Questions and Answers
What is determined first before sketching internal shear force and bending moment diagrams?
Support reactions at the fixed support
In the flexure formula, what does 'MX' represent?
Bending moment on the left side of a segment
What is the purpose of determining normal stress distribution using the flexure formula?
To assess the bending stress on both sides of the segment
How is shear stress calculated in the top segment of a beam according to the text?
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What does the shear formula not account for as per the limitations mentioned in the text?
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How is shear stress distribution described in a rectangular cross-sectional area according to the text?
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What is used to determine the absolute maximum shear stress in a beam?
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'Calculation of maximum shear stress involves determining centroid locations, moment of inertia, and applying which formula to different segments of the cross-section?'
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Study Notes
- The text discusses the analysis of internal shear force and bending moment in a beam under vertical force and fixed support.
- Support reactions at the fixed support are determined first to sketch internal shear force and bending moment diagrams.
- Bending moment on the left side of a segment is MX, and on the right side is MX plus DM, showing a difference in bending moment.
- The flexure formula is used to determine normal stress distribution on both sides of the segment due to bending moment.
- Integration of bending stress on different sides of the segment results in forces that create a pure couple moment equal to the bending moment.
- The shear formula, τ = VQ / IT, is derived to calculate shear stress in the top segment of the beam.
- Shear stress develops uniformly along the z-axis, and the shear formula limitations include not accounting for z-axis stress variation and angle boundary stress changes.
- The text explains the method of sections to determine shear stress distribution on a rectangular cross-sectional area.
- Shear stress distribution in a rectangular area is quadratic and parabolic in shape, with maximum shear stress at the centroidal location.
- The absolute maximum shear stress in a beam is determined using the internal shear force diagram and calculations on specific cross-sectional areas.
- Calculation of maximum shear stress involves determining centroid locations, moment of inertia, and applying the shear formula to different segments of the cross section.
- The text emphasizes the importance of understanding shear stress distributions for different cross-sectional areas for accurate structural analysis.
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