# Mechanics of Materials II

**Mechanical Engineering**

5.5 ECTS; 3º Ano, 1º Semestre, 15,0 T + 30,0 TP + 15,0 P + 3,50 OT

**Lecturer**

- Isabel Maria Duarte Pinheiro Nogueira

**Prerequisites**

Physical; Applied Mechanics;Mechanics of Materials I; Mechanical Behaviour of Materials.

**Objectives**

Students should learn how to determine beam stresses and deflections, articulated structures and columns using simplified methods, energy methods and finite element methods.

**Program**

1. Stress Analysis and Deformation:

1.1. Introduction

1.2. State Plane Stress

1.3. Principal stresses; Maximum voltage Court

1.4. Mohr's circle for the State Plane Stress

1.5. More general state voltages

1.6. Mohr Circle Application to Dimensional Analysis of Tensions

1.7. Fracture criteria for ductile materials in State Plane Stress

1.8. Fracture criteria for fragile materials in State Plane Stress

1.9. Stresses in Thin Walls tanks under pressure

1.10. Changes in the Plan status deformations

1:11. Mohr circle to the State Plan of deformations

1.12. Dimensional Analysis of Strain

1.13. Experimental Stress Analysis; Extensometry Electric

2. deformed calculation by integration of a beam

2.1. Introduction

2.2. Deformed a beam under Transverse Loading

2.3. Equation of the elastic curve

2.4. Determination of the tensile curve from a distributed load

2.5. Beams Statically Indeterminate

2.6. Overlay Method

2.7. Application Overlay Method in Beams Statically Indeterminate

3. Energy Methods

3.1. Introduction

3.2. Strain Energy

3.3. Strain Energy Density

3.4. Elastic deformation energy in Normal Tension

3.5. Elastic deformation energy in Corte voltages

3.6. Deformation energy for a General State of Stress

3.7. Impact loads

3.8. Scaling for Impact Load

3.9. Work and Energy uploads Concentrates

3.10. Deflection under concentrated load at Work Method - Energy

3.11. Working method and Energy in the presence of several shipments

3.12. Theorem Castigliano

3.13. Deformed by the Castigliano theorem

3.14. Statically Indeterminate Structures

4. Columns

4.1. Introduction

4.2. Stability of structure

4.3. Euler's formula for a bi-supported column

4.4. Extension of Euler columns of formula with other support

4.5. Off-center loading; Secant formula

4.6. Columns project under a focused charge

4.7. Columns project under an eccentric load

5. Finite Element Method:

5.1. Introduction to Finite Element Method

5.2. Using a commercial finite element code for the analysis of structures

**Evaluation Methodology**

Students are assessed through the works.

**Bibliography**

- Beer, F. e Johnston, E. e DeWolf, J. (2006). *Resistência dos Materiais*. (Vol. 1). (pp. 1-758). Brasil: McGraw-Hill Companies, Inc.

**Method of interaction**

Theoretical Lectures will describe and illustrate the application of fundamental principles. The classes wiil propose solving practical cases.

**Software used in class**