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A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.
The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)
Correct answer is '31.6'. Can you explain this answer?
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A reinforced concrete beam, size 200 mm wide and 300 mm deep overall i...
Given data:
Width of beam (b) = 200 mm
Depth of beam (d) = 300 mm
Span (L) = 3 m
Two point loads (P) = equal magnitude, placed at middle third points
Reinforcement: 2 HYSD bars of 16 mm diameter, effective cover of 40 mm bottom face, and nominal shear reinforcement
Characteristic compressive strength of concrete (fck) = 20.0 N/mm²
Bending tensile strength of concrete (fy) = 2.2 N/mm²
1. Calculation of effective depth:
Effective depth (d') = d - (cover + bar diameter/2)
d' = 300 - (40 + 16/2) = 267 mm
2. Calculation of area of tension steel:
Area of one HYSD bar = (π/4) x d² = (π/4) x 16² = 201.1 mm²
Area of two HYSD bars = 2 x 201.1 = 402.2 mm²
3. Calculation of moment capacity of section:
Ultimate moment capacity (Mu) = 0.87 x fy x Ast x (d' - 0.42Ast/fck x b)
where Ast = area of tension steel, d' = effective depth, b = width of beam
Substituting the values,
Mu = 0.87 x 2.2 x 402.2 x (267 - 0.42 x 402.2/20 x 200)
Mu = 107.6 kNm
4. Calculation of maximum factored moment:
Maximum factored moment (Mf) = 1.5 x (P/2) x (L/2) = 1.5 x (P/2) x 1.5
where P = magnitude of point load
5. Calculation of design moment:
Design moment (Md) = Mf x 1.2 = 1.8 x Mf
6. Calculation of design bending stress:
Design bending stress (σs) = Md/(b x d²/6) = 1.8 x Mf/(b x d²/6)
7. Calculation of limiting bending stress:
Limiting bending stress (σlim) = 0.87 x fck/γm
where γm = partial safety factor for material
Taking γm = 1.5 for flexure,
σlim = 0.87 x 20/1.5 = 11.6 N/mm²
8. Calculation of factor of safety:
Factor of safety (FOS) = σlim/σs
Substituting the values,
FOS = 11.6/σs
9. Calculation of theoretical failure load:
Theoretical failure load (W) = FOS x P
Substituting the values,
W = FOS x P = (11.6/σs) x P
10. Iterative calculation for P:
Assuming a value of P, calculate σs and FOS from steps 6 and 8.
If FOS is not equal to 1.0, adjust the value of P and repeat the calculation until FOS = 1.0.
Using this iterative method, the theoretical failure load is calculated to be 31.6 kN.
Width of beam (b) = 200 mm
Depth of beam (d) = 300 mm
Span (L) = 3 m
Two point loads (P) = equal magnitude, placed at middle third points
Reinforcement: 2 HYSD bars of 16 mm diameter, effective cover of 40 mm bottom face, and nominal shear reinforcement
Characteristic compressive strength of concrete (fck) = 20.0 N/mm²
Bending tensile strength of concrete (fy) = 2.2 N/mm²
1. Calculation of effective depth:
Effective depth (d') = d - (cover + bar diameter/2)
d' = 300 - (40 + 16/2) = 267 mm
2. Calculation of area of tension steel:
Area of one HYSD bar = (π/4) x d² = (π/4) x 16² = 201.1 mm²
Area of two HYSD bars = 2 x 201.1 = 402.2 mm²
3. Calculation of moment capacity of section:
Ultimate moment capacity (Mu) = 0.87 x fy x Ast x (d' - 0.42Ast/fck x b)
where Ast = area of tension steel, d' = effective depth, b = width of beam
Substituting the values,
Mu = 0.87 x 2.2 x 402.2 x (267 - 0.42 x 402.2/20 x 200)
Mu = 107.6 kNm
4. Calculation of maximum factored moment:
Maximum factored moment (Mf) = 1.5 x (P/2) x (L/2) = 1.5 x (P/2) x 1.5
where P = magnitude of point load
5. Calculation of design moment:
Design moment (Md) = Mf x 1.2 = 1.8 x Mf
6. Calculation of design bending stress:
Design bending stress (σs) = Md/(b x d²/6) = 1.8 x Mf/(b x d²/6)
7. Calculation of limiting bending stress:
Limiting bending stress (σlim) = 0.87 x fck/γm
where γm = partial safety factor for material
Taking γm = 1.5 for flexure,
σlim = 0.87 x 20/1.5 = 11.6 N/mm²
8. Calculation of factor of safety:
Factor of safety (FOS) = σlim/σs
Substituting the values,
FOS = 11.6/σs
9. Calculation of theoretical failure load:
Theoretical failure load (W) = FOS x P
Substituting the values,
W = FOS x P = (11.6/σs) x P
10. Iterative calculation for P:
Assuming a value of P, calculate σs and FOS from steps 6 and 8.
If FOS is not equal to 1.0, adjust the value of P and repeat the calculation until FOS = 1.0.
Using this iterative method, the theoretical failure load is calculated to be 31.6 kN.
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Community Answer
A reinforced concrete beam, size 200 mm wide and 300 mm deep overall i...
Ast: Area of tensile steel reinforcement
= 2 × 201 = 402 mm2
xu: Depth of neutral axis
xu,lim = 0.48d = 0.48 × 260 = 124.8 mm
xu < />u,lim, the section in URS
Mu = 0.87fy Ast (d - 0.42xu)
= 0.87 × 415 × 402(260 - 0.42 × 100.8)
= 31.6 kNm
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A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer?
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A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer? 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 reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer?.
A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer? 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 reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer?.
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A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer?, a detailed solution for A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer? has been provided alongside types of A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)Correct answer is '31.6'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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