PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [ ] Introduction, Fundamentals of Statics


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1 Page1 PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [ ] Introduction, Fundamentals of Statics 1. Differentiate between Scalar and Vector quantity. Write S.I. units of following quantities and categorize it as a scalar or vector. 1) Density, 2) Velocity. 3) Volume, 4) Momentum, 5) Work 2. Force is defined by its magnitude and other parameters. Name them. 3. Define the following terms: (a) Statics (b) Dynamics (c) Kinetics (d) Kinematics (e) Rigid body (f) Deformable body (g) Particles 4. Explain the law of parallelogram of forces and derive the equation for magnitude & direction of resultant force. 5. Determine magnitude and direction of resultant force of the force system shown in Figure A cord supported at A and B carries a load of 20 kn at D and a load of W at C as shown in Figure  2. Find the value of W so that CD remains horizontal. 7. Find magnitude, direction and location of resultant of force system with respect to point A shown in Figure 3. Figure 1 Figure 2 Figure 3
2 Page2 Application of Fundamentals of Statics 1 Discuss the various types of supports, beams, and load acting on the beam with symbolic sketches 2 Derive the relation between SF and BM in a beam subjected to general loading. 3 Explain the sign convention taken to compute shear force (SF) and bending moment (BM). 4 Find the reactions at supports for a beam loaded as shown in FIGURE 1. 5 Draws shear force and bending moment diagrams for beam shown in FIGURE 2. Giving values at all important points Figure 1 Figure 2
3 Page3 CENTRE OF GRAVITY & MOMENT OF INERTIA 1. State Pappus Guldinus theorem for surface of revolution. Also state Parallel and Perpendicular axis theorem 2. Derive expression of moment of inertia of rectangular section by first principal. 3. Determine the centroid of wire; bent as shown in Figure Determine the location of centroid and moment of inertia of the given lamina in Figure 2 about centroidal X axis. 5. Find center of gravity and moment of inertia of a lamina shown in the Figure 3. FIGURE  1 FIGURE  2 FIGURE  3
4 Page4 Torsion 1. Derive generalized formula for torsion of circular shaft (with usual notation) Determine the diameter of a solid shaft which will transmit 300 kw at 250 r.p.m. The 2. maximum shear stress should not exceed 30 N/mm 2 and twist should not be more than 1 in a shaft length of 2 m. Take modulus of rigidity = 10 5 N/mm. A hollow shaft has to transmit 300 kw power at 80 rpm. If the shear stress is not to 3. exceed 60 N/mm 2 and internal diameter is 60% of the external diameter, find the external and internal diameters when maximum torque is 1.4 times the average torque. G= 8 X 10 4 N/mm A solid steel shaft has to transmit 350 kw at 900 r.p.m. Find the diameter of the shaft if the shear stress is to be limited to 125 N/mm 2. Calculate the diameter of the shaft
5 Page5 SIMPLE STRESSES & STRAINS 1. Define Modulus of Elasticity, Poisson s ratio, Modulus of Rigidity, shear strain, volumetric strain and Bulk Modulus. 2. Explain Homogenous Material, Composite Element and prismatic Element. 3. Sketch the Characteristic Stress  Strain curve for mild steel under tension and show salient points on it. 4. Explain yield stress, ultimate stress and breaking stress with neat sketch for M.S specimen when subjected to tensile loading. 5. Derive the relation between bulk modulus and modulus of elasticity. 6. Determine the compressive stress developed in a punch of 10 mm diameter, used to make a hole of 10mm diameter in 8mm thick mild steel plate. The shear strength of mild steel is 300MPa. 7. A member is formed by connecting end to end a 300mm long steel bar of 50 mm X 50 mm square section with 300 mm long aluminum bar of 100 mm X 100 mm square section as shown in Figure 1. Determine the axial push required to produce the total decrease in length of 0.2 mm. Take ESteel = 2 X 10 5 MPa and Ealuminum= 0.7 X 10 5 MPa. 8. A stepped bar made of steel, copper and brass is under axial force as shown in Figure 2 and is in equilibrium. The diameter of steel is 12mm, diameter of copper is 16mm and the diameter of brass is 20 mm. Determine (i) Magnitude of unknown force P (ii) stresses in each material and (iii) Total change in length of the bar. Take Esteel = 200GPa, Ecopper = 100GPa and Ebrass = 80GPa 9. A bar ABC is loaded as shown in Figure  3, in which portion AB is of uniform section and portion BC is of tapering section. Calculate the value of load P so that the total deformation is 0.3 mm. Neglect the deformation due to self weight. Calculate the change in volume of portion AB. Take E= 110 GPa and 1/m= A wire is tied straight between two rigid poles 10 m apart has initial tensile stress 10 N/mm 2 at 32 C. Calculate stress in wire if temperature reduces to minus 8 C. Take E = 75 X 10 5 N/mm 2 and α = 20 X 106 / C. 11. A rectangular block of size 300 X 150 X 100 is subjected to forces as shown in Figure 4. If E = 75 GPa and Poisson s ratio is 0.25, calculate (i) Change in volume (ii) Modulus of rigidity and (iii) Bulk modulus. 12. A steel rod of 30 mm diameter is placed inside a copper tube of external diameter 50 mm and internal diameter 40mm, having length equal to 500 mm and connected rigidly at the ends as shown in Figure  5. The bar is subjected to axial pull of 150 kn. Find the stresses in each material and elongation of the composite bar. Take Esteel = 200 GPa and Ecopper = 100GPa.
6 Page6 Figure  1 Figure 3 Figure  2 Figure 4 Figure  5
7 Page7 PRINCIPLE STRESSES 1. What are principal planes and principal stresses? 2. Define the terms Complementary shear stress, Resultant stress, Angle of obliquity. 3. Plot Shear stress distribution diagram for Isection, Tsection, Hsection, Rectangular section, Circular section For the element shown in the following Figure 1, find the normal stress, tangential stress and resultant stress on the plane AB. Also, find principal stresses and principal planes. Use any method. A point in two dimensional stressed body is shown in Figure  2. Determine the magnitudes and directions of principal stresses, using analytical method. For the infinitesimal element shown in the Figure  3, find the normal stress, tangential stress and resultant stress on the plane AB. Figure 1 Figure 2 Figure 3
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