Past Year Questions: Bending & Shear Stresses | Solid Mechanics - Mechanical Engineering PDF Download

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)
Solution:
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 10⁹ mm⁴. 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) 240 N
(b) 480 N
(c) 60 N
(d) 120 N
Ans. (A)
Solution:

Shear Flow,

Distance between two nails l = 60 mm
∴ S.F. resisted by each nail = q x l = 240 N

Q.3 For a given loading on a rectangular plain concrete beam with an overall depth of 500 mm, the compressive strain and tensile strain developed at the extreme fibers are of the same magnitude of 2.5 x 10^-4. The curvature in the beam cross-section (in m^-1, round off to 3 decimal places), is _______.    [2019 : 1 Mark, Set-I]
Solution:
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_A = (-10 x 2 x 1) + 40 x 2
= 60 kNm

σ = My/I

Direct shear stress = 0
Principal stress,

So principal stress
= 90 N/mm² = 90 MPa

Q.5 A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 10¹¹ N/m². The maximum bending stress at the fixed end of the cantilever is    [2018 : 2 Marks, Set-I]
(a) 20.0 MPa
(b) 37.5 MPa
(c) 60.0 MPa
(d) 75.0 MPa
Ans. (B)
Solution:



⇒
= 37.5 x 10⁶ N/m² = 37.5 MPa

Q.6 A 450 mm long plain concrete prism is subjected to the concentrated vertical loads as shown in the figure. Cross section of the prism is given as 150 mm x 150 mm. Considering linear stress distribution across the cross-section, the modulus of rupture (expressed in MPa) is ___ .    [2016 : 2 Marks, Set-II]

Solution:

BM_Q = 11.25 x 150
= 1.6875 x 10⁶ N-mm
⇒
where,
⇒

Q.7 A simply supported reinforced concrete beam of length 10 m sags while undergoing shrinkage. Assuming a uniform curvature of 0.004 m-¹ along the span, the maximum deflection (in m) of the beam at mid-span is ______ .    [2015 : 2 Marks, Set-II]
Solution: Method - I

Radius,

= 249.95 m
Deflection = AA' = 250 - 249.95
= 0.05 m
Method-ll




⇒
δ = 0.05 m
= 71.12N/mm²

Q.8 A symmetric l-section (with width of each flange = 50 mm, thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm²) in the web at its junction with the top flange _____ .    [2013 : 1 Mark]
Solution:



Q.9 The “Plane section remain plane” assumption in bending theory implies    [2013 : 1 Mark]
(a) strain profile is linear
(b) stress profile is linear
(c) both profiles are linear
(d) shear deformation is neglected
Ans. (A)
Solution:

Since, E ∝ δy
So, strain varies linearly.

Q.10 Consider a simply supported beam with a uniformly distributed load having a neutral axis (NA) as shown. For points P(on the neutral axis) and Q (at the bottom of the beam) the state of stress is best represented by which of the following pairs?    [2011 : 1 Mark]





Ans. (B)
Solution:

Point P: Point Plies on NA, hence bending stress is zero at point P.
Point Palso lies at mid span, so shear force, V = 0
⇒ Shear stress, τ = 0
∴ State of stress of point Pwill be,

Point Q: At point Q flexural stress is maximum and nature of which is tensile due to downward loading. Point Q lies at the extreme of beam, therefore, shear stress at point Q is zero.
∴ State of stress of point Q will be,