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1. STRENGTH OF MATERIAL/MECHANICS OF MATERIAL / Course number - CEng2101 course title - strength of material program - BSc degree in civil engineering module – fundamental structural engineering theories Course objective Determine the mechanical behavior of solid bodies (stress, strain, strength, stiffness, deflection and stability) subjected to various types of loading Enhance for the determination of stress due to axial loading ,bending, shear, torsion or a combination Determine internal forces and bending moment at a section of beam and draw Axial force, shear force and bending moment diagrams

2. Cont.d To evaluate the external reactions ,the deformed shape and internal stresses in the structure To evaluate stress, strain for axial loading ,bending To evaluate torsional stress of a circular shaft and non circular members To analyze plane stress and stability of compressive members Enhance the determination of deflection for statically determinate structures Course description The course covers the following : introduction to , stress and strain of axially loaded members, internal actions in beams, torsion ,flexural and shearing stresses in beams, analysis of plane stress, deflection statically determinate structures and stability of compressive members.

3. Course outline Chapter 1: Introduction Chapter 2 : Stress and strain of axially loaded members 2.1. Introduction 2.2. Stress 2.2.1. normal stress under axial loading 2.2.2. Shearing stress 2.2.3. Allowable stresses and Allowable loads 2.2.4. Design of axially loaded members 2.3. Strain 2.3.1. normal strain under axial loading 2.3.2. stress- strain diagram 2.3.3. hook’s law , modulus of elasticity 2.4. deformation of members under axial loading 2.5. thermal strain 2.6. Poisson's Ratio and generalized Hook's law

4. Cont’d Chapter 3: Internal Actions in Beams 3.1. Introduction 3.2. Types of beams, loads and reaction 3.3. Diagrammatic representations of internal actions in beams 3.4. Axial force ,shear force and bending moments 3.5. Axial force ,shear force and bending moments diagrams 3.6. Relationships between loads ,shear forces and bending moment Chapter 4 : Torsion 4.1. Introduction 4.2. Torsion of circular shaft 4.3. Torsion of a thin-walled members 4.4. Torsional deformation in a circular shaft 4.5. Angle of twist

5. Cont’d Chapter 5: Flexural and shearing stress in beams 5.1. Introduction 5.2. stress due to pure bending 5.3. stress distribution 5.4. shearing stress in beams 5.5. unsymmetrical bending 5.6. stresses under combined loading Chapter 6: Analysis of plane stress 6.1. introduction 6.2. compound stresses , combined stresses 6.3. transformation of plane stress 6.4. . transformation of plane stress and strain 6.4.1. . transformation of plane stress 6.4.2. principal stresses : maximum shearing stress 6.4.3. Mohr’s circle of stress and strain

6. Cont’d Chapter 7 : Deflection of statically determinate structures 7 .1. direct integration method 7 .2. moment area method 7.3. conjugate beam method 7.4. virtual work method 7.5. principle of super position Chapter 8: Stability of compressive members 8.1. introduction 8.2. Buckling and stability 8.3. Euler’s formula for Pin-ended columns 8.4. Euler’s formula to columns with other end conditions

7. Cont’d Pre- requisites – GEng2042, CEng2051 References: A.kassimali , Structural Analysis 4 th edition. Christopher M.Shortt,2011 Dietmar Gross, Wolfgang Ehlers, Peter Wriggers , Statics-Formulas and problems, Springer- Verlag GmbH Germany 2017 Ferdinand P.Beer and E.Russel Johnston,Jr ., Mechanics of Materials 6 th edition. Mackgraw-Hill,2012 James M.Gere and Barry J.Goodno Mechanics of Materials 7 th Edition. Cengage Learning,2009 J.L Meriam , L.G Kraige Engineerning mechnics I, 8 TH Edition, Jhon Wiley Sons Singapore, 2016 Kenneth M.leet , Chia-Ming Uang and Anne M. Gilbert Fundamentals of Structural Analysis, 5 th edition. MackGraw-Hill eduction,2018 Michael E. Plesha,Gary L.Gray , Engineerning Mechnics :Statics, MackGraw-Hill Companies, Inc.2010 R.C. Hibbler,structural Analysis,8 th edition . Prentice Hall, Pearson Eduction , Inc.2012

8. Chapter 1: Introduction to strength of Materials 1.1. Introduction Mechanics of materials is a branch of applied mechanics that deals with the behavior of solid bodies subjected to various types of loading. Other names for this field of study are strength of materials and mechanics of deformable bodies . The solid bodies considered in this course include bars with axial loads, shafts in torsion , beams in bending , and columns in compression . The principal objective of mechanics of materials is to determine the stresses, strains, and displacements in structures and their components due to the loads acting on them . If we can find these quantities for all values of the loads up to the loads that cause failure, we will have a complete picture of the mechanical behavior of these structures . An understanding of mechanical behavior is essential for the safe design of all types of structures , whether airplanes and antennas, buildings and bridges, machines and motors, or ships and spacecraft. Theoretical analyses and experimental results have equally important roles in mechanics of materials .

9. Cont’d.. We use theories to derive formulas and equations for predicting mechanical behavior, but these expressions cannot be used in practical design unless the physical properties of the materials are known. Such properties are available only after careful experiments have been carried out in the laboratory. Furthermore , not all practical problems are amenable to theoretical analysis alone , and in such cases physical testing is a necessity . Mechanics of s o lid body can b e classified as mechanics of deformable bodies and mechanics of rigid bodies (Statics and Dynamics where deformation is to be ignored ). Mechanics of Materials (traditionally called Strength of Materials) is concerned with the analytical determination of the strength, stiffness and stability characteristics of structures or structural members. Strength : the maximum load carrying capacity before breaking or rupture. Stiffness : the ability to support loads without excessive deformation. Stability : the ability to carry (compressive) loads without a sudden change in configuration (or buckling).

10. 1.2 Mechanical properties of materials To ensure a safe design, specific material properties have to be taken into account. The essential information is collected by conducting different tests in a material testing laboratory. Some of the properties will be discussed below . Tensile Strength : - this is the ability of a material to withstand stretching loads without breaking The applied load P is trying to stretch the rod. Therefore , the rod is said to be in tension, so the material from which the rod is made needs to have sufficient tensile strength to resist the pull of the load. Fig . 1.1 Deformation of axially-loaded(tensile load) rod.

11. Mechanical properties of materials c o nt’d……. Tension test: the most commonly used tension tests for determining mechanical properties are: Strength, Ductility, Toughness, Elastic Modulus, Strain Hardening. Compressive strength : - this is the ability of a material to withstand compressive (squeezing) loads without being crushed or broken. This body component needs to be made from material with adequate compressive strength to resist the given load P . Fig . 1.2 axially-loaded(compressive load) rod. Shear strength : - this is the ability of a material to withstand offset loads, or transverse cutting (shearing actions) Fig. 1.3 (a) A rivet joining two metal bars together. (b). Shear failure

12. Mechanical properties of materials c o nt’d…….. Because the loads are not exactly in line, they are said to be off-set and, therefore, the load on the rivet is called a shearing load , i.e., the rivet is said to be in shear. If the rivet material does not have sufficient shear strength to resist the loads, the rivet will break (shear off) as shown in fig 1.3. b and the loads acting on them will move apart. The same effect can be caused by loads pushing on the ends of the two metal bars joined by the rivet. Toughness (impact resistance): - this is the ability of a material to withstand shatter . If a material shatters , it is brittle such as glass whereas rubbers and most plastic materials do not shatter, therefore, they are tough . Rigidity (stiffness ):- this is the measure of the ability not to deflect under an applied load . E.g . Under a light load cast iron deflects less than steel since cast iron is more rigid. But steel is much stronger than cast iron. Thus a material which is rigid is not necessarily strong. Brittleness : - materials that fail in tension at relatively low values of strain (deformation per unit length) are classified as brittle materials.

13. Mechanical properties of materials c o nt’d…….. Elasticity : - the ability of a material to deform under load and return to its original shape and size when the load is removed. If it is made from an elastic material it will be the same length before and after the load is applied, despite the fact that it will be longer whilst the load is being applied. This is only true for most materials if the load is relatively small and within the elastic range of the material being tested. Fig. 1.4 elastic extension of axially loaded bar

14. Mechanical properties of materials c o nt’d…….. Plasticity : - this property is the exact opposite to elasticity . It is the state of a material that has been loaded beyond the elastic state. The body which is under a load beyond the required to cause elastic deformation, then that material deforms permanently. It takes a permanent set and will not return to its original shape and size when the load is removed. Ductility and Malleability are particular cases of the property of plasticity . Ductility : -this is the term used when plastic deformation occurs as a result of applying a tension force . It is property of a material to sustain large strains at fracture. Malleability : -this is the term used when plastic deformation occurs as a result of applying a compressive load . A malleable material is required for processes as rolling and rivet heading. In forming the head of a rivet by hammering, the rivet needs to be made from a malleable material to withstand this treatment.

15. Mechanical properties of materials c o nt’d…….. Fig. 1.5 forming the head of a rivet by hammering Hardness : this is defined as the ability of a material to withstand scratching (abrasion) or indentation by another hard body. It is an indication of the wear resistance of the material. Hardness is often defined as the resistance of a material to penetration . The ball only makes a small indentation in the hard material, but it makes a very much deeper indentation in the softer material . Hardness is often tested in this manner. Fig. 1.6 Hardness test