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If the deflection at the free end of a cantilever beam of span 1 m, subjected UDL over entire span is 15 mm, then the slope at the free end is ________
  • a)
    0.02 radians
  • b)
    0.03 radians
  • c)
    0.04 radians
  • d)
    0.06 radians
Correct answer is option 'A'. Can you explain this answer?
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If the deflection at the free end of a cantilever beam of span 1 m, su...
Deflection at the free end of a cantilever beam subjected to udl,
Slope at free end subjected to udl, 
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If the deflection at the free end of a cantilever beam of span 1 m, su...
To find the slope at the free end of a cantilever beam under a uniformly distributed load (UDL) over the entire span, we can use the formula for deflection of a cantilever beam:

δ = (wL^4) / (8EI)

Where:
δ = deflection at the free end
w = UDL (uniformly distributed load)
L = span of the beam
E = modulus of elasticity of the beam material
I = moment of inertia of the beam cross-section

In this case, the deflection at the free end is given as 15 mm, the span is 1 m, and the UDL is not given. We need to find the slope at the free end, which is the rate of change of the deflection with respect to the length of the beam.

Let's assume the UDL is w kN/m. We can rearrange the formula to solve for the UDL:

w = (8EIδ) / (L^4)

Now we can substitute the given values into the equation:

w = (8 * E * I * 15 * 10^-3) / (1^4)

To simplify the equation, we need to know the values of E and I for the specific beam material and cross-section. Let's assume E = 200 GPa and I = 10^-6 m^4.

w = (8 * 200 * 10^9 * 10^-6 * 15 * 10^-3) / 1

w = 2.4 kN/m

Now that we have the UDL, we can find the slope at the free end using the equation for slope of a cantilever beam:

θ = (wL^3) / (6EI)

θ = (2.4 * 1^3) / (6 * 200 * 10^9 * 10^-6)

θ = 0.02 radians

Therefore, the slope at the free end of the cantilever beam is 0.02 radians, which corresponds to option A.
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If the deflection at the free end of a cantilever beam of span 1 m, subjected UDL over entire span is 15 mm, then the slope at the free end is ________a)0.02 radiansb)0.03 radiansc)0.04 radiansd)0.06 radiansCorrect answer is option 'A'. Can you explain this answer?
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