problem 1)(a) From the fourth order differential equation, compute natural frequency of cantilever beam of span 6m and flexural rigidity of 20000kN-m². Self weight of the beam is 1000kg/m.

(b) A single spring mass system has mass of 500kg, viscous damper having damping constant of 5000N-sec/rn and spring constant of 5x10⁶ N/m. This spring mass system is having initial displacement and velocity of 0.Olm and 2msec. Get the equation of motion of the mass. Also compute the time required to reduce its amplitude to 2% of the original amplitude.

problem 2)(a) Draw mathematical model of single degree of freedom system and derive dynamic equilibrium equation using D’Alembert’s principle.

b)  A three spring mass system has spring stiffness connected in series as 6000N/m, 3000N/m, 1000N/m and masses as 10kg, 10kg and 10kg from support respectively. Compute the natural frequencies of the system.

problem 3)a)  Briefly describe various kinds of machine foundation.

b) Describe a test procedure to evaluate the shear modulus of the soil.

problem 4)a) Differentiate between flexible and rigid foundation.

b) describe the steps involved in the analysis and design of block type machine foundation.

problem 5) Differentiate between centre of rigidity and centre of mass.

problem 6) Sketch neatly the detailing of reinforcement for two way three storey portal frame located in Zone-TV of our country.

problem 7) Describe the following

i) Effect of permeability of the structure

ii) Basic and Design wind speed

iii) Aero elastic and aerodynamics effects

problem 8) Describe the steps in designing the Chimneys with dynamic loading.

problem 9)a) prepare short notes on:

i) Magnitude of an earth quake

ii) Strong column weak beam design philosophy.

b) Derive formula to compute moment of resistance for rectangular shear walls.

problem 10) Describe following in context of shear walls:

i) General Dimensions

ii) Reinforcement detailing

iii) Adequacy of boundary elements

Consider the case of simple rectangular shear wall.