Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree offreedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless.Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = p.sin (wt)acting on the mass. The known properties of the SDOF and the applied forcing function are given below.• Mass of SDOF: m = 120 kip/g• Acceleration of gravity: g = 386 in/sec²Bending sectional stiffness of SDOF: EI=Height of SDOF: h= 3000 inches• Amplitude of forcing function: p. = 6 kipForcing frequency: f = 8 HzORESISPOLISO(a) Space Launch Systemon launching padp(t)->1015 lbfxin²111u(t)El, h(b) Equivalent single degree.of freedom system withoutlinear viscous damperRigidSupportp(t)→111u(t)EI, hCRigidSupport(c) Equivalent single degreeof freedom system withadded linear viscous damperFigure 1: Single-degree-of-freedom system in Problem 1.Please compute the following considering the steady-state response of the SDOF system. Do not considerthe transient response unless it is explicitly stated in the question.(a) The natural circular frequency and the natural period of the SDOF.(b) The maximum displacement of the mass u, = max(|u(t)|) and the maximum shear force in the SpaceLaunch System fso =max(|fs (t)).(c) The acceleration dynamic response factor of the SDOF.

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Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = p.sin (wt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. Mass of SDOF: m= 120 kip/g Acceleration of gravity: g = 386 in/sec² • Bending sectional stiffness of SDOF: EI 1015 lbfxin² Height of SDOF: h = 3000 inches Amplitude of forcing function: p. = 6 kip

Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = p.sin (wt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. Mass of SDOF: m= 120 kip/g Acceleration of gravity: g = 386 in/sec² • Bending sectional stiffness of SDOF: EI 1015 lbfxin² Height of SDOF: h = 3000 inches Amplitude of forcing function: p. = 6 kip

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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Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of
freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless.
Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = p.sin (wt)
acting on the mass. The known properties of the SDOF and the applied forcing function are given below.
• Mass of SDOF: m = 120 kip/g
• Acceleration of gravity: g = 386 in/sec²
Bending sectional stiffness of SDOF: EI=
Height of SDOF: h= 3000 inches
• Amplitude of forcing function: p. = 6 kip
Forcing frequency: f = 8 Hz
O
RESIS
POLIS
O
(a) Space Launch System
on launching pad
p(t)->
1015 lbfxin²
111
u(t)
El, h
(b) Equivalent single degree.
of freedom system without
linear viscous damper
Rigid
Support
p(t)→
111
u(t)
EI, h
C
Rigid
Support
(c) Equivalent single degree
of freedom system with
added linear viscous damper
Figure 1: Single-degree-of-freedom system in Problem 1.
Please compute the following considering the steady-state response of the SDOF system. Do not consider
the transient response unless it is explicitly stated in the question.
(a) The natural circular frequency and the natural period of the SDOF.
(b) The maximum displacement of the mass u, = max(|u(t)|) and the maximum shear force in the Space
Launch System fso =max(|fs (t)).
(c) The acceleration dynamic response factor of the SDOF.

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Step 4: Compute steady state amplitude

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Step 5: Determine the maximum shear force in the column

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