# ENGRMAE 150 Mechanics of Structures (2011-2012)

#### ENGRMAE 150 Mechanics of Structures

**ENGRMAE 150 Mechanics of Structures (Credit Units: 4)** Stresses and strains. Torsion. Bending. Beam deflection. Shear force and moment distributions in beams. Yielding and buckling of columns. Combined loading. Transformation of stresses and strain. Yielding criteria. Finite elements analysis of frames. Dynamics of a two-bar truss. Prerequisite: Engineering MAE30 or ENGR30; Mathematics 2J. Same as ENGR 150. Only one course from ENGRMAE 150, ENGR 150, ENGRCEE 150 may be taken for credit. (Design units: 2)

- Beer and Johnson, Mechanics of Materials, 5th Ed., McGraw-Hill, 2009.
- Chandrupatla and Belegundu, Introduction to Finite Elements In Engineering, 3rd ed., Prentice Hall, 2001.

1. Learn the fundamentals of stress, strain and elastic behavior. (EAC a)

2. Draw axial force, shear and bending moment diagrams of one-dimensional members subject to simple and combined loading. (EAC a)

3. Compute stress and strains in cables, bars, beams and columns; compute deflection of beams; and compute buckling load of compression members. (EAC a)

4. Learn the most widely used failure criteria to assess the safety of structures. (EAC a, EAC e, EAC f)

5. Learn the basic principles of mechanics of materials and apply them to assemblies of one-dimensional elements (trusses and frames). (EAC a, EAC e)

6. Understand how to code a finite element program (e.g. in MATLAB) for the analysis of arbitrarily complex trusses and frames. (EAC a, EAC e, EAC i)

7. Identify, formulate, and solve engineering problems that are related to the response of materials to various types of loads. (EAC c, EAC e, EAC i)

Newtonian mechanics, kinematics and dynamics of motion. Statics of solid bodies and structures. Differential and integral calculus of real functions in real variables. Linear algebra: elementary matrix manipulations. Familiarity with scientific programming.

- Stresses; Stress in Axially Loaded Members (1 week)
- Strains; Stress-Strain Diagram; Axial Deformation (1 week)
- Torsion (1 week)
- Shear Force and Bending Moment Diagrams (1 week)
- Bending Stress in Beams (1 week)
- Transverse Loading and Shearing Stress in Beams (1 week)
- Stresses Under Combined Loading (1 week)
- Transformation of Stresses; Design of Beams (1 week)
- Deflection of Beams; Statically Indeterminate Problems (1 week)
- Columns (1 week)

Meets for 3 hours of lecture and 1 hour of discussion each week for 10 weeks.

Students will use a commercial programming language (e.g. MATLAB) to write a finite element code that allows the solution of arbitrarily complex trusses and frames.

None.

Contributes towards the Aerospace and Mechanical Engineering Design.

Various design projects: For example, students will design, fabricate and test a minimum-weight truss structure that satisfies prescribed load-bearing requirements, subject to other design constraints. Students will design, fabricate and test a minimum-weight truss structure that satisfies prescribed load-bearing requirements subject to other design constraints. In addition to this, the design activity involves short design problems which are incorporated into the homework assignments and which introduce the phases of design. These problems address: (a) factor of safety and allowable stresses, (b) basic considerations for the design of prismatic beams, and (c) factors involved in the design and use of pressure vessels.

- Problem Sets: 35%
- Design Project: 10%
- Midterm Exam: 25%
- Final Exam: 30%
- Total: 100%

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 4.0 credit units

Engineering Science: 2.0 credit units

Engineering Design: 2.0 credit units