MCM610S Assignment 1
SEMESTER 1
2020
1. Determine the co-ordinates Xc and Yc of the centre of a 100mm
diameter circular hole cut in a thin plate so that this point will be the
centroid of the remaining shaded area shown in fig .1.
Figure 1
2. Prove that the slope and deflection of a simply supported beam of
length L and carrying a uniformly distributed load of w per unit
length over the entire length are given by:
Slope at supports =
−
𝑊𝐿2
24𝐸𝐼
and Deflection at center = −
5𝑊𝐿3
384𝐸𝐼
3. A beam ABC of length 9m has one support on the left end and the
other support at a distance of 6m from the left end. The beam carries
a point load of 1kN at right end and also carries a uniformly
distributed load of 4kN/m over a length of 3m as shown in fig.2.
Determine the slope and deflection at point c using McCaulay
method. Take E = 2 x 105N/mm2 and I = 5 x108mm4.
Figure 2
4. Determine Euler’s crippling load for an I-section joist 40cm x 20cm x
1cm x 5m long which is used as a strut with both ends fixed. Take
Young’s modulus for the joist as 2.1 x 105N/mm2.
Figure 3
5. A 1.5 m long column has circular cross-section of 5cm diameter. One
of the ends of the column is fixed in direction and position and the
other is free. Taking factor of safety of 3, calculate the safe load using:
a. Rankine’s formula take yield stress 𝜎𝑐 = 560N/mm2 and 𝛼 =
1
1600
for pinned ends.
b. Euler’s formula, young’s modulus for C.I. = 1.2 x 105N/mm2.
6. Two vertical forces are applied to abeam of the cross-section shown
in fig.4. Determine the maximum tensile and compressive stresses in
portion BC of the beam.
Figure 4