CIVL222 STRENGTH OF MATERIALS

Chapter 1General Introduction

Instructor: Dr. Mürüde ÇelikağOffice : CE Building Room CE230 and GE241 E-mail : murude.celikag@emu.edu.tr

1. INTRODUCTION

• Statics

• Dynamics

• Strength of Materials

There are three fundamental areas of Engineering Mechanics:

Study of the external effects of forces on rigid bodies. Deformation of bodies can be neglected.

Statics & Dynamics

P

Bar is assumed to be rigid and strong enough to carry the loads

Example

Deals with the relationship between externally applied loads and their internal effects on bodies. Deformation of bodies cannot be neglected.

Strength of Materials

P

Investigates the bar to ensure that it is strong enough not to break and bend without supporting the load

Example

Requires both dimensions and material properties to satisfy the acceptable level of strength and rigidity. A structure and its elements should not break/deform excessively under loads.

Mechanical Design

Engineering Parts

• strength• small deflections due to imposed loads while in operation• slender members should not buckle

• Analysis of stress and deformation

• Determination of the largest load that a structure can sustain without any damage, failure or compromise of function

• Determination of body shape and section of the most suitable construction material that is capable of resisting the forces acting on the structure under specific environmental conditions.

1.1 Main Objectives of Strength of Materials

1.2 Method of Analysis

• Mechanics of Materials theory uses assumptions, based on experimental

• Theory of Elasticity: Mathematical method that can provide “exact” results for simple problems, however, in general solutions are obtained with considerable difficulty.

Method of Equilibrium

• STATICS: laws of forces

• DEFORMATIONS: laws of material deformations,

e.g. Hook’s Law

• GEOMETRY: deformation of adjacent portions of

a member must be compatible.

Can be used for the complete analysis of structural members, however, the following basic principles of analysis should be considered.

Energy Methods

Can be used as an alternative to the equilibrium methods in order to analyze the stress and deformations. Both methods can provide solutions of acceptable accuracy for simple problems and can be used as the basis for numerical methods in more complex problems.

1.3 Conditions of Static Equilibrium

x x

y y

z z

Equations of Equilibrium

F 0Vector

M 0

F 0 M 0Scalar F 0 M 0

F 0 M 0

Branch of physical sciences concerned with the state of

rest or motion of bodies subjected to forces.

Mechanics:

Statics Dynamics

Rigid Bodies Deformable Bodies

Solid Mechanics Fluid Mechanics

Engineering Mechanics

Other Names1. Strength of Materials2. Mechanics of Materials3. Introduction to Solid Mechanics4. Mechanics of Deformable Bodies

Deformable Bodies

equilibrium (statics) materials selection

(e.g. wood, steel, concrete, aluminum) geometry

Depends on

Fundamental Concepts

• Force Equilibrium• Force - Deformation Behavior of

Materials• Geometry of Deformation

Fundamental Concepts

• Force Equilibrium• Force –Temperature - Deformation

Behavior of Materials• Geometry of Deformation

Deformable Body

A solid body that changes size and/or shape as a result of loads that are applied to it

or

as a result of temperature changes.

Definition

Changes in size and/or shape are referred to as

deformations

Look at the Diving Board

A

B

W

L1 L2

h

c

M

Statics

Given W, L1 and L2 calculate:

• Reaction at A• Reaction at B

Other Types of Questions1. What weight W would break the board?

2. What is the relationship between dc and W?

3. Would a tapered board be “better” than a constant thickness board?

4. Would an aluminum board be preferable to a fiberglass or a wooden board?

Answers

1. Requires us to consider the diving board as a deformable body

2. Need to consider not only reaction forces but localized effects of forces (i.e. stress distribution and strain distribution)

3. Need to consider material behavior (stress-strain behavior)

Analysis and Design

• Strength Problems

• Stiffness Problems

Strength Problems

Is the machine or structure “strong” enough?-------------------------------------

Will the object or structure or component support the loads to which it is subjected?

Stiffness Problems

Is the machine or structure “stiff” enough? ----------------------------------------

What is the change in shape or deformation of the object due to the loads? Is its deformation within acceptable limits?

Questions

1. What weight W would break the board? (STRENGTH)

2. What is the relationship between dc and W? (STIFFNESS)

Other Questions• What weight W would break the board?

(ANALYSIS)

• What is the relationship between dc and W? (ANALYSIS)

• Does the thickness of the board, h, affect dc?

• Would an aluminum board deflect more or less than a fiberglass or a wooden board?

• Does the position of support B change any of the answers?

Analysis/Design

• What weight W would break the board? (ANALYSIS)

• What is the relationship between dc and W? (ANALYSIS)

• Would a tapered board be “better” than a constant thickness board? (DESIGN)

• Would an aluminum board be preferable to a fiberglass or a wooden board? (DESIGN)

Fundamental Types of Equations

• The EQUILIBRIUM conditions must be satisfied.

• The GEOMETRY OF DEFORMATIONmust be described.

• The MATERIAL BEHAVIOR must be characterized.

Equilibrium

External forces, including reactions must balance.This is basically an application of the concepts andprinciples of statics. It is essential that accurateand complete FREE BODY DIAGRAMS bedrawn.

Geometry of Deformation

1. Definitions of extensional strain and shear strain.

2. Simplifications and idealizations.

3. Connectivity of members or geometric compatibility.

4. Boundary conditions and constraints.

Material Behavior

Constitutive behavior of materials (force-temperature-deformation

relationships)must be described.

These relationships can only be established experimentally!

Problem Solving Procedure

1. State the problem.

2. Plan the solution.

3. Carry out the solution.

4. Review the solution.

State the Problem

1. List the given data.

2. Draw any figures needed to describe the problem.

3. Identify the results to be obtained.

Plan the Solution1. Consider given data and results

desired.2. Identify basic principles involved.3. Recall applicable equations.4. Identify assumptions.5. Plan steps in the process.6. Estimate the answer!

Carry Out the Solution

1. Consistent units.

2. Significant digits.

3. Identify answers.

Review the Solution

1. Dimensionally correct

2. Reasonable values.

3. Correct algebraic sign.

4. Consistent with assumptions.

5. Presentation neat and orderly.

6. What point did the problem illustrate?

Review of Statics

x x

y y

z z

Equations of Equilibrium

F 0Vector

M 0

F 0 M 0Scalar F 0 M 0

F 0 M 0

Free Body Diagrams1. Determine the extent of the body to be included.

2. Completely isolate the body from supports and other attached bodies.

3. If internal resultants are desired, pass a sectioning plane through the member at the appropriate location.

4. Sketch the outline of the resulting Free Body.

Free Body Diagrams

5. Indicate on the sketch all externally applied loads.

6. Clearly indicate the location, magnitude and direction of each load.

Free Body Diagrams

7. At supports, connections and section cuts, show unknown forces and couples.

8. Assign a symbol to each unknown.

9. Use sign convention to assign positive sense to unknowns or assign it arbitrarily.

10.Label significant points and dimensions.

11.Show reference axes.

Free Body Diagram of Diving Board

A

B

W

L1 L2

hM

Identify the object

Isolate and sketch.

Show all forces including reactions.

External Loads

1. Concentrated Loads

Point Forces (F)

Couples (F - L)

2. Line Loads (F/L)

3. Surface Loads (F/L2)

4. Body Forces (F/L3)

External Loads

SUPPORT TYPES

Internal Resultants

xFAxial Force

x

y

z

xFx

y

z

xVy

Shear Forces

xVz

Internal Resultants

xFx

y

z

xVy

xVz Torque or Twisting Moment

xT

Internal Resultants

Internal ResultantsTorsion

xFx

y

z

xVy

xVz

Bending Moments

xT

xMy

xMz

Internal Resultants

Internal ResultantsBending Moment

xFx

y

z

xVy

xVz xT

xMy

xMz

Internal Resultants