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A simply supported beam of 10m span is carrying a load of 4.8kN at mid-span. If Young's modulus of elasticity (E) is 2 x 108 kN/m2 and moment of inertia (I) is 20 cm4 , then the maximum deflection will be
  • a)
    5.00 mm
  • b)
    2.50 mm
  • c)
    0.50 mm
  • d)
    0.25 mm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A simply supported beam of 10m span is carrying a load of 4.8kN at mi...
Maximum deflection (y) =
=
= 2.5mm
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A simply supported beam of 10m span is carrying a load of 4.8kN at mi...
Calculation of Maximum Deflection in a Simply Supported Beam

Given data:
- Span (L) = 10 m
- Load (W) = 4.8 kN
- Young's Modulus (E) = 2 x 108 kN/m2
- Moment of Inertia (I) = 20 cm4

1. Calculation of Reactions at Supports
The first step is to calculate the reactions at the supports of the beam. Since the beam is simply supported and carries a load at mid-span, the reactions will be equal and half of the load.

R1 = R2 = W/2 = 4.8/2 = 2.4 kN

2. Calculation of Maximum Bending Moment
The maximum bending moment occurs at mid-span where the load is applied. Therefore, the maximum bending moment can be calculated using the equation:

Mmax = WL/4 = 4.8 x 10/4 = 12 kNm

3. Calculation of Maximum Deflection
The maximum deflection can be calculated using the equation:

δmax = (5WL4)/(384EI)

where,
W = load
L = span
E = Young's modulus
I = moment of inertia

Converting I to m4:
I = 20 cm4 = 20 x 10-8 m4

Substituting the values:
δmax = (5 x 4.8 x 104)/(384 x 2 x 108 x 20 x 10-8)
δmax = 2.5 mm

Therefore, the maximum deflection of the simply supported beam carrying a load of 4.8 kN at mid-span is 2.5 mm. The correct answer is option B.
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