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For a cantilever beam dM/dx = constant for its whole length. What is the shape of SF diagram for the beam?
- a)A rectangle
- b)A triangle
- c)A parabola
- d)A hyperbola
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
For a cantilever beam dM/dx =constant for its whole length. What is th...
Explanation:
The given information dM/dx = constant suggests that the bending moment diagram for the cantilever beam will be a linear function of x, i.e., a straight line.
To obtain the shape of the shear force diagram, we need to integrate the bending moment equation with respect to x.
We know that the shear force at any point is equal to the rate of change of bending moment at that point.
Therefore,
dM/dx = V
where V is the shear force.
Integrating this equation with respect to x, we get
M = Vx + C
where C is the constant of integration.
The shape of the shear force diagram can be obtained by differentiating the bending moment equation with respect to x.
dM/dx = V
Therefore,
dV/dx = d2M/dx2 = 0
i.e., the shear force is constant throughout the length of the beam.
Hence, the shape of the shear force diagram for the cantilever beam when dM/dx = constant for its whole length is a triangle.
This is because the shear force is constant and hence, the area under the shear force diagram will be a triangle.
In this case, the maximum shear force occurs at the free end of the beam and is equal to the bending moment at that point.
The given information dM/dx = constant suggests that the bending moment diagram for the cantilever beam will be a linear function of x, i.e., a straight line.
To obtain the shape of the shear force diagram, we need to integrate the bending moment equation with respect to x.
We know that the shear force at any point is equal to the rate of change of bending moment at that point.
Therefore,
dM/dx = V
where V is the shear force.
Integrating this equation with respect to x, we get
M = Vx + C
where C is the constant of integration.
The shape of the shear force diagram can be obtained by differentiating the bending moment equation with respect to x.
dM/dx = V
Therefore,
dV/dx = d2M/dx2 = 0
i.e., the shear force is constant throughout the length of the beam.
Hence, the shape of the shear force diagram for the cantilever beam when dM/dx = constant for its whole length is a triangle.
This is because the shear force is constant and hence, the area under the shear force diagram will be a triangle.
In this case, the maximum shear force occurs at the free end of the beam and is equal to the bending moment at that point.
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For a cantilever beam dM/dx =constant for its whole length. What is the shape of SF diagram for the beam?a)A rectangleb)A trianglec)A parabolad)A hyperbolaCorrect answer is option 'B'. Can you explain this answer?
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