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A beam of uniform cross-section is subjected throughout its length to a uniform moment. Then the deflection shape of beam is
- a)Catenary
- b)A third degree parabola
- c)A circular arc
- d)4th degree parabola
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A beam of uniform cross-section is subjected throughout its length to...
The correct answer is option 'C': A circular arc.
Explanation:
- The deflection shape of a beam subjected to a uniform moment throughout its length is a circular arc.
- When a beam is subjected to a uniform moment, the resulting deflection shape is symmetric about the midpoint of the beam.
- The circular arc shape occurs because the beam is under pure bending, where the fibers on the convex side experience tension and the fibers on the concave side experience compression.
- The tension in the convex side and compression in the concave side cause the beam to bend in a circular arc shape.
- This circular arc shape is characteristic of beams subjected to pure bending, where the bending moment is constant along the beam's length.
- The maximum deflection occurs at the midpoint of the beam, where the curvature is highest.
- As we move away from the midpoint towards the supports, the curvature decreases and the deflection reduces.
- The deflection shape can be mathematically described using the equation of a circular arc.
- The equation for the deflection shape of a beam under pure bending is given by:
y = (M / EI) * (x^2 / 2)
Where y is the deflection at a point along the beam, M is the moment, E is the modulus of elasticity, and I is the moment of inertia of the beam's cross-section.
- This equation represents a third-degree parabola, as the deflection is proportional to the square of the distance from the midpoint.
- Therefore, the correct answer is option 'C': A circular arc, which corresponds to a third-degree parabola.
Explanation:
- The deflection shape of a beam subjected to a uniform moment throughout its length is a circular arc.
- When a beam is subjected to a uniform moment, the resulting deflection shape is symmetric about the midpoint of the beam.
- The circular arc shape occurs because the beam is under pure bending, where the fibers on the convex side experience tension and the fibers on the concave side experience compression.
- The tension in the convex side and compression in the concave side cause the beam to bend in a circular arc shape.
- This circular arc shape is characteristic of beams subjected to pure bending, where the bending moment is constant along the beam's length.
- The maximum deflection occurs at the midpoint of the beam, where the curvature is highest.
- As we move away from the midpoint towards the supports, the curvature decreases and the deflection reduces.
- The deflection shape can be mathematically described using the equation of a circular arc.
- The equation for the deflection shape of a beam under pure bending is given by:
y = (M / EI) * (x^2 / 2)
Where y is the deflection at a point along the beam, M is the moment, E is the modulus of elasticity, and I is the moment of inertia of the beam's cross-section.
- This equation represents a third-degree parabola, as the deflection is proportional to the square of the distance from the midpoint.
- Therefore, the correct answer is option 'C': A circular arc, which corresponds to a third-degree parabola.
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A beam of uniform cross-section is subjected throughout its length to a uniform moment. Then the deflection shape of beam isa)Catenaryb) A third degree parabolac) A circular arcd) 4th degree parabolaCorrect answer is option 'C'. Can you explain this answer?
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