=1sec
PART B

a. Explain the concept of shear building model for the analysis of a
multistoreyed building frame. http.e//uuw.kiilonline.com (5)

b Determine the mass orthonormalised modeshape vectors for a system whose mass
properties and mode shapes are as given. Take m = 10000 kg.

0.300 - 0.676 2.470
ml = 2m, = 1.5൩ m and 0.644 — 0.601 - 2.570
1.000 1.000 1.000 (4)

A tyuee storeyed building frame of storey height 3.2 m and beam span 8 m is loaded on the top beam with
a UDL of 25 kN/m and the other beams carry a 121 of 35 kN/m. If the columns have a uniform moment of
inertia of 5x107 mm4 and if ‏ع‎ 22105 N/ mm2, compute the frequencies and mode shapes of the frame using
Stodola's method. (9)

Evaluate steady state response at middle level at t = 0.15 sec when a three storeyed
frame is subjected to a harmonic load of 400 Sin (1.302t) kN at top level, considering
the contribution from all the modes. Given damping ratio = 0.05 for the system and
ml = mz 20000 kg and kl 1.5k, k2 = k3 = k, where k = 160 kN/mm.

43.872 0.3361-1.1572 2.512
{w}= 120.155 rad/sec and [0] = 0.7594 0.8047 - 2.427
167 1.000 1.000 1.000 (9)
PART C

a. Derive the differential equaaon of motion for the flexural vibraaon of beams

including shear deformation and rotary (6)

2
b. Plot the first three possible modeshapes of a beam with distributed mass under

the following support conditions: (i). Both ends hinged (ii). Both ends fixed (iii).

One end fixed and the other end free. (6)

a. Derive the equations of motion for a two degree of freedom system using
Lagrange's equation. (4)