Reference no: EM132399103

ASSIGNMENT - Behavioural Characteristics of elements of static and dynamic engineering systems

QUESTION 1

a) Find the reaction forces at the supports and draw shear force and bending moment diagrams for the simply supported beam shown in the Figure-1(a)

b) Find reactions of simply supported beam when a point load of 1000kg & 800 kg along with a uniform distributed load of 200kg /m is acting on it as shown in the Figure-1(b)

Question - 2

Select a standard rolled steel I-section for the simply supported beam shown in figure-2. A factor of safety of 4 is to apply and the ultimate tensile strength of the material is 600 MPa. The selected section must have the least possible weight. The weight of the beam itself may neglected when calculating the maximum bending moment.

Question - 3

A solid circular steel shaft, 75 mm diameter and 2m long is subjected to a torque of 900 Nm. Calculate (a) the maximum shear stress in the shaft, (b) the angle of twist (in degrees). Take the Modulus of Rigidity as 82.5 GN/m².

Question - 4

a) An object starting from rest moves with uniform acceleration of 3m/s² for 6 sec. Find its velocity and displacement after 6 seconds.

b) An object is shown straight down with an initial speed of 4m/s from a window which is 8 m above the ground. Find the time taken by the object to reach the ground.

c) A body starts from rest and accelerates witha uniform acceleration upto a speed of 10m/s for 5 sec. It then travels at 10m/s for 10 sec after which it is retarded to a speed of 5m/s. If the complete motion takes 25 sec, find :

i. The Acceleration,
ii. The Retardation and
iii. The total distance travelled.

Question 5

a) If a saturn V rocket with an apollo spacecraft attached has a combined mass of 2.9 ×10⁵ kg and is to reach a speed of 11.2 km/s, how much kinetic energy will it then have?

b) A 64 kg bicyclist rides his 7.7kg bicycle with a speed of 3.5 m/s. After 120m he reaches the top of a hill, with slope 1 in 30 measured along the slope. He then free wheels the 100 m to the bottom of the hill where his speed has increased to 9m/s. How much energy has he lost on the hill?

Question - 6

a) A particle having mass 10 g oscillates according to the equation x = (2.0 cm) sin {(100??⁻¹ )t + Π/6}

Find

i. The amplitude, the time period and the spring constant.

ii. The position, the velocity and the acceleration at t=0sec.

b) A simple pendulum is constructed by hanging a heavy ball with a 5.0 m string . It undergoes small oscillations.

i. How many oscillations does it make per second?

ii. What will be the frequency if the system is taken on the moon where the acceleration due to gravitation of the moon is 1.67m/s².