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

SOLVE STEP BY STEP The simple portico in the figure consists of a rigid lintel of length L supported by two cylindrical pillars of equal length and material. A triangular distributed load of maximum value q_0 is imposed on the lintel. Calculate the ratio between the cross sections of the columns so that buckling starts in both at the same time. Ignore the shortening of the pillars do 1 2

A cylindrical pressure vessel having a radius r = 14 in. and wall thickness t = 0.375 in. is subjected to internal pressure p = 375 psi. In addition, a torque T = 90 kip-ft acts at each end of the cylinder (see figure). (Assume that the structures behave linearly elastically and that the stresses caused by two or more loads may be superimposed to obtain the resultant stresses acting at a point. Consider both in-plane and out-of-plane shear stresses unless otherwise specified.) (a) Determine the maximum tensile stress omay and the maximum in-plane shear stress Tmay in the wall of the cylinder. (Enter the magnitudes in ksi.) o, = ksi Tmax ksi (b) If the allowable in-plane shear stress is 4.5 ksi, what is the maximum allowable torque T? (Enter the magnitude in kip-ft.) kip-ft (c) If T = 150 kip-ft and allowable in-plane shear and allowable normal stresses are 4.5 ksi and 11.5 ksi, respectively, what is the minimum required wall thickness (in inches)? in.

1) Find the transfer function from the force F (applied at x= L/3 the bar) to the motion Y of the location x=2L/3 a bar (with fixed-fixed) boundary conditions. Consider only the first mode of vibration with zero damping. The mass of the rod is M, mass-density of the rod is p, its length is L, Young's modulus is E, and cross-sectional area is A. 2) Find the response Y(t) for a unit step input with zero initial conditions. F(t) Y(t) →L/3 → 2L/3