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Questions and Answers
What method is primarily used to analyze the slope and deflection of statically determinate beams subjected to loads?
What method is primarily used to analyze the slope and deflection of statically determinate beams subjected to loads?
- Macauley's method (correct)
- Integration method
- Virtual work method
- Energy method
Which formula is used to calculate the critical load for long columns?
Which formula is used to calculate the critical load for long columns?
- Rankin's formula (correct)
- Lami's theorem
- Bernoulli's equation
- Newton's formula
When considering slope and deflection in beams, which of the following factors is NOT typically considered?
When considering slope and deflection in beams, which of the following factors is NOT typically considered?
- Temperature variations (correct)
- Beam material properties
- Type of loading
- Beam length and cross-sectional area
In the context of beam theory, what does Euler's formula specifically address?
In the context of beam theory, what does Euler's formula specifically address?
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What type of load does Macauley's method effectively handle when analyzing beam deflection?
What type of load does Macauley's method effectively handle when analyzing beam deflection?
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Study Notes
Slope & Deflection of Beams
- Slope: The angle that the tangent to the deflected beam makes with the original axis of the beam.
- Deflection: The vertical displacement of the beam from its original position.
- Statically Determinate Beams: Beams where reactions and internal forces can be determined using static equilibrium equations.
- Point Loads: Concentrated forces acting at a single point on the beam.
- Uniformly Distributed Loads: Loads distributed uniformly over a certain length of the beam.
- Moments: Forces causing rotation or twisting of the beam.
- Macaulay's Method: A method for calculating slope and deflection of beams by using a single equation to represent the different loading conditions of the beam.
Theory of Long Columns
- Long Columns: Columns with a slenderness ratio (length to radius of gyration) greater than a certain limit.
- Buckling: The sudden failure of a long column under compressive load.
- Euler's Formula: A formula that predicts the critical buckling load for a long column.
- Rankine's Formula: An empirical formula that takes into account both elastic and inelastic buckling behavior, providing a more accurate prediction for different materials and load conditions.
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