A cantilever beam with a lumped mass W is constrained by a spring and a viscous dashpot damped, as shown in figure 3 below. If L= 60 in, EI= 10^3 lb-in^2 , c= 20 lb-s/in , W= 2000 lbs, k= 2kips/in, u0 = 0.5in, u0 (u with the dot in the middle up) = 10 in/s , determine (1) the displacement at t= 1.5 seconds, u( t=1.5) , and (2) the velocity at t= 1.5 seconds, u(t= 1.5) (u with a dot up in the middle again). **Figure 3: Cantilever Beam**This diagram illustrates a cantilever beam system. The beam is fixed at one end, while the other end is free. Important components and labels in the diagram are:- **EI**: Represents the flexural rigidity of the beam, where E is the modulus of elasticity and I is the moment of inertia.- **L**: The length of the cantilever beam from the fixed support to the free end.- **k**: A spring constant attached vertically to the free end of the beam, indicating a spring system.- **c**: A damper represented by a dashpot at the free end, exhibiting damping characteristics.- **W**: The load or weight that is connected at the free end of the beam, subjected to motion.- **u(t)**: Represents the displacement of the load W as a function of time, indicating dynamic motion.This illustration is typically used in engineering to demonstrate concepts of structural analysis, vibrations, and dynamic systems.

Answered: Image /qna-images/answer/4344638f-1f99-41b1-8568-f3019ec9d484.jpg

Answered: A cantilever beam with a lumped mass W…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

A cantilever beam with a lumped mass W is constrained by a spring and a viscous dashpot damped, as shown in figure 3 below. If L= 60 in, EI= 10^3 lb-in^2 , c= 20 lb-s/in , W= 2000 lbs, k= 2kips/in, u0 = 0.5in, u0 (u with the dot in the middle up) = 10 in/s , determine (1) the displacement at t= 1.5 seconds, u( t=1.5) , and (2) the velocity at t= 1.5 seconds, u(t= 1.5) (u with a dot up in the middle again).

**Figure 3: Cantilever Beam**

This diagram illustrates a cantilever beam system. The beam is fixed at one end, while the other end is free. Important components and labels in the diagram are:

- **EI**: Represents the flexural rigidity of the beam, where E is the modulus of elasticity and I is the moment of inertia.
- **L**: The length of the cantilever beam from the fixed support to the free end.
- **k**: A spring constant attached vertically to the free end of the beam, indicating a spring system.
- **c**: A damper represented by a dashpot at the free end, exhibiting damping characteristics.
- **W**: The load or weight that is connected at the free end of the beam, subjected to motion.
- **u(t)**: Represents the displacement of the load W as a function of time, indicating dynamic motion.

This illustration is typically used in engineering to demonstrate concepts of structural analysis, vibrations, and dynamic systems.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 8 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions