Shear Force and Bending Moment · Strength of Materials Or Solid Mechanics · GATE CE

In the frame shown in the figure (not to scale), all four members (AB, BC, CD, and AD) have the same length and same constant flexural rigidity. All the joints A, B, C, and D are rigid joints. The midpoints of AB, BC, CD, and AD, are denoted by E, F, G, and H, respectively. The frame is in unstable equilibrium under the shown forces of magnitude 𝑃 acting at E and G. Which of the following statements is/are TRUE?

Consider a simply supported beam PQ as shown in the figure. A truck having 100 kN on the front axle and 200 kN on the rear axle, moves from left to right. The spacing between the axles is 3 m. The maximum bending moment at point R is _________ kNm. (in integer)

A simply supported beam is subjected to a uniformly distributed load. Which one of the following statements is true?

The following statements are related to bending of beams:

$${\rm I}.$$ The slope of the bending moment diagram is equal to the shear force.
$${\rm II}.$$ The slope of the shear force diagram is equal to the load intensity.
$${\rm III}.$$ The slope of the curvature is equal to the flexural rotation.
$${\rm IV}.$$ The second derivative of the deflection is equal to the curvature.

The only FALSE statements is

A curved number with a straight vertical leg is carrying a vertical load at $$Z,$$ as shown in the figure. The stress resultants in the $$XY$$ segment are. Bending movement, shear force and axial force

A cantilever beam curved in plan and subjected to lateral loads will develop at any section

A beams having a double cantilever attached at mid span is showing in the figure. The nature of forces in beam $$'ab'$$ is

A beam is subjected to a system of coplanar forces as shown in the figure. The magnitude of vertical reaction at Support P is ______ N (round off to one decimal place). 

Consider the beam shown in the figure (not to scale), on a hinge support at end A and a roller support at end B. The beam has a constant flexural rigidity, and is subjected to the external moments of magnitude M at one-third spans, as shown in the figure. Which of the following statements is/are TRUE?

Consider the three prismatic beams with the clamped supports $$P,Q$$ and $$R$$ as shown in the figures.

Given that the modulus of elasticity, $$E$$ is $$2.5 \times {10^4}\,\,MPa;$$ and the moment of inertia, $${\rm I}$$ is $$8 \times {10^3}\,\,m{m^4},$$ the correct comparison of the magnitudes of the shear force $$S$$ and the bending moment $$M$$ developed at the supports is

The values of axial stress $$\left( \sigma \right)$$ in $$kN/{m^2},$$ bending moment $$(M)$$ in $$kNm,$$ and shear force $$(V)$$ in $$kN$$ acting at point $$P$$ for the arrangement shown in the figure are respectively.

A uniform beam weighing $$1800$$ $$N$$ is supported at $$E$$ and $$F$$ by cable $$ABCD$$. Determine the tension (in $$N$$) in segment $$AB$$ of this cable (correct to $$1$$-decimal place). Assume the cables $$ABCD$$, $$BE$$ and $$CF$$ to be weightless ________

Two people weighing W each are sitting on a plank of length $$L$$ floating on water at $$L/4$$ from either end. Neglecting the weight of the plank, the bending moment at the center of the plank is

For the simply supported beam of length $$L,$$ subjected to a uniformly distributed moment $$(M)$$ $$kN$$-$$m$$ per unit length as shown in the figure, the bending moment (in $$kN$$-$$m$$) at the mid-span of the beam is

Match List- $${\rm I}$$ (Shear Force Diagrams) beams with List- $${\rm II}$$ (Diagram of beams with supports and loading) and select the correct answer by using the codes given below the lists:

A simply supported beam $$AB$$ has the bending moment diagram as shown in the following figure :

The beam is possibly under the action of following loads

The bending Moment diagram for a beam is given below:

The shear force at sections $$aa'$$ and $$bb'$$ respectively are of the magnitude

A three-span continuous beam has an internal hinge at $$B.$$ Section $$B$$ is at the mid-span of $$A.C.$$ Section $$E$$ is at the mid-span of $$CG$$. The $$20$$ $$kN$$ load is applied at section $$B$$ whereas $$10$$ $$kN$$ loads are applied at sections $$D$$ and $$F$$ as shown in the figure. Span $$GH$$ is subjected to uniformly distributed load of magnitude $$5$$ $$kN/m$$. For the loading shown, shear force immediate to the right of section $$E$$ is $$9.84$$ $$kN$$ upwards and the sagging moment at section $$E$$ is $$10.31$$ $$kN$$-$$m.$$

The vertical reaction at support $$H$$ is

A three-span continuous beam has an internal hinge at $$B.$$ Section $$B$$ is at the mid-span of $$A.C.$$ Section $$E$$ is at the mid-span of $$CG$$. The $$20$$ $$kN$$ load is applied at section $$B$$ whereas $$10$$ $$kN$$ loads are applied at sections $$D$$ and $$F$$ as shown in the figure. Span $$GH$$ is subjected to uniformly distributed load of magnitude $$5$$ $$kN/m$$. For the loading shown, shear force immediate to the right of section $$E$$ is $$9.84$$ $$kN$$ upwards and the sagging moment at section $$E$$ is $$10.31$$ $$kN$$-$$m.$$

The magnitude of the shear force immediate to the left and immediate to the right of section $$B$$ are, respectively

List - $${\rm I}$$ shows different loads acting on a beam and list - $${\rm II}$$ shows different bending moment distributions. Match the load with the corresponding bending moment diagram.

For the loading given in the figure below, two statements ( $${\rm I}$$ and $${\rm II}$$ ) are made.

$${\rm I}.$$ $$\,\,\,\,\,\,\,\,\,$$Member $$AB$$ carries shear force and bending moment
$${\rm II}.$$ $$\,\,\,\,\,\,\,$$Member $$BC$$ carries axial load and shear force

Which of the following is true ?

A frame $$ABCD$$ is supported by a roller at $$A$$ and is on a hinge at $$C$$ as shown below:

The reaction at the roller end $$A$$ is given by