Università degli Studi di Bari. mechanics 1. Load system determination. Joint load. Stress-strain distribution. Biological response 2/45 3/45

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1 Università degli Studi di Bari mechanics 1 Load system determination Joint load Stress-strain distribution Biological response 2/45 3/45

2 ? 4/45 The human body machine Energy transformation Work development 5/45 Bodies interaction Movement external effects Deformation internal effects 6/45

3 Material chemical bond strenght 7/45 Material properties mechanical structure of materials macrostructure 8/45 macrostructure Material is: continuous and homogeneous mechanical described by its average properties which are obtained from specimen evaluation isotropic 9/45

4 Mechanics Statics - study of systems that are in a constant state of motion, whether at rest with no motion or moving at a constant velocity without acceleration Statics involves all forces acting on the body being in balance resulting in the body being in equilibrium 10/45 The body The body is a system modelled as: point Kinetics study rigid body Static study deformable body Stress strain description Body mass 11/45 Newton s 1 st Law of Motion An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. 12/45

5 load Load is the parameter which defines the effects of bodies interaction. It is a vector (four features) a quantity possessing magnitude, direction, sense and one application point A D E B C 13/45 F Load system; Stress strain distribution; Behaviour of material. Aims A D E B C E 14/45 Vector magnitude, direction, sense and one application point 15/45

6 Components of Force The magnitude or how much force is applied; direction: The way in which the force is applied; The point of application : Where the force is applied on the body; the sense of a vector is specified by the order of two points on a line parallel to the vector 16/45 Components of Force y Fx F Fy o x 17/45 Components of Force F 1 F 2 F 1 R F 1 R = F 1 + F 2 F i F n F 2 18/45

7 Newton s 2 nd Law of Motion A force or torque acting on a body will produce an acceleration proportional to the force or torque F = ma M= I α 19/45 Newton s 3 rd Law of Motion For every action there is an equal and opposite reaction (torque and/or force) 20/45 load static dynamic distributed concentrated 21/45

8 Moments of Force (Torque) The turning effect of a force is known as the moment. It is the product of the force multiplied by the perpendicular distance from the line of action of the force to the pivot or point where the object will turn. Momentum (quantity( of motion) - equal to mass times velocity F d M = F d P 22/45 Moments of Force 23/45 transport moment P C = M = F d F d P F C P global effect of F in P 24/45

9 force effects External movement force translation moment rotation Internal shape changement shape changement strain stress force linear changement moment angular changement 25/45 force effects External movement rigid body Internal shape changement deformable body 26/45 27/45

10 Rigid body Rigid body: a system of mass points where the distances between all pairs of points remain constant independently from the load applied system. If there are N free particles, there are 3N degrees of freedom For a rigid body, the number of degrees of freedom is reduced by the constraints expressed in the form: r = ij c ij How many independent coordinates does a rigid body have? 28/45 degrees of freedom independent coordinates = degrees of freedom (d.o.f.) Y A X Z A rigid body into the space has 6 d.o.f. : 3 translationals and 3 rotationals 29/45 constraints something that limits or restricts someone or something A B In order to cancel each d.o.f. a specific constraint have to be implemented 30/45

11 constraints A reaction force is developed when a constraint is active A B 31/45 constraint reaction forces? constraints A 32/45 constraints LABILE ISOSTATIC IPERSTATIC d.o.f. (3 in the plan - 6 in the space) 33/45

12 constraints ISOSTATIC BODY When constraints number is equal to d.o.f. without any omission or repetition 34/45 Ball-and-socket joint 35/45 Hinge joint 36/45

13 37/45 constraints