Docsity.com: A Comprehensive Collection of Academic Documents, Slides of Applied Solid Mechanics

Download Docsity.com: A Comprehensive Collection of Academic Documents and more Slides Applied Solid Mechanics in PDF only on Docsity! Forces and Moments EPRI ONICSTIS ECM CoM ICT as WNW CLA EVE siearirs elit docsity.com  Outline * What is mechanics? * Scalars and vectors ® Forces are vectors * Transmissibility of forces * Resolution of colinear forces * Moments and couples docsity.com Elastically Deformable Body ¢ Bodies that undergo reversible deformations ¢ Examples: ¢ rubber bands * springs ¢ steel, concrete and wood structures under small ares Kes BaeTcTECOD ITS ¢ If structure deforms slightly, we can use original geometry for entire analysis docsity.com  Inelastically Deformable Body ¢ Bodies that undergo irreversible deformations due to forces ¢ Examples: ¢ bent paper clip ¢ steel, concrete and wood structures under large Crop unsralb Coy ets aCe Ratio. ely ICM EMO CSO inelastic deformations, geometry changes docsity.com  Statics Sa Lem DUMMY ald SELB (ers) ¢ Determining that the various forces acting on a body are in equilibrium. \ applied force : re=y- [miele meee) reaction forces docsity.com  Parallelogram Law. If two forces, represented by vectors AB and AC, acting under an angle a are applied to a body at a point A, their action is equivalent to the action of one force , represented by the vector AD , obtained as the diagnal of the parallogram constructed on the vectors AB and AC and directed as shown in FIG BO D D ra Loa ow A C é  Force Components ¢ Force can be replaced by x and y components docsity.com  Forces in 3 Dimensions ¢ In 3 dimensions, forces can be replaced by 3 components along x, y and z axes: F=(F,, F,,F,)=(,,F,,F,) or F=F,i+ F, j+ F,k i, j and k are unit vectors in x, y, and z = @ docsity.com Colinear Forces ¢ Forces acting along the same line of action. ¢ The magnitude of a single equivalent force is the same as the sum of the colinear forces (®) eo eg SY docsity.com Equilibrium Law: Two forces can be in equilibrium only if they are equal in magnitude ,Opposite in direction and colinear in action. docsity.com  Concurrent Forces ¢ Pass through the same point in space &) 2D Case 3D case NY docsity.com  Transmissibility ¢ Extension of the concept of colinear ieneee If a force is exerted on a rope or a cable, then Yo VM OCe MOULTRIE Rom-T ET equal force if the system does not move. A _ MY docsity.com  Action and Reaction n “ “ ‘ \ & | Raced yn por \ \ . | J { : ) =f ¥ ; \ z\ | J \ Z — “ ss 7 ta) Pe 4 5) ae “ " (a) no. no. 10 Free body diagrams ® docsity.com  Law of action /reaction Any pressure ona support causes an equal and opposite pressure from the support so that action and reaction are two equal and opposite (Gerces _ Equilibrium of three forces in plane ~_ -~— ene eee me docsity.com  Resolution of Forces .... con’t. * To compute the resultant of several concurrent forces: ¢ first determine the angle of each force with respect to + X axis ° find x and y components for each force; and * sum colinear forces ¢ Note: You must be systematic about the angles. I will show you one system. (® docsity.com  Determine angles wrt +X axis F; Note: by measuring all angles from + x axis, sines and cosines will reflect whether F,, and F, are positive or negative. docsity.com  Sum colinear forces in x and y F, cos 6, 4 ——— > a4 F3 Cos 6; ey ] = an) i ie eee ee ze E, and =f <n@ = sing: aay Note: all forces are summed because the sines and & cosines will indicate whether the component is in the UE positive or negative direction. dacsity com  Determine Magnitude and Direction of Resultant Force ¢ Then compute the resultant force: Dams VitcRestvLLiCe(oae-naTel id (ee a ae 2 ¢ direction (ae rl 0 et (a A F.) Gwenls Er2¢ lb docsity.com docsity.com Spreadsheet Solution Problem 9.11 Fx E Force Ma i Cos Fcos(theta) Fsin(theta Ib lb Ib 45 0.866 39.0 22.5 72 0.866 62.4 -36.0 32 0.000 0.0 -32.0 38 -0.866 ed -19.0 68.4 9.5 Resultant Magnitude of Force = 69.1 Angle of the Resultant Force = 79 Moments and Couples * A moment about a point is defined as the product of a force magnitude and the perpendicular distance from the force line of action to that point. Moment Magnitude, |M| = |F|*d ae) kee perpendicular distance fl | |  (Mik Fe OD = Yar— Xa (5) BWM, -0 Me, = 0 ® docsity.com  Moments, con’t. ¢ The following yield identical moments about A: UR dh oy san  Moment = + |OA| sind *F docsity.com What is the total moment about corner A? aan | SON OPE oa aemmen OTN Tan) 400 (sin 45°) N EON 100 N I SaemaOlN | 6 m by 6m square rN 6m rs] O (e = (200 - 100 N) *6m+ (100 sin 45°N)* 3m -(50N)*6m= 371Nm SS e z docsity.com  Leen ently ¢ Forces are vectors. ee fe] arcle lee fe) pene * you must decompose into components ¢ add magnitudes of colinear components ¢ called resolution ¢ Moments are caused by forces acting at a perpendicular distance from a point docsity.com