Calculate the maximum deflection of a simply...
Calculate the maximum deflection of a simply supported beam if the maximum slope at A is 0.0075 radians and the distance of the centre of gravity of bending moment diagram to support A is 1.33 meters.
• a)
9.975 mm
• b)
9.5 mm
• c)
9.25 mm
• d)
9.785 mm
Correct answer is option 'A'. Can you explain this answer?
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Calculate the maximum deflection of a simply supported beam if the ma...
The deflection occurs at support A = A/EI = 0.0075 radians
Maximum deflection = Ax/EI = 0.0075 × 1.33
y = 9.975 mm.
Hence, the correct option is (A)
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Calculate the maximum deflection of a simply supported beam if the ma...
Maximum Deflection of a Simply Supported Beam:

Given:
Maximum slope at A (θ) = 0.0075 radians
Distance of the center of gravity of bending moment diagram to support A = 1.33 meters

To calculate the maximum deflection of a simply supported beam, we can use the following equation:

δ = (θ * L^2) / (8 * D)

where:
δ = maximum deflection
θ = maximum slope at A
L = distance between supports
D = flexural rigidity of the beam

In this case, the beam is simply supported, which means it is supported at both ends and has a fixed support at one end (A) and a roller support at the other end.

Now, let's solve the problem step by step.

Step 1: Calculate the distance between supports (L)
The distance between support A and the center of gravity of the bending moment diagram is given as 1.33 meters.

So, the distance between supports (L) = 2 * 1.33 meters = 2.66 meters

Step 2: Calculate the flexural rigidity of the beam (D)
The flexural rigidity of the beam depends on the material properties and the cross-sectional shape of the beam. It is represented by the product of the modulus of elasticity (E) and the moment of inertia (I) of the beam.

Since the cross-sectional shape and material properties are not given in the question, we cannot calculate the exact value of D. However, we can assume a value for D based on typical values for common materials.

Let's assume a value of D = 1,000,000 Nm^2 for the beam.

Step 3: Calculate the maximum deflection (δ)
Using the equation mentioned earlier:

δ = (θ * L^2) / (8 * D)

Substituting the given values:

δ = (0.0075 * (2.66)^2) / (8 * 1,000,000)
= 0.020006 Nm

Converting the deflection from Newton-meters to millimeters:

δ = 0.020006 * 1000
= 20.006 mm

So, the maximum deflection of the simply supported beam is approximately 20.006 mm.

Therefore, none of the given options (A, B, C, D) matches the correct answer.
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Calculate the maximum deflection of a simply supported beam if the maximum slope at A is 0.0075 radians and the distance of the centre of gravity of bending moment diagram to support A is 1.33 meters.a)9.975 mmb)9.5 mmc)9.25 mmd)9.785 mmCorrect answer is option 'A'. Can you explain this answer?
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