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A rectangular beam of 300×650mm overall depth is provided for simply support ed span of 6m subject ed to live load 25kn excludeding self weight.find out stress devloped in steel and concrete if modular ratio is 1. area of steel 5 bars of 25mm use wsm?
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A rectangular beam of 300×650mm overall depth is provided for simply s...
Given data:
- Overall depth of the rectangular beam: 300×650 mm
- Span: 6 m
- Live load: 25 kN
- Modular ratio: 1
- Area of steel: 5 bars of 25 mm

Step 1: Calculation of Moment of Inertia
The moment of inertia (I) is calculated using the formula:
I = (b × d^3) / 12
Where b is the breadth of the beam and d is the overall depth.

Given b = 300 mm and d = 650 mm, we can substitute the values in the formula to get the moment of inertia.
I = (300 × 650^3) / 12

Step 2: Calculation of Maximum Bending Moment
The maximum bending moment (M) can be calculated using the formula:
M = (w × l^2) / 8
Where w is the total load on the beam and l is the span.

The total load on the beam is the sum of the live load and the self-weight of the beam. Since the self-weight is not given, we need to assume an approximate value based on the density of concrete.

Assuming the self-weight of the beam is 25 kN/m, we can calculate the total load on the beam as:
Total load = Live load + Self-weight
Total load = 25 + (25 × 6)
Total load = 175 kN

Substituting the values of w = 175 kN and l = 6 m in the formula, we can calculate the maximum bending moment (M).

Step 3: Calculation of Modular Ratio
Given the modular ratio is 1, we can directly use this value in the calculations.

Step 4: Calculation of Stress in Steel and Concrete
The stress in concrete (σ_c) can be calculated using the formula:
σ_c = (M × y) / I_c
Where y is the distance of the steel reinforcement from the extreme compression fiber and I_c is the moment of inertia of the concrete section.

The stress in steel (σ_s) can be calculated using the formula:
σ_s = (M × y) / I_s
Where I_s is the moment of inertia of the steel reinforcement.

The values of M and I are already calculated in previous steps. The distance of steel reinforcement from the extreme compression fiber can be assumed as 50 mm (half the overall depth of the beam).

Substituting the values in the formulas, we can calculate the stress in steel and concrete.

Summary:
- The moment of inertia (I) is calculated using the formula I = (b × d^3) / 12.
- The maximum bending moment (M) is calculated using the formula M = (w × l^2) / 8.
- The stress in concrete (σ_c) is calculated using the formula σ_c = (M × y) / I_c.
- The stress in steel (σ_s) is calculated using the formula σ_s = (M × y) / I_s.

Please note that the actual self-weight of the beam should be considered for more accurate calculations. This answer assumes an approximate self-weight value.
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A rectangular beam of 300×650mm overall depth is provided for simply support ed span of 6m subject ed to live load 25kn excludeding self weight.find out stress devloped in steel and concrete if modular ratio is 1. area of steel 5 bars of 25mm use wsm?
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A rectangular beam of 300×650mm overall depth is provided for simply support ed span of 6m subject ed to live load 25kn excludeding self weight.find out stress devloped in steel and concrete if modular ratio is 1. area of steel 5 bars of 25mm use wsm? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A rectangular beam of 300×650mm overall depth is provided for simply support ed span of 6m subject ed to live load 25kn excludeding self weight.find out stress devloped in steel and concrete if modular ratio is 1. area of steel 5 bars of 25mm use wsm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular beam of 300×650mm overall depth is provided for simply support ed span of 6m subject ed to live load 25kn excludeding self weight.find out stress devloped in steel and concrete if modular ratio is 1. area of steel 5 bars of 25mm use wsm?.
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