Mechanics of Materials MAE 243 (Section 002)Spring 2008Dr. Konstantinos A. Sierros

General info M, W, F 8:00-8:50 A.M. at Room G-83 ESB Office: Room G-19 ESB E-mail: kostas.sierros@mail.wvu.edu Tel: 304-293-3111 ext.2310Course notes: http://www.mae.wvu.edu/~cairns/teaching.html USER NAME: cairns PASSWORD: materials Facebook : Konstantinos Sierros (using courses: Mechanics of Materials) Office hours: M, W 9:00-10:30 A.M. or by appointment

Course textbookMechanics of Materials, 6th edition, James M. Gere, Thomson, Brooks/Cole, 2006

Why do we study Mechanics of Materials?Anyone concerned with the strength and physical performance of natural/man-made structures should study Mechanics of Materials

Why do we study Mechanics of Materials?SAFETY and COST !!

Structural integrity of materials is important

1.1: Introduction to Mechanics of MaterialsDefinition: Mechanics of materials is a branch of applied mechanics that deals with the behaviour of solid bodies subjected to various types of loading Compression Tension (stretched) Bending Torsion (twisted) Shearing

1.1: Introduction to Mechanics of MaterialsFundamental concepts stress and strain deformation and displacement elasticity and inelasticity load-carrying capacity Design and analysis of mechanical and structural systems

1.1: Introduction to Mechanics of Materials Examination of stresses and strains inside real bodies of finite dimensions that deform under loads In order to determine stresses and strains we use:Physical properties of materialsTheoretical laws and concepts

Problem solving Draw the free-body diagram Check your diagram Calculate the unknowns Check your working Compute the problem Check your working Write the solution Check your working

Free body diagrams I

Free body diagrams II

Statics example200kNA steel beam with a tensile strength of 700 MPA is loaded as shown. Assuming that the beam is made from hollow square tubing with the dimensions shown will the loading in the x direction exceed the failure stress?342m0.02m0.01m

200kN342m160kN120kN120N160kN240kN.mStep 1: Free body diagram

Step 2: Calculate moment of inertia0.02m0.02m0.01mI=1/12 x (0.024)- 1/12 x (0.014) m4=1.25 x 10-8 m4A=0.022-0.012 m2=0.0003 m2

Step 3: Shear and moment diagrams200kN342mVx120Mx-240

Stress due to axial loading

Stress due to bending

ANS: Total stress greater than failure stress therefore failure will occur

Step 4: Calculation of maximum tensile stress

Key to success Ask questions and seek help if you feel like it!!!