The neutral axis of the cross-section a beam is that axis at which the bending stress is
σb ∝ y
y → Linear distance from neutral axis. Thus, bending stress is zero at neutral axis and maximum at outermost fibres.
The intensity of bending stress in the cross section at any point distance y from the neutral axis is proportional to (l is moment of inertia)
f ∝ y
The bending stress calculated by using the formula M = fz is absolutely accurate when the bending moment
1. Variation is linear
2. Variation is parabolic (2nd degree)
3. Is constant
4. None of the above
A beam of uniform cross-section is subjected throughout its length to a uniform moment. Then the deflection shape of beam is
If E = elasticity modulus, I = moment of inertia about the neutral axis and M = bending moment in pure bending under the symmetric loading of a beam , the radius of curvature of the beam
1. increases with E
2. increases with M
3. Decreases with I
4. Decreases with M
Which of these are correct?
R increases with E R decrease with M Statement 1 and 4 are correct.
A mild steel beam is simply supported. It has a constant moment of inertia = 106 mm4. The entire length of the beam is subjected to a constant BM of 107 Nmm. E = 2 × 105 N/mm2. What is the radius curvature of the bent beam in meters?
A rectangular bar of width b and depth ‘d’ is being used as a cantilever. The loading in a plane parallel to the side b. the section modulus is
Section modulus, Z
A beam is said to be uniform strength if
A rectangular section beam subjected to a bending moment M varying along its length is required to develop the same maximum bending stress at any cross-section. If the depth of the section is constant, then its width will vary as
Where, σ is the maximum bending stress at any cross-section throughout its length. If depth is also constant then b ∝ M
Wire of diameter ‘d’ is wound round a cylinder. The diameter of the cylinder is ‘D’. The bending stress (maximum) induced in the wire is
For a rectangular section beam, if the beam depth is doubled, keeping the width, length and loading same, the bending stress is decreased by a factor
The ratio of width to depth of a strongest beam that can be cut out of a cylindrical log of wood is
D2 = b2 + t2 t2
= (D2 − b2) We have,
Stronger beam will have higher Z.
ow, t2 = D2 − b2
In a beam of circular cross-section, the shear stress variation due to shear force across a cross-section is
Where V is shear force at section A is area of cross section.
In a beam of solid circular cross-section, what is the ratio of maximum shear stress to the average shear stress?
What is the nature of distribution of shear stress in a rectangular beam?
A simply supported beam of rectangular cross-section is under transverse loading. Regarding the shear stress distribution across any section, the ratio of maximum shear stress to mean shear stress is
In case of a beam of I-section subjected to transverse shear force ‘F’, the maximum shear stress occurs the
The distribution of shear stress of a beam is shown in the given figure.
The cross-section of the beam is
The shear stress distribution over a beam cross-section is shown in the figure below. The beam is of
A cantilever is loaded by a concentrated load P at the free end as shown. The shear stress in the element LMNOPQRS is under consideration. This of the following figure represents the shear stress directions cantilever?
The direction of shear stress will be as shown in option (A).