• Document: Engineering Mechanics Statics
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Engineering Mechanics – Statics Instructor R. Ganesh Narayanan Department of Mechanical Engineering IIT Guwahati Batch: Jan - May 2008 R. Ganesh Narayanan 1 -These lecture slides were prepared and used by me to conduct lectures for 1st year B. Tech. students as part of ME 101 – Engineering Mechanics course at IITG. - Theories, Figures, Problems, Concepts used in the slides to fulfill the course requirements are taken from the following textbooks - Kindly assume that the referencing of the following books have been done in this slide - I take responsibility for any mistakes in solving the problems. Readers are requested to rectify when using the same - I thank the following authors for making their books available for reference R. Ganesh Narayanan 1. Vector Mechanics for Engineers – Statics & Dynamics, Beer & Johnston; 7th edition 2. Engineering Mechanics Statics & Dynamics, Shames; 4th edition 3. Engineering Mechanics Statics Vol. 1, Engineering Mechanics Dynamics Vol. 2, Meriam & Kraige; 5th edition 4. Schaum’s solved problems series Vol. 1: Statics; Vol. 2: Dynamics, Joseph F. Shelley Batch: Jan - May 2008 R. Ganesh Narayanan 2 Engineering mechanics - Deals with effect of forces on objects Mechanics principles used in vibration, spacecraft design, fluid flow, electrical, mechanical m/c design etc. Statics: deals with effect of force on bodies which are not moving Dynamics: deals with force effect on moving bodies We consider RIGID BODIES – Non deformable R. Ganesh Narayanan 3 Scalar quantity: Only magnitude; time, volume, speed, density, mass… Vector quantity: Both direction and magnitude; Force, displacement, velocity, acceleration, moment… V = IvI n, where IvI = magnitude, n = unit vector n = V / IvI n - dimensionless and in direction of vector ‘V’ y j In our course: x i i, j, k – unit vectors z k R. Ganesh Narayanan 4 Dot product of vectors: A.B = AB cos θ; A.B = B.A (commutative) A A.(B+C) = A.B+A.C (distributive operation) θ B i.i=1 A.B = (Axi+Ayj+Azk).(Bxi+Byj+Bzk) = AxBx+AyBy+AzBz i.j=0 Cross product of vectors: A x B = C; ICI = IAI IBI Sin θ; AxB = -(BxA) C x (A+B) = C x A + C x B j i j k i j k k x j = -i; Ax AY AZ ixi=0 BX BY BZ k i R. Ganesh Narayanan 5 AxB = (Axi+Ayj+Azk)x(Bxi+B yj+Bzk) = (AyBz- AzBy)i+( )j+( )k Force: - action of one body on another - required force can move a body in the direction of action, otherwise no effect - some times plastic deformation, failure is possible - Magnitude, direction, point of application; VECTOR Force, Direction of motion P kN Body moves P, kN Force Body does < P kN not move bulging R. Ganesh Narayanan 6 Force system: θ Magnitude, direction and point of application is important P Bracket WIRE External effect: Forces applied (applied force); Forces exerted by bracket, bolts, foundation….. (reactive force) Internal effect: Deformation, strain pattern – permanent strain; depends on material properties of bracket, bolts… R. Ganesh Narayanan 7 Transmissibility principle: A force may be applied at any point on a line of action without changing the resultant effects of the force applied external to rigid body on which it acts Magnitude, direction and line of action is important; not point of application Line of action P P R. Ganesh Narayanan 8 Concurrent force: Forces are said to be concurrent at a point if their lines of action intersect at that point Parallelogram law of forces

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