Calculate the increase in vertical stress below the ground surface along the centerline of the tank using Boussinesq’s theory.

Question

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) = posin(ωt) 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 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hz

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Chapter 10, Problem 10.19P

To determine

Calculate the increase in vertical stress below the ground surface along the centerline of the tank using Boussinesq’s theory.

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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) = posin(ωt) 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 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hz

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