**Problem 12-6: Analysis of a Cantilevered Beam****Objective:**Determine the elastic curve for a cantilevered beam subjected to a couple moment \( M_o \). Calculate the maximum slope and maximum deflection of the beam. Assume that \( EI \) (the product of modulus of elasticity and moment of inertia) is constant.**Diagram Explanation:**- The diagram illustrates a cantilever beam fixed at point \( A \) and free at point \( B \).- A couple moment \( M_o \) is applied at the free end \( B \).- The beam has a total length denoted by \( L \).- \( x \) is the variable used for distance along the length of the beam from the fixed point.**Key Points to Consider:**- The elastic curve represents the deflected shape of the beam under the applied load.- The slope of the elastic curve at any point on the beam represents the angle of deflection.- The maximum deflection occurs at the free end of the cantilever beam.- Ensure calculations assume \( EI \) is constant, simplifying the determination of deflection and slope.**Approach:**Use integration methods to derive expressions for the slope and deflection based on the boundary conditions of the cantilever beam. Analyze how \( M_o \) and \( L \) influence these factors.

12-6. Determine the elastic curve for the cantilevered beam, which is subjected to the couple momeat M, Also calculate the maximum slope and maximum dellcction of the beam. A7 is constant. L- Prob. 12-6

12-6. Determine the elastic curve for the cantilevered beam, which is subjected to the couple momeat M, Also calculate the maximum slope and maximum dellcction of the beam. A7 is constant. L- Prob. 12-6

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

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

**Problem 12-6: Analysis of a Cantilevered Beam**

**Objective:**
Determine the elastic curve for a cantilevered beam subjected to a couple moment \( M_o \). Calculate the maximum slope and maximum deflection of the beam. Assume that \( EI \) (the product of modulus of elasticity and moment of inertia) is constant.

**Diagram Explanation:**
- The diagram illustrates a cantilever beam fixed at point \( A \) and free at point \( B \).
- A couple moment \( M_o \) is applied at the free end \( B \).
- The beam has a total length denoted by \( L \).
- \( x \) is the variable used for distance along the length of the beam from the fixed point.

**Key Points to Consider:**
- The elastic curve represents the deflected shape of the beam under the applied load.
- The slope of the elastic curve at any point on the beam represents the angle of deflection.
- The maximum deflection occurs at the free end of the cantilever beam.
- Ensure calculations assume \( EI \) is constant, simplifying the determination of deflection and slope.

**Approach:**
Use integration methods to derive expressions for the slope and deflection based on the boundary conditions of the cantilever beam. Analyze how \( M_o \) and \( L \) influence these factors.

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