Four identical hollow cylindrical columns of mild steel support a big structure of a mass 50,000 kg. The inner and outer radii of each column are 30 and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.

Asked by Abhisek | 1 year ago |  94

1 Answer

Solution :-

Mass of the big structure, M = 50,000 kg

Total force exerted on the four columns= total weight of the structure=50000×9.8N

The compressional force on each column 

=\( \dfrac{Mg}{4}\) =\( \dfrac{(50000×9.8)}{4N}\)= 122500 N

Therefore, Stress = 122500 N

Young’s modulus of steel, Y=2×1011 Pa

Young’s modulus, Y= \( \dfrac{Stress}{Strain}\)

Strain = \(\dfrac{Young’s\; modulus}{Stress}\)

Strain = (F/A)/Y

Inner radius of the column, r = 30 cm = 0.3 m

Outer radius of the column, R = 60 cm = 0.6 m

Where,

Area, A=π(R2−r2)=π((0.6)2−(0.3)2) = 0.27 π m2

Strain =\(\dfrac{122500}{0.27 \times 3.14×2×10^{11}}\)

=7.22×10−7

Hence, the compressional strain of each column is 7.22×10−7.

Answered by Pragya Singh | 1 year ago

Related Questions

A mild steel wire of cross-sectional area 0.60 x 10 -2 cm2 and length 2 m is stretched ( not beyond its elastic limit ) horizontally between two columns. If a 100g mass is hung at the midpoint of the wire, find the depression at the midpoint.

Class 11 Physics Mechanical Properties of Solids View Answer

The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of the water. The water pressure at the bottom of the trench is about 1.1 × 108 Pa. A steel ball of initial volume 0.32 mis dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom?

Class 11 Physics Mechanical Properties of Solids View Answer

Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 × 10Pa? Assume that each rivet is to carry one-quarter of the load.

Class 11 Physics Mechanical Properties of Solids View Answer

 A mild steel wire of length 1.0 m and cross-sectional area 0.50 × 10-2 cm2 is stretched, well within its elastic limit, horizontally between two pillars. A mass of 100 g is suspended from the mid-point of the wire. Calculate the depression at the midpoint.

Class 11 Physics Mechanical Properties of Solids View Answer

A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in the figure. The cross-sectional areas of wires A and B are 1.0 mmand 2.0 mm2, respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.

A rod of length 1.05 m having negligible mass is supported at its ends by two  wires of steel (wire A) and aluminium (wire B) Of equal lengths as shown in  Fig.

Class 11 Physics Mechanical Properties of Solids View Answer