Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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Conjugate Beam: Find theta C, delta C using conjugate beam method
(constant EI)
Transcribed Image Text:**Title: Conjugate Beam Method for Deflection Analysis**
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**Objective:**
To find the slope (\(\Theta_c\)) and deflection (\(\delta_c\)) at point C using the Conjugate Beam Method.
**Description:**
The problem involves a beam fixed at point A with a length \(L\). There is a point load \(P\) applied at point C, located at a distance \(x\) from A. The load causes a moment \(PL\).
- **Beam Details:**
- Length: \(L\)
- Point of interest: C
- Load applied: \(P\) at point C
- Distance from fixed support A to point C: \(x\)
- Moment caused by load: \(PL\)
- Material's flexural rigidity assumed constant (\(EI\)).
**Goal:**
Use the conjugate beam method to determine:
- The slope at point C, \(\Theta_c\)
- The deflection at point C, \(\delta_c\)
**Approach:**
The conjugate beam method involves analyzing an imaginary beam (the "conjugate beam") with the same length as the original. Reactions and loads on this beam correspond to the bending moments and slopes from the original beam.
**Note:**
To fully solve the problem, apply equilibrium equations and use appropriate boundary conditions and material properties to calculate \(\Theta_c\) and \(\delta_c\) at point C.
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- part darrow_forwardConsider the cantilever beam in the figure,subject to a concentrated force P = 20kip at Band a concentrated moment Mo = 100k-ft at C.Knowing that a = 5ft, use the conjugate beammethod to calculate the following in terms ofgeneric E and I:(a) The slope of point C(b)The deflection of point Barrow_forwardProblem 5 The cantilever beam shown below is non-prismatic and is loaded with a concentrated load at free end B. Determine: a) the vertical deflection at B, b) the rotation at B (use either double integration or moment area) A is ft I₁ = 6000 in 4 10 ft = 3000 in 4 H 20 B K E=29000 ksiarrow_forward
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