Semester: BE 3 rd Subject :Mechanics of Solids (2130003) Year: 2018-19 Faculty: Mr. Rohan S. Kariya Class: MA Tutorial 1 1 Define force and explain different type of force system with figures. 2 Explain types of forces. Discuss principle of superposition of forces and principle of transmissibility of forces with an example. 3 State parallelogram law of forces. The sum of two concurrent forces P and Q is 270 N and their resultant is 180 N. the angle between the force P and resultant R is 90 o. Find the magnitude of each force and angle between them. 4 The greatest and least resultants of two forces acting on a body are 35 KN and 5 KN respectively. Determine the magnitude of two forces. What would be the angle between two forces if the magnitude of the resultant is stated to be 25 KN? 5 Determine the resultant of two concurrent forces 100 KN compressive and 80 KN tensile acting at a point with angle between them is 60 o. Also find angle made by resultant with 80 KN force. 6 State Triangle law of forces. A system of forces made of two forces of equal magnitude. Determine, using the triangle law of forces, the angle between two forces if magnitude of resultant force is equal to the magnitude of one of the forces. 7 Find magnitude and direction of resultant for a concurrent force system shown in figure. 8 State Lami s theorem and prove it.
Tutorial 2 1 Differentiate: Moment of a force and couple. Also explain characteristics of a couple. 2 State and prove Varigon s theorem. 3 For the system of forces on a lamina OABC is shown in figure. Find magnitude and direction of the resultant force. Also locate the resultant either showing perpendicular distance from point O or the point of the intersection on X axis/ Y axis. 4 For a coplanar non-concurrent force system shown in figure, determine magnitude, direction and position w.r.t. point A of resultant force. 5 Find magnitude, direction and location of resultant of force system w.r.t. O shown in figure.
6 Find equilibrant of the force system shown in figure. 7 Three forces are acting on a weightless equilateral triangular plate as shown in figure. Determine the magnitude, direction and position of the resultant force. 8 Determine the magnitude, direction and position of the resultant force of the force system shown in figure w.r.t point A.
9 Figure shows triangular plate XYZ subjected to three forces. Find magnitude and direction of the resultant force and locate it on any one extended edge of the plate. Neglect weight of the plate. 10 Determine the resultant and locate the same w.r.t. point A of a non-concurrent force system shown in figure.
Tutorial 3 1 Enumerate various types of supports with neat symbolic sketches, showing possible reactions. 2 Derive relation between the rate of loading, shear force and bending moment with usual notations. 3 Determine the support reactions of the beam shown in figure. 4 Determine the reactions at support A and B for the beam loaded as shown in figure. 5 Determine the support reactions at the beam as shown in figure. 6 Determine the support reactions at A and B for beam shown in figure. 7 Draw S.F. and B.M. diagram for a beam loaded shown in figure.
8 Draw S.F. and B.M. diagram for a beam shown in figure. 9 Draw shear force and bending moment diagram for the beam shown in figure.
Tutorial 4 1 Calculate the support reactions of the beam shown in figure 2 Calculate shear force and bending moment at points A, B, C, D and E. for the beam shown in figure also plot neat shear force and bending moment diagrams indicating values at above points. Locate point of contraflexure from support B. 3 Draw shear force and bending moment diagram of the beams shown in figure. 4 Draw shear force and bending moment diagram of the beam loaded as shown in figure. 5 Determine load P such that the reactions at A & B are equal for the beam shown in figure. Draw shear force and bending moment diagrams and locate point of contraflexure.
6 A simply supported overhanging beam ABCD is loaded as shown in figure. Calculate shear force and bending moments at salient points and plot shear force and bending moment diagrams. Also locate point of contraflexure from support A. 7 Compute SF & BM at critical points and plot SF & BM diagram for a beam shown in figure. 8 Draw shear force and bending moment diagram for a beam shown below. 9 Draw shear force and bending moment diagram for a beam shown in figure.
10 Draw shear force and bending moment diagram for the beam loaded as shown in figure.
Tutorial 5 1 Distinguish between centroid and centre of gravity. 2 Define: centroid, centre of gravity, centre of mass, Axis of symmetry. 3 State and explain Pappus-Guldinus theorems. 4 Find the centroid of plane area as shown in figure. 5 Determine the position of the centre of gravity of the plane figure shown in below. 6 Determine centroid of wire shown in figure. 7 Determine centroid of bar bent in to a shape as shown in figure.
8 Find centre of gravity of a lamina shown in figure below. 9 Find centre of gravity for a plane area shown in fig. 10 A lamina of a uniform thickness is hung through a weightless hook at point B such that side AB remains horizontal; as shown in fig. Determine the length AB of the lamina. 11 Determine centroid of the plane area in which a circular part of 40mm radius, has been removed as shown in fig.
12 Find C.G. of the system shown in figure. 13 Determine volume of revolution generated by revolving plane laminaabcdea shown in fig., about y y axis, to 2π rad. Write statement of theorem used for calculating volume. 14 Find surface area of the glass to manufacture an electric bulb shown in fig., using first theorem of Pappu-Guldinus.
15 Determine the centroid of the shaded area shown in figure. Also calculate the volume of the article generated by revolving the area about vertical axis AB. Tutorial 6
1 Determine the second moment of area of a rectangle about an axis through the centroid and parallel to base. Also find moment of area about the base of the rectangle. 2 Using first principle, obtain moment of inertia of triangular lamina about centroidal axis parallel to base. 3 State and prove parallel axis theorem and Perpendicular axis theorem with usual notations. 4 Determine the location of centroid and moment of inertia of the given lamina in figureabout centroidal X axis. 5 Show that moment of inertia about horizontal centroidal axis of T section shown in fig.is 3.1422 x 10 6 mm 4. Also find radius of gyration about horizontal centroidal axis. 6 Find Moment of Inertia of a lamina shown in the fig. about horizontal centroidal axis. 7 Determine the location of centroid, I XX and I YY of lamina shown in Fig.
8 Determine the polar moment of inertia about the axes passing through the centroid of quarter circle shaped lamina with radius equal to 10cm. 9 Calculate the Moment of inertia of the shaded area shown in fig.5 about the vertical axis AB.
Tutorial 7 1 Define following: Stress, Strain, Elasticity, Modulus of elasticity, Hooke s law, axial load, transverse load, prismatic bar, non-prismatic bar, composite bar, compound bar 2 Derive an equation for the elongation of a tapered circular bar under the action of axial tensile load. 3 Derive an equation for the elongation of a tapered rectangular bar under the action of axial tensile load. 4 A circular rod of diameter 20 mm and 500 mm long is subjected to a tensile force 50kN. The modulus of elasticity for steel may be taken as 200 kn/mm 2. Find stress, strain and elongation of the bar due to applied load. 5 An assembly of steel bars as shown in the fig. is in equilibrium. Find force P and the net elongation of the assembly. Take Es = 2 x 10 5 MPa. 6 A stepped bar is loaded as shown in Fig.. Calculate the stresses in each part and total change in the length of the bar. Take Esteel= 200 GPa, Ecopper=100 GPa and Ebrass=80 GPa. 7 Find stress and deformation in each part of rod ABCD shown in fig. 8 A stepped bar made of steel, copper and brass is under axial force as shown in figureand is in equilibrium. The diameter of steel is 12mm, diameter of copper is 16mm and the diameter of brass is 20mm.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 Find the total deformation of a steel rod subjected to a force of 250kN, as shown in Fig. Length of rod is 1000mm and Modulus of Elasticity of steel is 200GPa 10 A steel member ABCD with three different circular cross-section andlengths as follows, is subjected to an axial pull of 150kN. Computethe net change in the length of the member if the modulus ofelasticity (E)=200GPa. AB: diameter=40mm and length=750mm BC: diameter=25mm and length=1000mm CD: diameter=30mm and length=1200mm 11 A steel rod of 30mm diameter is placed inside a copper tube of externaldiameter 50mm and internal diameter 40mm, having length equal to 500mmand connected rigidly at the ends as shown in figure. The bar issubjected to axial pull of 150kN. Find the stresses in each material andelongation of the composite bar. Take Esteel = 200 GPa and Ecopper = 100GPa.