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A cantilever of length 6 m carries two point loads of 2 kN and 3 kN at a distance of 1 m and 6 m from the fixed end respectively. In addition to this, the beam also carries a UDL of 1kN/m over a length of 2 m at a distance of 3m from the fixed end. Find the bending moment at the fixed end. (1) 28kNm (2) 50kNm (3) 10kNm (4) 45kNm?
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A cantilever of length 6 m carries two point loads of 2 kN and 3 kN a...
**Given:**
Length of the cantilever (L) = 6 m
Point load 1 (P1) = 2 kN
Distance of P1 from the fixed end (x1) = 1 m
Point load 2 (P2) = 3 kN
Distance of P2 from the fixed end (x2) = 6 m
UDL (w) = 1 kN/m
Length of UDL (l) = 2 m
Distance of UDL from the fixed end (x3) = 3 m
**To find:**
Bending moment at the fixed end
**Assumptions:**
1. The cantilever is uniform and homogeneous.
2. The loads are applied vertically.
3. The beam is loaded in the elastic range.
4. The UDL is applied over a small length, and its effect can be considered as a point load at the centroid of the UDL.
**Solution:**
To find the bending moment at the fixed end, we can consider the equilibrium conditions of the cantilever at that point.
1. Calculate the moment due to the point loads:
- Moment due to P1 = P1 * x1 = 2 kN * 1 m = 2 kNm (clockwise)
- Moment due to P2 = P2 * x2 = 3 kN * 6 m = 18 kNm (clockwise)
2. Calculate the moment due to the UDL:
- The centroid of the UDL is located at (x3 + l/2) = 3 m + 2 m/2 = 4 m from the fixed end.
- The total load due to the UDL is w * l = 1 kN/m * 2 m = 2 kN.
- Moment due to the UDL = Load * Distance = 2 kN * 4 m = 8 kNm (clockwise)
3. Calculate the net moment at the fixed end:
- Net moment = Moment due to P1 + Moment due to P2 + Moment due to UDL
- Net moment = 2 kNm (clockwise) + 18 kNm (clockwise) + 8 kNm (clockwise) = 28 kNm (clockwise)
Therefore, the bending moment at the fixed end is 28 kNm (clockwise).
Hence, the correct option is (1) 28 kNm.
Length of the cantilever (L) = 6 m
Point load 1 (P1) = 2 kN
Distance of P1 from the fixed end (x1) = 1 m
Point load 2 (P2) = 3 kN
Distance of P2 from the fixed end (x2) = 6 m
UDL (w) = 1 kN/m
Length of UDL (l) = 2 m
Distance of UDL from the fixed end (x3) = 3 m
**To find:**
Bending moment at the fixed end
**Assumptions:**
1. The cantilever is uniform and homogeneous.
2. The loads are applied vertically.
3. The beam is loaded in the elastic range.
4. The UDL is applied over a small length, and its effect can be considered as a point load at the centroid of the UDL.
**Solution:**
To find the bending moment at the fixed end, we can consider the equilibrium conditions of the cantilever at that point.
1. Calculate the moment due to the point loads:
- Moment due to P1 = P1 * x1 = 2 kN * 1 m = 2 kNm (clockwise)
- Moment due to P2 = P2 * x2 = 3 kN * 6 m = 18 kNm (clockwise)
2. Calculate the moment due to the UDL:
- The centroid of the UDL is located at (x3 + l/2) = 3 m + 2 m/2 = 4 m from the fixed end.
- The total load due to the UDL is w * l = 1 kN/m * 2 m = 2 kN.
- Moment due to the UDL = Load * Distance = 2 kN * 4 m = 8 kNm (clockwise)
3. Calculate the net moment at the fixed end:
- Net moment = Moment due to P1 + Moment due to P2 + Moment due to UDL
- Net moment = 2 kNm (clockwise) + 18 kNm (clockwise) + 8 kNm (clockwise) = 28 kNm (clockwise)
Therefore, the bending moment at the fixed end is 28 kNm (clockwise).
Hence, the correct option is (1) 28 kNm.
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A cantilever of length 6 m carries two point loads of 2 kN and 3 kN at a distance of 1 m and 6 m from the fixed end respectively. In addition to this, the beam also carries a UDL of 1kN/m over a length of 2 m at a distance of 3m from the fixed end. Find the bending moment at the fixed end. (1) 28kNm (2) 50kNm (3) 10kNm (4) 45kNm?
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A cantilever of length 6 m carries two point loads of 2 kN and 3 kN at a distance of 1 m and 6 m from the fixed end respectively. In addition to this, the beam also carries a UDL of 1kN/m over a length of 2 m at a distance of 3m from the fixed end. Find the bending moment at the fixed end. (1) 28kNm (2) 50kNm (3) 10kNm (4) 45kNm? 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 cantilever of length 6 m carries two point loads of 2 kN and 3 kN at a distance of 1 m and 6 m from the fixed end respectively. In addition to this, the beam also carries a UDL of 1kN/m over a length of 2 m at a distance of 3m from the fixed end. Find the bending moment at the fixed end. (1) 28kNm (2) 50kNm (3) 10kNm (4) 45kNm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever of length 6 m carries two point loads of 2 kN and 3 kN at a distance of 1 m and 6 m from the fixed end respectively. In addition to this, the beam also carries a UDL of 1kN/m over a length of 2 m at a distance of 3m from the fixed end. Find the bending moment at the fixed end. (1) 28kNm (2) 50kNm (3) 10kNm (4) 45kNm?.
A cantilever of length 6 m carries two point loads of 2 kN and 3 kN at a distance of 1 m and 6 m from the fixed end respectively. In addition to this, the beam also carries a UDL of 1kN/m over a length of 2 m at a distance of 3m from the fixed end. Find the bending moment at the fixed end. (1) 28kNm (2) 50kNm (3) 10kNm (4) 45kNm? 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 cantilever of length 6 m carries two point loads of 2 kN and 3 kN at a distance of 1 m and 6 m from the fixed end respectively. In addition to this, the beam also carries a UDL of 1kN/m over a length of 2 m at a distance of 3m from the fixed end. Find the bending moment at the fixed end. (1) 28kNm (2) 50kNm (3) 10kNm (4) 45kNm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever of length 6 m carries two point loads of 2 kN and 3 kN at a distance of 1 m and 6 m from the fixed end respectively. In addition to this, the beam also carries a UDL of 1kN/m over a length of 2 m at a distance of 3m from the fixed end. Find the bending moment at the fixed end. (1) 28kNm (2) 50kNm (3) 10kNm (4) 45kNm?.
Solutions for A cantilever of length 6 m carries two point loads of 2 kN and 3 kN at a distance of 1 m and 6 m from the fixed end respectively. In addition to this, the beam also carries a UDL of 1kN/m over a length of 2 m at a distance of 3m from the fixed end. Find the bending moment at the fixed end. (1) 28kNm (2) 50kNm (3) 10kNm (4) 45kNm? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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