Engineering Mechanics Statics

EEPIS

2012

Objectives

• To understand how to analyze the strength of the structures and materials in order to make good design in engineering

Missions

• To understand the resultant of force system

• To understand the free body diagram and equilibrium eq.

• To understand the types of structure

• To determine the center of mass, inertial moment, and center of force

• To determine internal load

• To understand the mechanical properties of material

• To determine axial load, torque, bending moment, & deformation

Logistics

• Hibbeler, R C., 2004. Statics and Mechanics of Materials, Prentice Hall, Inc

• Merriam, J L, Kraige L G., 2002. Engineering Mechanics Statics, John Wiley and Sons, Inc.

• Hibbeler, R C., 2007. Engineering Mechanics Statics, Prentice Hall, Inc

• Hibbeler, R C, 2011, Mechanics of Materials, Prentice Hall, Inc

Parameters

• Teamwork is recommended

• Mark:– Mid Exam : 25%– Final Exam : 40%– Assignment : 35%

• Cheating is intolerable

1.1 WHAT IS MECHANICS OF MATERIALS ?

1.2 THE FUNDAMENTALS CONCEPTS OF DEFORMABLE-BODY MECHANICS

1.3 PROBLEM - SOLVING PROCEDURES

1.4 REVIEW OF STATIC EQUILIBRIUM ; EQUILIBRIUM OF DEFORMABLE BODIES

1.5 PROBLEMS

1.1 WHAT IS MECHANICS OF MATERIALS

• Mechanics : branch of physical science concerned with the

condition of rest or motion of bodies due to forces

• Statics : mechanics of bodies at rest

• Dynamics : mechanics of bodies in motion

• Statics and dynamics applied for particles and rigid bodies

• Static and dynamics are also fundamental to mechanics of

materials

• Mechanics of materials = strength of materials = mechanics of

solids = mechanics of deformable bodies

1.1 WHAT IS MECHANICS OF MATERIALS (Cont’)

• Deformable bodies is a solid that changes size and/or shape

due to loads or temperature applied

• An example of a deformable body is the diving board

• Diving board change size and/or shape due to the weight of the

diver

• Deformation can be small, invisible to naked eyes

1.1 WHAT IS MECHANICS OF MATERIALS (Cont’)

• Statics can provide the reaction at A and B, if W, L1 , L2 are given

• Mechanics of materials can answer to the following questions :

- W which would cause the diving board to break, and

where it would occur

- the relation of C and W

- would a taper board be ‘better’ than constant thickness

- would fiber glass be preferable than aluminum

1.2 THE FUNDAMENTAL CONCEPTS OF DEFORMABLE-BODY MECHANICS

• Three fundamental concepts :

1. The equilibrium conditions must be satisfied

2. The geometry of deformation must be described

3. The material behavior (i.e. force-temperature-deformation relationship) must be characterized

Equilibrium :

• Principles of statics equations of equilibrium are fundamental

to the study of deformable body mechanics

Geometry of Deformation, including

• Definition of extensional strain and shear strain

• Simplification and idealization (e.g. rigid member, fixed support,

displacements are small)

• Connectivity of members, or geometric compability

• Boundary condition and other constraint

1.3 PROBLEM- SOLVING PROCEDURE

1. Select the system of interest

2. Reduce the real system to an idealized model

3. Convert the idealized model to a mathematical model

4. Perform a test to compare predicted responses to the behavior of

actual system

5. If prediction does not agree with prediction, make changes,

repeat step 1 - 4

• Diving board deformable

• Support rigid

• Diving board BD rigid

• Support deformable

FREE-BODY DIAGRAM (FBD)

• Isolate body of interest (including from it supports)

• Indicate all applied loads

• Show unknown forces and couples at support or connection to

other bodies

• Label significant points and include significant dimensions

SUPPORT REACTION AND MEMBER CONNECTIONS

A support gives reaction and also enforces constraint

1.4 REVIEW OF STATIC EQUILIBRIUM

Equation of equilibrium

• F = 0

(M)o = 0

• For a set of rectangular Cartesian axes, x, y, z

Fx = 0 ( Mx)o = 0

Fy = 0 ( My)o = 0

Fz = 0 ( Mz)o = 0

• Statically determinate : number of unknown = number of

independent equilibrium equation

• Statically indeterminate : number of unknown > number of

independent equilibrium equation

• Redundant : can be removed without destroying the equilibrium

MATERIAL BEHAVIOR

• Also termed constitutive behavior of materials: described the

material behavior (force-temperature-deformation relationships)

• obtained by conducting experiments

EXTERNAL LOADS

• Concentrated loads, including point forces (F) and couples (F.L)

• Line loads (F/L)

• Surface loads (F/L2)

• Body forces (F/L3)

INTERNAL RESULTANTS

• Internal resultants : forces couples that are internal to the original body

• Internal resultants can be obtained by virtually cutting the structure at the interested location

• Six internal resultants resulting from general loading

S-3A Full Scale Static Test. (http://www.voughtaircraft.com/ProdProg/qtls/testOps/StructuresTestLab/testHist.htm#fullScaleAir

S-3A Full Scale Static Test. (http://www.voughtaircraft.com/ProdProg/qtls/testOps/StructuresTestLab/testHist.htm#fullScaleAir