STRUCTURAL DYNAMICS: ASSIGNMENT #1

 

JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY

ASSIGNMENT 1 FOR FOURTH YEAR SECOND SEMESTER BACHELOR OF SCIENCE IN CIVIL ENGINEERING

ECE 2416 – THEORY OF STRUCTURES VI (STRUCTURAL DYNAMICS)

INSTRUCTIONS

§  Attempt ALL questions

§  Work in groups of 5 students (Each student to attempt 1 question and then compile your work into a single report per group)

§  Submission deadline: Wednesday 10/12/2021 on or before 1.00 PM

 

1.    The undamped SDOF system of Fig. 1a is subjected to the half sine­-wave loading of Fig. 1b. Calculate the displacement and spring force history for the time 0 < t < 0.6 sec by numerical evaluation of the Duhamel integral with a time interval of 0.1 sec. 

Fig. 1

2.  Demonstrate, starting from basic principles, that the equation of motion expressed with reference to the static equilibrium position of the dynamic system is not affected by gravity forces.

3.    A one-story building, idealized as a 4-m-high frame with two columns hinged at the base and a rigid beam, has a natural period of 0.5 sec. Each column is a standard UB steel section with properties for bending about its major axis as I_x = 2772 cm⁴, S = 252 cm³; E = 200,000 MPa. Neglecting damping, determine the maximum displacement at the top of the frame and maximum bending stress in the columns of this frame due to a rectangular pulse force of amplitude 20 kN and duration t_d = 0.2 sec.

4.  Assume a shear building model for the frame shown in Fig. 2 and determine the natural frequencies and normal modes.

Fig. 2

 

5.   For the two-storey shear building shown in Fig. 3, m₁ = m₂ = m and  k₁ = k₂ = k . Calculate and sketch the fundamental and the second mode of vibration for this system.

Fig. 3

 

 ~~~~~ENDS~~~~

~~~~~BEST OF LUCK~~~