EMCH 213Strength of Materials

3 credits · Engineering Mechanics · Penn State

Axial stress and strain; torsion; stresses in beams; elastic curves and deflection of beams; combined stress; columns. E MCH 213 E MCH 213 Strength of Materials (3) In this elementary course on the strength of materials the response of some simple structural components is analyzed in a consistent manner using i) equilibrium equations, ii) material law equations, and iii) the geometry of deformation. The components analyzed include rods subjected to axial loading, shafts loaded in torsion, slender beams in bending, thin-walled pressure vessels, slender columns susceptible to buckling, as well as some more complex structures and loads where stress transformations are used to determine principal stresses and the maximum shear stress. The free body diagram is indispensable in each of these applications for relating the applied loads to the internal forces and moments and plotting internal force diagrams. Material behavior is restricted to be that of materials in the linear elastic range. A description of the geometry of deformation is necessary to determine internal forces and moments in statically indeterminate problems. The underlying mathematics are boundary value problems where governing differential equations are solved subject to known boundary conditions. Students will be able to:a) Identify kinematic modes of deformation (axial, bending, torsional, buckling and two dimensional) and associated stress states on infinitesimal elements and sketch stress distribution over cross sections b) Analyze determinate and indeterminate problems to determine fundamental stress states associated with kinematic modes of deformation c) Apply strength of materials equations (and formulas) to the solution of engineering and design problems d) Recognize and extract fundamental modes in combined loading and do the appropriate stress analysis e) Extract material properties (modulus of elasticity, yield stress, Poisson's ratio) from data and apply these in the solution of problems f) Calculate the geometric properties (moments of inertia, centroids, etc) of structural elements and apply these in the solution of problems.which will enable them to solve real engineering problems.