Determine the least-weight W-shape to support a concentrated dead load of 24 kips plus the beam self-weight and a concentrated live load of 15 kips on a 30ft span. The concentrated loads are located at the midpoint of the span. Lateral supports are provided at the supports and at the load point. Use A992 steel and Cb = 1.0. Design for flexure by (a) LFRD and (b) ASD.

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.

Afour cylinder four-stroke in-line engine has a stroke of 160mm, connecting rod length of 150mm, a reciprocating mass of 3kg and its firing order is 1-3-4-2. the spacing between cylinders is 100mm. i. show that the engine is in balance with regard to the primary inertia forces and primary 3. a and secondary inertia couples. li determine the out of balance secondary inertia force ii. propose ways of balancing this out of balance force and discuss the challenges that will arise

Thermal stresses are developed in a metal when its a) initial temperature is changed b) final temperature is changed c) density is changed d) thermal deformation is prevented e) expansion is prevented f) contraction is prevented