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A overhanging beam of ABC loaded as shown in figure. Determine the deflection at point
C. Take E= 2 x 105 N/mm2
and I= 5 x 108 mm?
C. Take E= 2 x 105 N/mm2
and I= 5 x 108 mm?
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A overhanging beam of ABC loaded as shown in figure. Determine the def...
Problem Statement: Determine the deflection at point C of an overhanging beam of ABC loaded as shown in figure. Take E=2x105 N/mm2 and I=5x108 mm2.
Solution:
Step 1: Draw the free body diagram of the beam and determine the reactions at A and B.
∑MA=0: -RA x 500 + 90 x 300 + 80 x 600 = 0
RA = 108 kN
∑Fy=0: RA + RB - 90 - 80 = 0
RB = 62 kN
Step 2: Determine the equation of the deflection curve.
Using double integration method, the equation of the deflection curve is given by:
y(x) = (wx/24EI) [x3 - 2Lx2 + (L2 - 4x2)]
where, w = load per unit length = (90 + 80)/600 = 0.25 kN/mm
L = length of the beam between A and B = 600 mm
Step 3: Determine the deflection at point C.
Substituting x = 900 mm in the equation of the deflection curve, we get:
y(900) = (0.25 x 900/24 x 2 x 105 x 5 x 108) [(900)3 - 2 x 600 x (900)2 + (6002 - 4 x 9002)]
y(900) = -0.83 mm (approx.)
Therefore, the deflection at point C is -0.83 mm.
Conclusion: The deflection at point C of
Solution:
Step 1: Draw the free body diagram of the beam and determine the reactions at A and B.
∑MA=0: -RA x 500 + 90 x 300 + 80 x 600 = 0
RA = 108 kN
∑Fy=0: RA + RB - 90 - 80 = 0
RB = 62 kN
Step 2: Determine the equation of the deflection curve.
Using double integration method, the equation of the deflection curve is given by:
y(x) = (wx/24EI) [x3 - 2Lx2 + (L2 - 4x2)]
where, w = load per unit length = (90 + 80)/600 = 0.25 kN/mm
L = length of the beam between A and B = 600 mm
Step 3: Determine the deflection at point C.
Substituting x = 900 mm in the equation of the deflection curve, we get:
y(900) = (0.25 x 900/24 x 2 x 105 x 5 x 108) [(900)3 - 2 x 600 x (900)2 + (6002 - 4 x 9002)]
y(900) = -0.83 mm (approx.)
Therefore, the deflection at point C is -0.83 mm.
Conclusion: The deflection at point C of
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A overhanging beam of ABC loaded as shown in figure. Determine the deflection at pointC. Take E= 2 x 105 N/mm2and I= 5 x 108 mm?
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A overhanging beam of ABC loaded as shown in figure. Determine the deflection at pointC. Take E= 2 x 105 N/mm2and I= 5 x 108 mm? 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 overhanging beam of ABC loaded as shown in figure. Determine the deflection at pointC. Take E= 2 x 105 N/mm2and I= 5 x 108 mm? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A overhanging beam of ABC loaded as shown in figure. Determine the deflection at pointC. Take E= 2 x 105 N/mm2and I= 5 x 108 mm?.
A overhanging beam of ABC loaded as shown in figure. Determine the deflection at pointC. Take E= 2 x 105 N/mm2and I= 5 x 108 mm? 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 overhanging beam of ABC loaded as shown in figure. Determine the deflection at pointC. Take E= 2 x 105 N/mm2and I= 5 x 108 mm? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A overhanging beam of ABC loaded as shown in figure. Determine the deflection at pointC. Take E= 2 x 105 N/mm2and I= 5 x 108 mm?.
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