Please answer THE PROBLEM in number 2-4 1.Using Duhamel's Integral, show that the response of an undamped SDOF system subjectedto step force excitation is given by the equationPou(t) =은 [1-cos ant]Using Duhamel's Integral, show that the response of an undamped SDOF system subjected2.to a ramp force excitation is given by the equationsin wnt]u(t) = (Ust)o FWntr3.Using Duhamel's Integral, show that the response of an undamped SDOF system subjectedto a step force with finite rise time excitation is given by the equation1u(t) = (Ust)o |1(sin w,t – sin w, (t – t,))|WntrUsing Duhamel's Integral, show that the response of an undamped SDOF system subjectedto a step force with finite rise time excitation is given by the equation4.u(t) = (ust)o [(cos w„ (t – ta) – cos wnt)]

Consider the given equation ut=pok1-cosωnt An undamped SDOF system is subjected to a ramp impulse

Answered: Using Duhamel's Integral, show that the…

Using Duhamel's Integral, show that the response of an undamped SDOF system subjected to a ramp force excitation is given by the equation 2.

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

Methods to Determine Vertical Stress

The load applied to the soil is transferred to the underground. The presence of water at soil pores and solid grains above the soil are the primary components that are responsible for the effective load transfer. Due to the load acting, the internal component of the soil or the underground formations undergoes deformations or a tectonic shift. The amount of deformation depends upon the amount of load acting on the soil surface, which indeed, depends on the weight of everything present above the soil. Due to this, the underground soil element develops internal stresses which try to resist the tectonic changes.

Question

Please answer THE PROBLEM in number 2-4

1.
Using Duhamel's Integral, show that the response of an undamped SDOF system subjected
to step force excitation is given by the equation
Po
u(t) =
은 [1-cos ant]
Using Duhamel's Integral, show that the response of an undamped SDOF system subjected
2.
to a ramp force excitation is given by the equation
sin wnt]
u(t) = (Ust)o F
Wntr
3.
Using Duhamel's Integral, show that the response of an undamped SDOF system subjected
to a step force with finite rise time excitation is given by the equation
1
u(t) = (Ust)o |1
(sin w,t – sin w, (t – t,))|
Wntr
Using Duhamel's Integral, show that the response of an undamped SDOF system subjected
to a step force with finite rise time excitation is given by the equation
4.
u(t) = (ust)o [(cos w„ (t – ta) – cos wnt)]

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