Pure Bending · Strength of Materials · GATE ME

A beam is undergoing pure bending as shown in the figure. The stress (𝜎)-strain (𝜀) curve for the material is also given. The yield stress of the material is 𝜎𝑌. Which of the option(s) given represent(s) the bending stress distribution at cross-section AA after plastic yielding? 

Consider a beam with circular cross-section of diameter $$d.$$ The ratio of the second moment of area about the neutral axis to the section modulus of the area is

The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity $${{\rm I}_1}$$ while the circular cross-section has flexural rigidity $${{\rm I}_2}$$. Both sections have the same cross-sectional area. The ratio $${{\rm I}_1}$$/$${{\rm I}_2}$$ is

The beams, one having square cross section and another circular cross-section,are subjected to the same amount of bending moment. If the cross sectional area as well as the material of both the beams are the same then

A simply-supported beam of length $$3L$$ is subjected to the loading shown in the figure.

It is given that $$P = 1$$ $$N,$$ $$L = 1$$ $$m$$ and Young’s modulus $$E = 200$$ $$GP$$a. The cross-section is a square with dimension $$100$$ $$mm$$. The bending stress (in Pa) at the point A located at the top surface of the beam at a distance of $$1.5L$$ from the left end is _____________ .

(Indicate compressive stress by a negative sign and tensile stress by a positive sign).

For the component loaded with a force $$F$$ as shown in the figure, the axial stress at the corner point $$P$$ is

A simply supported beam of span length $$6$$m and $$75$$ mm diameter carries a udl of $$1.5$$ kN/m

What is the maximum value of bending moment?

A simply supported beam of span length $$6$$m and $$75$$ mm diameter carries a udl of $$1.5$$ kN/m

What is the maximum value of bending stress?

A mass less beam has a loading pattern as shown in figure. The beam is rectangular cross-section with a width of 30 mm and height of 100 mm.

The maximum magnitude of bending stress (in MPa) is given by

A cantilever beam has the square cross section of 10 mm $$ \times $$ 10 mm. It carries a transverse load of 10 N. Considering only the bottom fibres of the beam, the correct representation of the longitudinal variation of the bending stress is

A mass less beam has a loading pattern as shown in figure. The beam is rectangular cross-section with a width of 30 mm and height of 100 mm.

The maximum bending moment occurs at

A tapered cantilever beam of constant thickness is loaded as shown in the sketch below. The bending stress will be:

A 6 metre long supported wooden beam of rectangular section 10 cm $$ \times $$ 20 cm deep is strengthened by mild steel plates 0.5 cm $$ \times $$ 10 cm wide at the top and bottom fibre over the entire length. Find the minimum supportable uniformly distributed load considering failures in steel and wood due to flexure. Weakening of wood due to screws and weakening of the steel plates due to drilled holes may be ignored.
Permissible tensile stress for steel = 156.8 N/mm²
Permissible tensile stress for steel = 14.89 N/mm²
Young's modulus of mild steel = 1.96 $$ \times $$ 10⁵ N/mm²
Young's modulus of wood = 0.117 $$ \times $$ 10⁵ N/mm²