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

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Chapter2: Loads On Structures
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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.
Transcribed Image Text: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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