Mechanics of Solids — Winter 2020

Define (i) Equilibrant (ii) Moment (iii) Resolution of forces

State and prove Parallelogram Law of Forces.

Find magnitude and direction of resultant of forces system as shown in figure 1.

State Principle of Transmissibility of forces and Principle of Superposition?

Determine Center of Gravity. of lamina shown in fig

Derive equation for Iand Ifor rectangular section with Base ‘B’ and xx yy Height ‘H’.

Define (i) Linear Strain (ii) Lateral Strain (iii) Volumetric Strain

Explain Stress-Strain diagram for Ductile Material.

Abronze bar is fastened between a steel bar and an Aluminium bar as shown in figure 4. Axial load are applied at the position shown. Find the largest value of ‘P’ that will not exceed an overall deformation of mm of the following stresses: Material Stress Modulus of Area (mm2) (MPa) Elasticity (E) Steel 140 200 GPa 560 Bronze 120 83 GPa 750 Aluminium 80 70 GPa 360

Define (i) Factor of Safety (ii) Allowable Stress (iii) Ultimate Stress

Derive equation to find volumetric strain for rectangular bar specimen.

The bar shown in fig 5 is subjected to a tensile load of 150 KN. If the stress in the middle portion is limited to 160 N/mm2, find the cross section dimension of the middle portion. Find also the length of the middle portion if the total elongation of bar is 0.2 mm (the bar had square cross section) Take E=200 GPa and L+2a450 mm.

Define: (i) Bending Moment (ii) Point of Contra-flexure

Derive with usual notation the relation between shear force and Bending moment.

Determine shear force and bending moment of fig 6. Also draw SFS and BMD.

Define: Angle of Friction and Coefficient of Friction?

Derive the Flexure formula for pure bending?

Find the minimum value of horizontal force Papplied to the lower block that will keep the system in equilibrium as shown in figure 7. The1 coefficient of friction between the lower block and floor is 0.25, between the upper block and vertical wall is 0.3 and between the block is 0.2.

Define: (i) Moment of Inertia (ii) Radius of Gyration

Explain first theorem of Pappus-Guldinus.

Draw shear force and bending moment diagram for a cantilever which is loaded by transverse load of 400 N,300 N, 800 Nand 500 Nat a distance of 0.5 m,1 m, 1.5m and 2 m from a fixed end shown in fig 8. The total length of cantilever is 2 meter.

Write down the assumption made in theory of bending?

Explain Mohr’s circle method?

The principal stresses at a point in the section of a member are 100 N/mm2 and 50 N/mm2 both tensile as shown in fig 9. Find the normal, tangential and resultant stresses across a plane passing through that point inclined at 600 to the plane having 100 N/mm2 stress.