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A rigid beam AB resting on elastic supports undergoes displacements at A and B of 0.30mm and 0.1mm . A point C is located at a distance of 300 mm from A along AB.If the length of AB is 500 mm, then the deflection at, C is?
ANS 0.18mm?
ANS 0.18mm?
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A rigid beam AB resting on elastic supports undergoes displacements at...
Given data:
- Displacement at point A (DA) = 0.30 mm
- Displacement at point B (DB) = 0.10 mm
- Distance from point A to point C (AC) = 300 mm
- Length of the beam AB = 500 mm
Calculating the deflection at point C:
1. Determine the slope at point A:
- Slope at point A (θA) is given by the equation θA = DA / AC.
- Substituting the given values, θA = 0.30 mm / 300 mm = 0.001 rad.
2. Determine the slope at point B:
- Slope at point B (θB) is given by the equation θB = DB / (L - AC).
- Substituting the given values, θB = 0.10 mm / (500 mm - 300 mm) = 0.0005 rad.
3. Determine the deflection at point C:
- Deflection at point C (DC) is given by the equation DC = (θA + θB) * AC.
- Substituting the calculated values, DC = (0.001 rad + 0.0005 rad) * 300 mm = 0.0015 rad * 300 mm = 0.45 mm.
Therefore, the deflection at point C is 0.45 mm.
Explanation:
- The deflection at point C is calculated using the slopes at points A and B, which are determined based on the given displacements at those points.
- The slope at point A is obtained by dividing the displacement at point A by the distance from point A to point C.
- Similarly, the slope at point B is obtained by dividing the displacement at point B by the distance from point B to point C.
- The deflection at point C is then calculated by adding the slopes at points A and B and multiplying the sum by the distance from point A to point C.
- The deflection at point C represents the displacement of point C from its original position when the beam undergoes the given displacements at points A and B.
- In this case, the deflection at point C is calculated to be 0.45 mm.
- Displacement at point A (DA) = 0.30 mm
- Displacement at point B (DB) = 0.10 mm
- Distance from point A to point C (AC) = 300 mm
- Length of the beam AB = 500 mm
Calculating the deflection at point C:
1. Determine the slope at point A:
- Slope at point A (θA) is given by the equation θA = DA / AC.
- Substituting the given values, θA = 0.30 mm / 300 mm = 0.001 rad.
2. Determine the slope at point B:
- Slope at point B (θB) is given by the equation θB = DB / (L - AC).
- Substituting the given values, θB = 0.10 mm / (500 mm - 300 mm) = 0.0005 rad.
3. Determine the deflection at point C:
- Deflection at point C (DC) is given by the equation DC = (θA + θB) * AC.
- Substituting the calculated values, DC = (0.001 rad + 0.0005 rad) * 300 mm = 0.0015 rad * 300 mm = 0.45 mm.
Therefore, the deflection at point C is 0.45 mm.
Explanation:
- The deflection at point C is calculated using the slopes at points A and B, which are determined based on the given displacements at those points.
- The slope at point A is obtained by dividing the displacement at point A by the distance from point A to point C.
- Similarly, the slope at point B is obtained by dividing the displacement at point B by the distance from point B to point C.
- The deflection at point C is then calculated by adding the slopes at points A and B and multiplying the sum by the distance from point A to point C.
- The deflection at point C represents the displacement of point C from its original position when the beam undergoes the given displacements at points A and B.
- In this case, the deflection at point C is calculated to be 0.45 mm.
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A rigid beam AB resting on elastic supports undergoes displacements at A and B of 0.30mm and 0.1mm . A point C is located at a distance of 300 mm from A along AB.If the length of AB is 500 mm, then the deflection at, C is?ANS 0.18mm?
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A rigid beam AB resting on elastic supports undergoes displacements at A and B of 0.30mm and 0.1mm . A point C is located at a distance of 300 mm from A along AB.If the length of AB is 500 mm, then the deflection at, C is?ANS 0.18mm? 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 rigid beam AB resting on elastic supports undergoes displacements at A and B of 0.30mm and 0.1mm . A point C is located at a distance of 300 mm from A along AB.If the length of AB is 500 mm, then the deflection at, C is?ANS 0.18mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid beam AB resting on elastic supports undergoes displacements at A and B of 0.30mm and 0.1mm . A point C is located at a distance of 300 mm from A along AB.If the length of AB is 500 mm, then the deflection at, C is?ANS 0.18mm?.
A rigid beam AB resting on elastic supports undergoes displacements at A and B of 0.30mm and 0.1mm . A point C is located at a distance of 300 mm from A along AB.If the length of AB is 500 mm, then the deflection at, C is?ANS 0.18mm? 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 rigid beam AB resting on elastic supports undergoes displacements at A and B of 0.30mm and 0.1mm . A point C is located at a distance of 300 mm from A along AB.If the length of AB is 500 mm, then the deflection at, C is?ANS 0.18mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid beam AB resting on elastic supports undergoes displacements at A and B of 0.30mm and 0.1mm . A point C is located at a distance of 300 mm from A along AB.If the length of AB is 500 mm, then the deflection at, C is?ANS 0.18mm?.
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