A simply supported beam spans 20 ft and carries a uniformly distributed dead load of 0.8 kip/ft, including the beam self-weight, and a live load of 2.3 kip/ft. Determine the minimum required plastic section modulus (Zx) and select the lightest-weight W-shape to carry the moment. Consider only the limit state of yielding and use A992 steel.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Which of the following components of a pid controlled accumulates the error over time and responds to system error after the error has been accumulated? a)- proportional b)- derivative c)- integral d)- on/off.

Acertain flow of air (at stp) has a velocity distribution given by v i (in ft/s). if this flow is going through a 4 ft square area in the yz-plane (centered at the origin), what is the mass flow rate (in lbm/s)?