear stress = 0

Principal stress,

So principal stress

= 90 N/mm

(a) 20.0 MPa

(b) 37.5 MPa

(c) 60.0 MPa

(d) 75.0 MPa

Ans.

⇒

= 37.5 x 10

BM

= 1.6875 x 10

⇒

where,

⇒

Radius,

= 249.95 m

Deflection = AA' = 250 - 249.95

= 0.05 m

δ

= 71.12N/mm

(a) strain profile is linear

(b) stress profile is linear

(c) both profiles are linear

(d) shear deformation is neglected

Ans.

Since, E ∝ δy

So, strain varies linearly.

Ans.

Point Palso lies at mid span, so shear force, V = 0

⇒ Shear stress, τ = 0

∴ State of stress of point Pwill be,

∴ State of stress of point Q will be,

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