Conjugate Beam: Find theta C, delta C using conjugate beam method(constant EI) **Title: Conjugate Beam Method for Deflection Analysis**---**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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Answered: Conjugate Beam: (constant EI) A t L…

Engineering

Civil Engineering

Conjugate Beam: (constant EI) A t L Find Ou, Su using Conjugate x * PL Beam method

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Matrix Algebra for Structural analysis

Structural analysis is a process in which the effects of different loads and internal forces, acting on structures and their elements are determined. This method of analysis is effective in detecting the failure loads of the structural elements and the design can be altered before commencing the construction process, which ensures proper strength and safety of the structures.

Question

Conjugate Beam: Find theta C, delta C using conjugate beam method

(constant EI)

**Title: Conjugate Beam Method for Deflection Analysis**

---

**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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