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(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
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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Answer: Vmax=PL³/3EI ↓
Transcribed Image Text:Answer: Vmax=PL³/3EI ↓
(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
Transcribed Image Text:(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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