SSC JE Exam > SSC JE Questions > Slope at the supports of a simply supported b...
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Slope at the supports of a simply supported beam of effective span L with a central point loadW is given by
- a)WL2/8EI
- b)WL2/12EI
- c)WL2/16EI
- d)WL2/24EI
Correct answer is option 'C'. Can you explain this answer?
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Slope at the supports of a simply supported beam of effective span L w...
Explanation:
To find the slope at the supports of a simply supported beam with a central point load, we can use the formula for the deflection of a simply supported beam under a point load.
The formula for the deflection of a simply supported beam under a point load is given by:
δ = (W * L^2) / (8 * E * I)
Where:
- δ is the deflection at the center of the beam
- W is the point load applied at the center of the beam
- L is the effective span of the beam
- E is the modulus of elasticity of the material
- I is the moment of inertia of the beam cross-section
To find the slope at the supports, we need to differentiate the deflection equation with respect to x (the distance from the support). The slope is given by the first derivative of the deflection equation.
Steps:
1. Differentiate the deflection equation with respect to x:
dδ/dx = (d/dx) [(W * L^2) / (8 * E * I)]
2. Simplify the equation by taking the derivative of each term:
dδ/dx = (W * L^2) / (8 * E * I) * (d/dx) (1)
3. The derivative of a constant term is zero, so the equation simplifies to:
dδ/dx = (W * L^2) / (8 * E * I) * 0
4. The slope at the supports is zero, indicating that there is no change in the slope at the supports of the simply supported beam.
Therefore, the correct answer is option 'c) WL^2/16EI'. The slope at the supports of a simply supported beam with a central point load is zero.
To find the slope at the supports of a simply supported beam with a central point load, we can use the formula for the deflection of a simply supported beam under a point load.
The formula for the deflection of a simply supported beam under a point load is given by:
δ = (W * L^2) / (8 * E * I)
Where:
- δ is the deflection at the center of the beam
- W is the point load applied at the center of the beam
- L is the effective span of the beam
- E is the modulus of elasticity of the material
- I is the moment of inertia of the beam cross-section
To find the slope at the supports, we need to differentiate the deflection equation with respect to x (the distance from the support). The slope is given by the first derivative of the deflection equation.
Steps:
1. Differentiate the deflection equation with respect to x:
dδ/dx = (d/dx) [(W * L^2) / (8 * E * I)]
2. Simplify the equation by taking the derivative of each term:
dδ/dx = (W * L^2) / (8 * E * I) * (d/dx) (1)
3. The derivative of a constant term is zero, so the equation simplifies to:
dδ/dx = (W * L^2) / (8 * E * I) * 0
4. The slope at the supports is zero, indicating that there is no change in the slope at the supports of the simply supported beam.
Therefore, the correct answer is option 'c) WL^2/16EI'. The slope at the supports of a simply supported beam with a central point load is zero.
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Slope at the supports of a simply supported beam of effective span L with a central point loadW is given bya)WL2/8EIb)WL2/12EIc)WL2/16EId)WL2/24EICorrect answer is option 'C'. Can you explain this answer?
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