Chapter 1 General Introduction Instructor: Dr. Mürüde Çelikağ Office : CE Building Room CE230 and GE241

Transcription

1 CIVL222 STRENGTH OF MATERIALS Chapter 1 General Introduction Instructor: Dr. Mürüde Çelikağ Office : CE Building Room CE230 and GE241 murude.celikag@emu.edu.tr

2 1. INTRODUCTION There are three fundamental areas of Engineering Mechanics: Statics Dynamics Strength of Materials

3 Statics & Dynamics Study of the external effects of forces on rigid bodies. Deformation of bodies can be neglected. Example P Bar is assumed to be rigid and strong enough to carry the loads

4 Strength of Materials Deals with the relationship between externally applied loads and their internal effects on bodies. Deformation of bodies cannot be neglected. Example P Investigates the bar to ensure that it is strong enough not to break and bend without supporting the load

5 Mechanical Design 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. Engineering Parts strength small deflections due to imposed loads while in operation slender members should not buckle

6 1.1 Main Objectives of Strength of Materials 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.

7 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.

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

9 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.

10 1.3 Conditions of Static Equilibrium Equations of Equilibrium F 0 Vector M 0 Fx 0 Mx 0 Scalar Fy 0 My 0 Fz 0 Mz 0

11 Mechanics: Branch of physical sciences concerned with the state of rest or motion of bodies subjected to forces.

12 Engineering Mechanics Solid Mechanics Fluid Mechanics Rigid Bodies Deformable Bodies Statics Dynamics

13 Other Names 1. Strength of Materials 2. Mechanics of Materials 3. Introduction to Solid Mechanics 4. Mechanics of Deformable Bodies

14 Deformable Bodies Depends on equilibrium (statics) materials selection (e.g. wood, steel, concrete, aluminum) geometry

15 Fundamental Concepts Force Equilibrium Force - Deformation Behavior of Materials Geometry of Deformation

16 Fundamental Concepts Force Equilibrium Force Temperature - Deformation Behavior of Materials Geometry of Deformation

17 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.

18 Definition Changes in size and/or shape are referred to as deformations

19 Look at the Diving Board

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22 A L 1 L 2 W M h c B

23 Statics Given W, L 1 and L 2 calculate: Reaction at A Reaction at B

24 Other Types of Questions 1. What weight W would break the board? 2. What is the relationship between d c 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?

25 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 (stressstrain behavior)

26 Analysis and Design Strength Problems Stiffness Problems

27 Strength Problems Is the machine or structure strong enough? Will the object or structure or component support the loads to which it is subjected?

28 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?

29 Questions 1. What weight W would break the board? (STRENGTH) 2. What is the relationship between d c and W? (STIFFNESS)

30 Other Questions What weight W would break the board? (ANALYSIS) What is the relationship between d c and W? (ANALYSIS) Does the thickness of the board, h, affect d c? 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?

31 Analysis/Design What weight W would break the board? (ANALYSIS) What is the relationship between d c 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)

32 Fundamental Types of Equations The EQUILIBRIUM conditions must be satisfied. The GEOMETRY OF DEFORMATION must be described. The MATERIAL BEHAVIOR must be characterized.

33 Equilibrium External forces, including reactions must balance. This is basically an application of the concepts and principles of statics. It is essential that accurate and complete FREE BODY DIAGRAMS be drawn.

34 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.

35 Material Behavior Constitutive behavior of materials (force-temperature-deformation relationships) must be described. These relationships can only be established experimentally!

36 Problem Solving Procedure 1. State the problem. 2. Plan the solution. 3. Carry out the solution. 4. Review the solution.

37 State the Problem 1. List the given data. 2. Draw any figures needed to describe the problem. 3. Identify the results to be obtained.

38 Plan the Solution 1. 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!

39 Carry Out the Solution 1. Consistent units. 2. Significant digits. 3. Identify answers.

40 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?

41 Review of Statics Equations of Equilibrium F 0 Vector M 0 Fx 0 Mx 0 Scalar Fy 0 My 0 Fz 0 Mz 0

42 Free Body Diagrams 1. 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.

43 Free Body Diagrams 5. Indicate on the sketch all externally applied loads. 6. Clearly indicate the location, magnitude and direction of each load.

44 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.

45 Free Body Diagram of Diving Board L 1 L 2 M A h W B

46 Identify the object

47 Isolate and sketch.

48 Show all forces including reactions.

49 External Loads 1. Concentrated Loads Point Forces (F) Couples (F - L) 2. Line Loads (F/L) 3. Surface Loads (F/L 2 ) 4. Body Forces (F/L 3 )

50 External Loads

51 SUPPORT TYPES

52 Internal Resultants y F x Axial Force x z

53 Internal Resultants y V y x Shear Forces F x x z V z x

54 Internal Resultants y V y x z V z x F x x T x Torque or Twisting Moment

55 Torsion Internal Resultants

56 Internal Resultants y Bending Moments M y x V y x F x x z M z x V z x T x

57 Bending Moment Internal Resultants

58 Internal Resultants y M y x V y x F x x z M z x V z x T x