Two beams a square of side ‘a’ and one with rectangular sides ‘a’ in width and 2a in depth are compared. The ratio of moment of inertia of square to rectangular section is
A beam cross-section is used in two different orientations as shown in the figure given below.
σA = 2σB
The ratio of the curvature of the 3 loose beams. (b × d) placed one over the other to an integral beam (b × nd) is
R = Radius of curvature
The maximum compressive stress at the top of a beam was 1600kg/cm2 and the corresponding tensile stress at its bottom was 800 kg/cm2. If the depth of the beam was 15 cm the neutral axis from the top will be
Stress diagram By similar triangle
Xu = 10 cm
The width of the strongest beam of rectangular section that can be cut out of a cylindrical log of wood whose diameter is 30 cm would be (in cm)
A cantilever of constant depth carries a uniformly distributed load on the whole span. To make the maximum stress at all sections the same, the breadth of the section at a distance ‘x’ from the free end should proportional to
∴ The breadth is proportional to x2 .
A beam of T-section has I = 1000 cm4 and depth 10 cm. Flange of the section is in tension. If the maximum tensile stress is two times the maximum compressive stress, what is section modulus in compression?
= 150 cm3
For the configuration of loading shown in the given figure, the stress in fiber AB is given by
σAB = σbending (T) + σaxial(C)
A beam having rectangular cross section 200mm wide and 400mm deep is simply supported over a span of 5m. It is carrying a concentrated load of 10 kN at the centre of the span. The maximum bending stress developed at quarter span of the beam is
Moment at quarter span, M = 5 × 1.25 = 6.25 kNm
Maximum bending stress,
M = fZ
f = 1.172 N/mm2
Two beams of cross-section circular and square have the same length, same allowable bending stress and the same moment of resistance. The weight of the beam with circular section is K times that of the square section, where ‘K’ is
K = 1.118
For a rectangular section, keeping breadth ‘’b’’ constant, the depth ‘’d’’ for uniform strength beam will have relation with bending moment ‘’M’’ as
M = σb × Z
M = σb × bd2 / 6
M ∝ b
M ∝ d2
d ∝ √M
If a beam is cut in halves horizontally and the two halves are laid side by side, it can in comparison to the original beam carry
A hollow beam of square section with external dimensions of 50.0 mm and thickness 5.0 mm can sustain a stress of 100 MPa. Its capacity in flexure is
A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?
For a particular beam σy is constant
∴ MR ∝ Z
When beam is laid flat, then
∴ Moment capacity increases by 41.4%.
A T-section beam is simply supported and subjected to a uniform distributed load over its whole span. Maximum longitudinal stress in the beam occurs at
YBottom > YTop
Since the bottom fiber is farthest from the neutral axis. It will experience maximum longitudinal stress.
Y is the distance of fiber from the neutral axis.
The ratio of flexibility of ‘n’ loose beams (b × d) placed one over the other to the flexibility of one integral beam (nb × d) is
Hence, Flexibility ⍺EI
Hence the answer is (A).
A solid circular cross-section cantilever beam of diameter ϕ = 100 mm carries a shear force of 10 kN at the free end. The maximum shear stress is
A wooden beam of rectangular cross section 100mm × 200mm is formed by gluing two identical beams of square cross section. If the safe shear stress of the glue is 3 N⁄mm2, the safe shear strength
F = 40 × 103N
= 40 kN
The given figure (all dimensions are in mm) shows an I-section of the beam.
If a beam of rectangular cross-section is subject to a vertical shear force S, then how much shear force will be carried by the upper one third of the section?
Shear stress at EF is given by
Shear force carried by elementary strip of thickness ‘dy’
dF = τ × !rea of elementary strip