STRENGTH OF MATERIALS

ASSIGNMENT-1

  1. (a). Define Hooke’s law, Young’s modulus(E), Bulk modulus(K), Rigidity modulus(G) and Poisson’s ratio? Derive the relationship between Elastic modulii?

(b). A steel rod of 30mm diameter is enclosed by a copper tube of 45mm external diameter and 35mm internal diameter. The composite bar of length 300mm is subjected to an axial tensile force of 50kN. Find the stresses in each bar and the load carried by each bar. Take E for steel as 210Gpa and E for copper as 110Gpa.

  1. (a). Derive the expression for strain energy stored in a body due to gradually applied loads and impact loads?

(b). A load P falls from a height of 15mm on a collar at the lower end of a vertical steel bar 1.5m long and 28mm in diameter. If the maximum instantaneous elongation is 3mm. Determine the corresponding stress and the magnitude of load P ?

  1. (a). Define SFD &BMD?

(b). Draw SFD & BMD for the cantilever beam loaded as shown in figure

100 kN/m 30 kN/m

3m

4m

  1. (a). Define point of Contraflexure?

(b). Draw SFD & BMD for the beam shown in figure

20kN/m 30 kN/m 100kN

4m 1m 3m 3m

  1. (a). List out the assumptions made in the derivation of bending equation?

(b). An un-symmetrical I-section beam of length 6m has equal over hangs of 1.5m at both ends. The cross section has top flange 150mm×12mm, web 10mm×176mm and bottom flange 100mm×12mm. Determine the maximum UDL the beam can support, if permissible stresses are limited to 90 N/mm2 in compression and 150 N/mm2 in tension.

STRENGTH OF MATERIALS

ASSIGNMENT-2

  1. (a). sketch the shear stress distribution across the depth of a circular section?

(b). The shear force acting on a section of a beam is 50kN. The section of the beam is of T shaped with dimensions 100mm×100mm×20mm as shown in figure. The moment of inertia about the horizontal neutral axis is 314.221×104. Calculate the shear stress at the neutral axis and at the junction of web and flange.

100mm

20mm

100mm

80mm

20mm

  1. (a). Define principle plane and principle stresses?

(b). An element in a plane is subjected to normal stresses p1=150Mpa, p2=50Mpa in two mutually perpendicular directions accompanied by a shear stress is 40Mpa. Determine the stresses acting on element rotated through an angle by 400 clock wise. Also determine the principle stresses and the planes on which they act and draw the Mohr’s circle.

  1. Discuss in detail about various theories of failures?
  1. (a). Define conjugate beam method?

(b). Determine the slopes at ends and deflection at mid span section of a beam located as shown in figure Using conjugate beam method. Take elastic modulus as E.

150kN

I 2I I

2m 4m 2m

  1. Determine using Macaulay’s method

(a). Deflection at C

(b). max. deflection

(c). Slope at end A.

20kN 10kN/m

A D C B

1m 1m 2m