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A steal beam of hollow section of outer side 120 mm and inner side 100 mm is used on a span of 5 m. the beam is subjectred to u.d.l on entire span of intensity 25 kN/m and a point load 50kN at a distance of 2.5 m from left end. Determine the maximum bending stress in the beam in MPa. *?
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A steal beam of hollow section of outer side 120 mm and inner side 100...
Problem Statement:
A steal beam of hollow section of outer side 120 mm and inner side 100 mm is used on a span of 5 m. The beam is subjected to u.d.l on the entire span of intensity 25 kN/m and a point load 50kN at a distance of 2.5 m from the left end. Determine the maximum bending stress in the beam in MPa.
Solution:
Given,
Step 1: Calculation of Maximum Bending Moment
We will calculate the maximum bending moment by considering the worst-case scenario, i.e., when the point load is at the center of the beam.
Maximum Bending Moment (M) = (UDL x L^2)/8 + P x (L/2 - a)
M = (25 x 5^2)/8 + 50 x (5/2 - 2.5) = 125 kNm
Step 2: Calculation of Section Modulus
The section modulus is the measure of the strength of the beam's cross-sectional shape. It indicates how much stress the beam can withstand.
Section Modulus (Z) = (π/32) x (D^4 - d^4)
Z = (π/32) x (120^4 - 100^4) = 724.77 x 10^6 mm^3
Step 3: Calculation of Maximum Bending Stress
We will calculate the maximum bending stress using the bending moment and section modulus.
Maximum Bending Stress (σ) = M/Z
σ = 125 x 10^6/724.77 x 10^6 = 0.172 MPa
Conclusion:
The maximum bending stress in the beam is 0.172 MPa.
A steal beam of hollow section of outer side 120 mm and inner side 100 mm is used on a span of 5 m. The beam is subjected to u.d.l on the entire span of intensity 25 kN/m and a point load 50kN at a distance of 2.5 m from the left end. Determine the maximum bending stress in the beam in MPa.
Solution:
Given,
- Outer diameter of the beam (D) = 120 mm
- Inner diameter of the beam (d) = 100 mm
- Span of the beam (L) = 5 m
- Uniformly Distributed Load (UDL) (w) = 25 kN/m
- Point Load (P) = 50 kN
- Distance of the Point Load from the left end (a) = 2.5 m
Step 1: Calculation of Maximum Bending Moment
We will calculate the maximum bending moment by considering the worst-case scenario, i.e., when the point load is at the center of the beam.
Maximum Bending Moment (M) = (UDL x L^2)/8 + P x (L/2 - a)
M = (25 x 5^2)/8 + 50 x (5/2 - 2.5) = 125 kNm
Step 2: Calculation of Section Modulus
The section modulus is the measure of the strength of the beam's cross-sectional shape. It indicates how much stress the beam can withstand.
Section Modulus (Z) = (π/32) x (D^4 - d^4)
Z = (π/32) x (120^4 - 100^4) = 724.77 x 10^6 mm^3
Step 3: Calculation of Maximum Bending Stress
We will calculate the maximum bending stress using the bending moment and section modulus.
Maximum Bending Stress (σ) = M/Z
σ = 125 x 10^6/724.77 x 10^6 = 0.172 MPa
Conclusion:
The maximum bending stress in the beam is 0.172 MPa.
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A steal beam of hollow section of outer side 120 mm and inner side 100 mm is used on a span of 5 m. the beam is subjectred to u.d.l on entire span of intensity 25 kN/m and a point load 50kN at a distance of 2.5 m from left end. Determine the maximum bending stress in the beam in MPa. *?
Question Description
A steal beam of hollow section of outer side 120 mm and inner side 100 mm is used on a span of 5 m. the beam is subjectred to u.d.l on entire span of intensity 25 kN/m and a point load 50kN at a distance of 2.5 m from left end. Determine the maximum bending stress in the beam in MPa. *? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A steal beam of hollow section of outer side 120 mm and inner side 100 mm is used on a span of 5 m. the beam is subjectred to u.d.l on entire span of intensity 25 kN/m and a point load 50kN at a distance of 2.5 m from left end. Determine the maximum bending stress in the beam in MPa. *? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A steal beam of hollow section of outer side 120 mm and inner side 100 mm is used on a span of 5 m. the beam is subjectred to u.d.l on entire span of intensity 25 kN/m and a point load 50kN at a distance of 2.5 m from left end. Determine the maximum bending stress in the beam in MPa. *?.
A steal beam of hollow section of outer side 120 mm and inner side 100 mm is used on a span of 5 m. the beam is subjectred to u.d.l on entire span of intensity 25 kN/m and a point load 50kN at a distance of 2.5 m from left end. Determine the maximum bending stress in the beam in MPa. *? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A steal beam of hollow section of outer side 120 mm and inner side 100 mm is used on a span of 5 m. the beam is subjectred to u.d.l on entire span of intensity 25 kN/m and a point load 50kN at a distance of 2.5 m from left end. Determine the maximum bending stress in the beam in MPa. *? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A steal beam of hollow section of outer side 120 mm and inner side 100 mm is used on a span of 5 m. the beam is subjectred to u.d.l on entire span of intensity 25 kN/m and a point load 50kN at a distance of 2.5 m from left end. Determine the maximum bending stress in the beam in MPa. *?.
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