ENGINEERING MECHANICS
Posted on by Amol Ashok Kamble
- To impart knowledge of basic phenomena in Engineering Mechanics and to lay a foundation for its Engineering applications by studying Statics and Dynamics
- To develop a scientific approach amongst the students toward the analysis and design of various structural elements
- To enable problem-solving abilities and inculcate experimental, observational, and investigatory skills among the learners
- To prepare the student for higher level courses in analysis and design of Engineering structures
- Apply fundamentals of Engineering Mechanics to analyze the effects of a system forces acting on a rigid body.
- Analytical and graphical methods analyze various statically determinate beams and pin-jointed trusses.
- Locate the centroid and center of Gravity and calculate the moment of Inertia of the plane lamina.
- Apply knowledge of Kinematics and Kinetics of rigid body motion to solve problems of bodies in motion.
- Use Work Energy methods for analyzing linear and rotational motion.
Course Curriculum
- Basic units, SI units, body, rigid body, particle, scalar quantities, vector quantities, Idealization of engineering problems, force, the law of transmissibility of force, a moment of a force, couple, moment of a couple, resultant, parallelogram law of forces, triangle law of forces, polygon law of forces. Varignon’s theorem
- Composition of co-planar concurrent and non-concurrent forces: analytical method, graphical method, Bow’s notation.
- Equilibrium of co-planar forces, analytical and graphical conditions of equilibrium, different types of supports, free body diagrams, Lami’s theorem.
- Friction, types of friction, limiting friction, laws of Friction, Static and Dynamic friction, inclined planes, ladders, support reactions of statically determinate beams with point loads, inclined loads, uniformly distributed loads, uniformly varying loads, and couples.
- Principle of virtual work (concept only), introduction to forces in space.
- Pin-jointed statically determinate plane trusses-perfect frames, assumptions, determination of nature and magnitude of a force in a member, simple trusses; zero force members.
- Analysis of trusses by method of joints, method of sections, and graphical method.
- Centre of gravity, the centroid of a composite area, the Centroid of simple figures from the first principle, the Centroid of composite sections; the Centre of Gravity and its implication.
- Moment of inertia- Definition, a moment of inertia of plane, sections from first principles, Theorems of the moment of inertia, perpendicular axis theorem, parallel axis theorem, a moment of inertia of symmetrical and unsymmetrical sections, a radius of gyration, polar moment of inertia. Concept of Centre of mass.
- Rectilinear motion, equations of motion, motion curves and their applications, relative velocity- simple problems.
- Curvilinear motion, angular motion, the relation between angular motion and linear motion, equation of angular motion, tangential and radial acceleration.
- Newton’s laws of motion for linear motion and angular motion, D’Alembert’s principle, rectilinear motion on a rough inclined plane, motion of a lift, and motion of connected bodies.
- Circular motion, the kinetics of rotation-torque, mass moment of inertia, problems on centroidal rotation
- Potential energy, the kinetic energy of linear motion, the principle of conservation of energy, work-energy equation.
- Impulse momentum method, collision, Impact- central, eccentric, direct, oblique, elastic, plastic, coefficient of restitution, Loss of kinetic energy due to impact
- Mechanical Vibrations: - Basic terminology, free and forced vibrations, resonance and its effects, Degree of freedom.
Unit No 01: Resultant of coplanar forces
EM 1.1
Five forces acting at a point on a body as shown in fig. 2 and the body is in equilibrium. Find the force F5 in magnitude and direction.
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EM 1.2
A bracket is subjected to three forces and a couple as shown in Fig.II.1. Determine magnitude, direction and the line of action of the resultant
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EM 1.3
Determine the resultant of the parallel
coplanar force system shown in fig.1 Locate the resultant with its direction.
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EM 1.4
A small ring is situated at the centre of a hexgon, and is supported by six strings drawn tight, all in the same plane and radiating from the centre of the ring and each connected to a different angular point of the hexagon. The tensions in four consequitive strings are 10 N, 35 N, 45 N and 30 N respectively. Find the tensions in the two remaining strings the system is in equilibrium.
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EM 1.5
Two identical prismatic bars PQ and
RS each weighing 60 N are welded together to form a Tee and are suspended in
the vertical plane as shown in figure 1. Calculate the angle θ that the bar PQ
will make with the vertical, when a vertical load of 80 N is applied at S:
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EM 1.5
Determine the magnitude, the direction
of the resultant and its least distance from A for an equilateral plate of
sides 200 mm acted upon by four forces as shown in figure 1. Points D and E
are the midpoints of the respective lines.
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Unit No 02: Equilibrium of Rigid Bodies
EM 2.1
Two smooth cylinders with diameter 250 mm and 400 mm and weight 500 N and 800 N respectively, are kept in a grove with saluting surfaces making angle 60° and 30° as shown in figure.2. Determine the reaction at contact point A, B and C.
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EM 2.2
Two smooth cylinders with radius
and weights as shown in Fig. 1 are kept in a groove with slanting surfaces.
Determine the reactions at contact points. Two smooth cylinders with radius and weights as shown in Fig. 1 are kept in a groove with slanting surfaces. Determine the reactions at contact points.
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EM 2.3
Two cylinders of diameters 200 mm each and weight 100 N, rest in a horizontal channel having vertical walls, the distance between which is 360 mm. Find the reactions at the points of contacts A, B, C, and D as shown in Fig.2.
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EM 2.4
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EM 2.5
A ladder AB 3 meters in length and weighing 18 kg is placed against a wall with B at the floor level and A on the wall, the line AB making 60° with the floor. The coefficient of friction between the wall and the ladder is 0.25 and that between the floor and the ladder is 0.35. In addition to self-weight of the ladder, it has to support a man weighing 90 Kg at its top at A. To prevent slipping a force F is applied horizontally at the level of the floor. Find the minimum force required for this condition.
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EM 2.6
Analyze the beam shown in Fig. 3.
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EM 2.7
An overhanging beam is on rollers at A and is hinged at B and is loaded as shown in Fig. 2. Determine the reactions at A and B.
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EM 2.8
Find the reactions at A and B on the structure as shown in Fig. 2.
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EM 2.9
Find support reaction for the beam loaded and supported as shown in figure
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EM 2.10
Determine the reactions at supports A, C, and D in the structure shown in Figure (3).
Unit No 03: Analysis
of Pin-Jointed Plane Frames
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