(4) Cantilever beam AB supports a point load, P, at the free end. Here is a visualization of the beam's deflected shape (deformed geometry). What is the maximum deflection of the beam? Use the integration method. x Step 1. Write (x). (x) = (1/EI) M(x) dx (don't forget C₁) Step 2. Write v(x). v(x) = f(x) dx (don't forget C₂) Step 3. How many constraint (boundary condition) equations are needed to solve the constants of integration? Step 4. Write out the constraint (boundary condition) equations. Step 5. Use the boundary condition equations to solve C₁ and C₂. Step 6. Write the final equations for (x) and v(x). Don't forget to specify the domain of x. Step 7. Find some ways to check your answer, such as... ■ Do all terms in the polynomial for have units of radians? ■ Do all terms in the polynomial for v have units of length? ■ The moment diagram is linear, so that makes v(x) cubic. Do you have an x³ term in your v(x) equation? M Graph your v(x) function¹ by setting (L=10) and (P/EI = 0.001). Does the plot look like your qualitative sketch (for 0

(4) Cantilever beam AB supports a point load, P, at the free end. Here is a visualization of the beam's deflected shape (deformed geometry). What is the maximum deflection of the beam? Use the integration method. x Step 1. Write (x). (x) = (1/EI) M(x) dx (don't forget C₁) Step 2. Write v(x). v(x) = f(x) dx (don't forget C₂) Step 3. How many constraint (boundary condition) equations are needed to solve the constants of integration? Step 4. Write out the constraint (boundary condition) equations. Step 5. Use the boundary condition equations to solve C₁ and C₂. Step 6. Write the final equations for (x) and v(x). Don't forget to specify the domain of x. Step 7. Find some ways to check your answer, such as... ■ Do all terms in the polynomial for have units of radians? ■ Do all terms in the polynomial for v have units of length? ■ The moment diagram is linear, so that makes v(x) cubic. Do you have an x³ term in your v(x) equation? M Graph your v(x) function¹ by setting (L=10) and (P/EI = 0.001). Does the plot look like your qualitative sketch (for 0

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

(4) Cantilever beam AB supports a point load, P, at the free end. Here is a visualization of the beam's deflected
shape (deformed geometry). What is the maximum deflection of the beam? Use the integration method.
x
Step 1. Write (x).
0(x) = (1/EI) M(x) dx (don't forget C₁)
Step 2. Write v(x).
v(x) = f(x) dx (don't forget C₂)
Step 3. How many constraint (boundary condition) equations are
needed to solve the constants of integration?
Step 4. Write out the constraint (boundary condition) equations.
Step 5. Use the boundary condition equations to solve C₁ and C₂.
Step 6. Write the final equations for (x) and v(x).
Don't forget to specify the domain of x.
Step 7. Find some ways to check your answer, such as...
■ Do all terms in the polynomial for have units of radians?
■ Do all terms in the polynomial for v have units of length?
The moment diagram is linear, so that makes v(x) cubic.
Do you have an x³3 term in your v(x) equation?
M
Graph your v(x) function¹ by setting (L=10) and (P/EI= 0.001).
Does the plot look like your qualitative sketch (for 0<x<10)?
Step 8. Now that you are confident in your work, solve for Vmax-
P
A
P
x
ectangar Snip
M(0)=0
15
M(x)=-Px
M(x)=-Px
V(x) = -P
Mmax = PL
B
P DRAW V(X) HERE

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