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A simple beam with an overhang is supported at points A and B (Fig. 4-15a). A uniform load of intensity q = 6 kN/m acts throughout the length of the beam and a concentrated load P = 28 kN acts at a point 3 m from the left-hand support. The span length is 8 m and the length of the overhang is 2 m. Calculate the shear force V and bending moment M at cross section D located 5 m from the left-hand support?
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A simple beam with an overhang is supported at points A and B (Fig. 4-...
Solution:
Step 1: Calculation of reaction forces
We can find the reaction forces at the supports by taking moments about point A.
Sum of moments about A = 0
(6 kN/m × 8 m) × (8 m/2) + P × (8 m - 3 m) - RB × 2 m = 0
RB = 60 kN
Taking moments about point B
Sum of moments about B = 0
RA × 10 m - (6 kN/m × 8 m) × (8 m/2) - P × 3 m = 0
RA = 40 kN
Step 2: Calculating the shear force diagram
We can now draw the shear force diagram by starting at the left-hand end of the beam and moving towards cross section D, taking into account the reaction forces and the loads acting on the beam.
At the left-hand end of the beam, the shear force is zero. Moving towards the right, we encounter the concentrated load of 28 kN at a distance of 3 m from the left-hand support. This creates a sudden jump in the shear force, which becomes 28 kN upwards.
Between the concentrated load and cross section D, a uniform load of intensity 6 kN/m acts. This creates a linearly decreasing shear force diagram, which becomes zero at cross section D.
Therefore, the shear force at cross section D is:
VD = RA - (6 kN/m × 5 m) - 28 kN = 2 kN upwards
Step 3: Calculating the bending moment diagram
We can now draw the bending moment diagram by starting at the left-hand end of the beam and moving towards cross section D, using the shear force diagram and taking into account the reaction forces and the loads acting on the beam.
At the left-hand end of the beam, the bending moment is zero. Moving towards the right, we encounter the concentrated load of 28 kN at a distance of 3 m from the left-hand support. This creates a sudden change in the bending moment, which becomes:
MB = 28 kN × (8 m - 3 m) = 140 kNm (clockwise)
Between the concentrated load and cross section D, a uniform load of intensity 6 kN/m acts. This creates a linearly increasing bending moment diagram, which becomes:
MD = RA × 5 m - (6 kN/m × 5 m × 2.5 m) - 28 kN × 2 m = -20 kNm (clockwise)
Therefore, the bending moment at cross section D is:
MD = -20 kNm (clockwise)
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A simple beam with an overhang is supported at points A and B (Fig. 4-15a). A uniform load of intensity q = 6 kN/m acts throughout the length of the beam and a concentrated load P = 28 kN acts at a point 3 m from the left-hand support. The span length is 8 m and the length of the overhang is 2 m. Calculate the shear force V and bending moment M at cross section D located 5 m from the left-hand support?
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A simple beam with an overhang is supported at points A and B (Fig. 4-15a). A uniform load of intensity q = 6 kN/m acts throughout the length of the beam and a concentrated load P = 28 kN acts at a point 3 m from the left-hand support. The span length is 8 m and the length of the overhang is 2 m. Calculate the shear force V and bending moment M at cross section D located 5 m from the left-hand support? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A simple beam with an overhang is supported at points A and B (Fig. 4-15a). A uniform load of intensity q = 6 kN/m acts throughout the length of the beam and a concentrated load P = 28 kN acts at a point 3 m from the left-hand support. The span length is 8 m and the length of the overhang is 2 m. Calculate the shear force V and bending moment M at cross section D located 5 m from the left-hand support? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simple beam with an overhang is supported at points A and B (Fig. 4-15a). A uniform load of intensity q = 6 kN/m acts throughout the length of the beam and a concentrated load P = 28 kN acts at a point 3 m from the left-hand support. The span length is 8 m and the length of the overhang is 2 m. Calculate the shear force V and bending moment M at cross section D located 5 m from the left-hand support?.
A simple beam with an overhang is supported at points A and B (Fig. 4-15a). A uniform load of intensity q = 6 kN/m acts throughout the length of the beam and a concentrated load P = 28 kN acts at a point 3 m from the left-hand support. The span length is 8 m and the length of the overhang is 2 m. Calculate the shear force V and bending moment M at cross section D located 5 m from the left-hand support? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A simple beam with an overhang is supported at points A and B (Fig. 4-15a). A uniform load of intensity q = 6 kN/m acts throughout the length of the beam and a concentrated load P = 28 kN acts at a point 3 m from the left-hand support. The span length is 8 m and the length of the overhang is 2 m. Calculate the shear force V and bending moment M at cross section D located 5 m from the left-hand support? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simple beam with an overhang is supported at points A and B (Fig. 4-15a). A uniform load of intensity q = 6 kN/m acts throughout the length of the beam and a concentrated load P = 28 kN acts at a point 3 m from the left-hand support. The span length is 8 m and the length of the overhang is 2 m. Calculate the shear force V and bending moment M at cross section D located 5 m from the left-hand support?.
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