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7.23. Mechanics of Materials I (Mandatory)

7.23.1. Justification ↑ Back to top

Mechanics of Materials I studies the behavior of deformable solid bodies subjected to different types of loading. For the civil engineer, understanding concepts such as stress, strain, and elasticity is fundamental, since these allow the strength and stiffness of structural elements to be predicted. This knowledge is the basis for the safe design of beams, columns, and shafts, ensuring that materials operate within their allowable limits.

7.23.2. Generales Goals ↑ Back to top

1. Understand the concepts of stress and strain under axial, torsional, and bending loads.
2. Analyze the mechanical properties of materials from tension and compression tests.
3. Determine internal stresses and deformations in statically determinate structural elements.

7.23.3. Contribution to Outcomes ↑ Back to top

ABET-1) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. (Usage)

ABET-6) An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions. (Usage)

7.23.4. Content ↑ Back to top

7.23.4.1. Mechanics of Materials and Structural Behavior (24 hours) [Skills ABET-1,ABET-6] ↑ Back to top

Bibliography: (Gere and Goodno, 2017; Hibbeler, 2017a)

Topics

1. Stress and strain concepts including normal, shear, and principal stresses
2. Axial loading and deformation of members
3. Torsion of circular and non-circular sections
4. Bending stress and deflection in beams
5. Shear stress distribution in beams
6. Combined loading and stress transformation
7. Buckling of columns and stability analysis
8. Fatigue and fracture mechanics
9. Elastic and plastic behavior of materials
10. Energy methods for structural analysis

Learning Outcomes

1. Define stress, strain, and their relationships through constitutive laws [Familiarity]
2. Calculate stresses and deformations in members under axial loading [Usage]
3. Determine torsional stresses and angles of twist in shafts [Usage]
4. Analyze bending stress distribution and deflection in beams [Assessment]
5. Compute shear stress distribution in beam cross-sections [Usage]
6. Apply stress transformation equations for combined loading conditions [Assessment]
7. Evaluate column stability and calculate critical buckling loads [Assessment]
8. Explain fatigue failure mechanisms and predict fatigue life [Familiarity]
9. Distinguish between elastic and plastic material behavior under loading [Usage]
10. Use energy methods to solve deflection and indeterminate structural problems [Usage]

7.23.4.2. Axial Stress and Strain (16 hours) [Skills ABET-1,ABET-6] ↑ Back to top

Bibliography: (Hibbeler, 2017a)

Topics

1. Average normal and shear stress.
2. Normal and shear strain.
3. Hooke's law and the modulus of elasticity.
4. Axially loaded members: changes in length and statically indeterminate systems.

Learning Outcomes

1. Calculate stresses and deformations in bars subjected to axial load considering cross-sectional variations [Assessment].
2. Solve simple statically indeterminate structure problems using the deformation method [Usage].

7.23.4.3. Torsion and Pure Bending (20 hours) [Skills ABET-1,ABET-6] ↑ Back to top

Bibliography: (Gere and Goodno, 2017)

Topics

1. Torsion in circular shafts: the torsion formula and angle of twist.
2. Pure bending: bending deformation and the elastic flexure formula.
3. Shear stresses in beams: the shear flow formula.
4. Design of prismatic beams for strength.

Learning Outcomes

1. Determine the distribution of shear stresses in circular sections subjected to torque [Usage].
2. Calculate the maximum tensile and compressive stresses in beams under various bending moments [Assessment].

7.23.4.4. Stress Transformation and Combined Loading (20 hours) [Skills ABET-1,ABET-6] ↑ Back to top

Bibliography: (Hibbeler, 2017a; Gere and Goodno, 2017)

Topics

1. Plane stress transformation: general equations.
2. Mohr's circle for plane stress and strain.
3. Principal stresses and maximum shear stress.
4. Stress analysis under combined loading (axial, bending, and torsion).

Learning Outcomes

1. Use Mohr's circle to identify the planes where maximum stresses occur [Assessment].
2. Analyze the state of stress at a critical point of an element subjected to multiple types of loading [Assessment].

7.23.5. Bibliography ↑ Back to top

Gere, J. and Goodno, B. (2017). Mechanics of Materials. Cengage Learning, 9th edition.

Hibbeler, R. (2017a). Mechanics of Materials. Pearson, 10th edition.