Math Problem Statement
w = 38 kN/m . Determine the magnitude of the internal shear force at point C in the beam.
Solution
To determine the internal shear force at point in the beam, we need to analyze the given diagram, including the loading conditions and the supports.
Given:
- The beam has a uniformly distributed load (UDL) .
- The UDL acts over a length of .
- The beam is supported at points and , with point located at the midpoint between these supports.
- The distances between points , , and are each .
Steps to Solve:
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Calculate the total load from the UDL: The UDL covers , so the total load is:
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Determine the reactions at the supports and : Since the beam is symmetric and the loading is also symmetric, the reactions at and should be equal.
The total downward force on the beam is . Therefore, each support reaction is:
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Calculate the shear force just to the left of point : Moving from point towards , the shear force at any section is the reaction at minus the UDL up to that point.
For point , located from :
Conclusion:
The magnitude of the internal shear force at point is . The negative sign indicates that the shear force is acting downwards at point .
Would you like more details on this calculation, or do you have any questions?
Here are 5 related questions to consider:
- What would be the shear force at a point between and but not at ?
- How would the shear force diagram look for this beam?
- What is the moment at point given the same loading conditions?
- How would the reaction forces change if the load were not uniformly distributed?
- What is the significance of the shear force sign (positive or negative)?
Tip: When solving beam problems, always start by calculating support reactions before determining internal forces like shear or bending moments.
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Math Problem Analysis
Mathematical Concepts
Mechanics
Structural Analysis
Formulas
Shear Force Formula
Theorems
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Suitable Grade Level
College
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