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# Department of Mechanical Engineering

### MCEN 2063 - Mechanics of Solids

• Analyze statically indeterminate problems
• Analyze stresses in members subjected to temperature changes as well as applied loads.
• Understand the displacement method for systems with many elements subjected to axial loading.
• Develop the force-displacement relationships for trusses using the displacement method in a matrix analysis framework.
• Learn how to use load cells, an Instron tester, and dial indicators from a design optimization project involving an indeterminate structure.
• Learn to work on a small team as part of this project.

• Understand the basic relationships between torque, angular deflection,
shear stress, shear strain, and torsional stiffness.
• Determine stresses and deflections for statically determinant and indeterminate systems.
• Use the displacement method for torsional systems.
• Calculate power transmitted to rotating parts and its relationship to torque and speed.
• Become familiar with motors, angular measurement, and rotating components through a design optimization project involving the design of a rotating shaft.
• Learn to work in small teams.

3. Shear and Bending in Beams

• Develop both shear and bending moment diagrams.
• Understand and derive the differential equations relating load, shear and bending moment.
• Solve for shear and bending moments in a beam when the applied loads are described by singularity functions.

4. Beam Flexure

• Derive and determine shear and normal stress.
• Derive and determine deflections in beams subjected to bending.
• Perform stress and deflection analyses of beams containing non-uniform cross-sections.
• Use double integration and superposition methods to obtain beam deflections.
• Solve simple statically indeterminate problems.
• Learn to apply strain gages, perform some simple machining, and understand
• Wheatstone bridges via a design optimization project involving the design of a beam subjected to a given load.

5. Stress and Strain

• Understand the general state of stress at a point on a body in three dimensions.
• Understand the equilibrium relationships of stress components at a point in a body in a state of plane stress or plane strain.
• Perform stress and strain transformations and determine the principal and maximum shear stresses in a body.
• Calculate the stresses in thin walled pressure vessels(cylindrical and spherical).
• Develop the relationship between strain and displacement in a body subjected to plane strain or plane stress.
• Understand the relationship between stress and strain for linear elastic materials.

• Calculate the stresses in a body subjected to combined axial, bending and/or torsional loading.

7. Buckling

• Derive relationships leading to the calculation of critical buckling loads for axial loaded beams with different boundary conditions.

Catalog Description

Shear force and bending moment; Torsion; Stresses in beams; Deflection of beams; Matrix analysis of frame structures; Analysis of stress and strain in 2-D and 3-D (field equations, transformations); Energy methods; Stress concentrations; Columns. Lectures and homework assignments involve computer work and hands-on laboratory work in the ITLL, documented by written reports. Prerequisites: MCEN 2023

Prepared by J. Zable and M. Dunn 1/21/98