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Strength of Materials 2
| Code: | L.EC018 | Acronym: | RM2 |
| Keywords | |
|---|---|
| Classification | Keyword |
| OFICIAL | Basic Sciences |
Instance: 2025/2026 - 2S 
| Active? | Yes |
| Responsible unit: | Department of Civil and Georesources Engineering |
| Course/CS Responsible: | Bachelor in Civil Engineering |
Cycles of Study/Courses
| Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
|---|---|---|---|---|---|---|---|
| L.EC | 239 | Syllabus | 2 | - | 6 | 65 | 162 |
Teaching Staff - Responsibilities
| Teacher | Responsibility |
|---|---|
| Álvaro Alberto de Matos Ferreira da Cunha |
Teaching - Hours
| Lectures: | 2,50 |
| Recitations: | 2,50 |
| Type | Teacher | Classes | Hour |
|---|---|---|---|
| Lectures | Totals | 2 | 5,00 |
| Álvaro Alberto de Matos Ferreira da Cunha | 5,00 | ||
| Recitations | Totals | 8 | 20,00 |
| José Eduardo Tavares Quintanilha de Menezes | 2,50 | ||
| Aires Manuel Silva Colaço | 2,50 | ||
| Miguel Ângelo Carvalho Ferraz | 2,50 | ||
| Sérgio Bouça Pereira | 2,50 | ||
| Carlos Filipe Ferreira de Sousa | 2,50 | ||
| Álvaro Alberto de Matos Ferreira da Cunha | 1,25 | ||
| Luís Filipe Pereira Juvandes | 6,25 |
Fields changed: Observations, Obtenção de frequência
Teaching language
PortugueseObs.: Estudantes estrangeiros que frequentem a unidade curricular pela primeira vez devem compreender e falar Português.
Objectives
JUSTIFICATION:
Strength of Materials is an essential area of knowledge in a Civil Engineering degree. It deals with the different models of material behavior, which in the simplest case may be linear-elastic isotropic, and in other cases may include plasticity or brittle rupture effects, among others. It also studies the effects of applied forces and strains imposed on structures composed of linear parts, allowing the resulting stresses and strains to be calculated using simple models. It deals not only with homogeneous members, but also with structural elements composed of two or more materials.
OBJECTIVES:
The main objective of the Strength of Materials 2 course is to develop the engineering student's ability to analyse a given structural problem in a simple and logical way and apply some well-known fundamental principles to its solution. The aim is for the student to be able to determine the stresses and strains in any cross-section of a linear member that is a part of a reticulated isostatic or one time hyperstatic structure, as well as in pipes and vessels.
The problems of safety verification and design of real structures are solved in a simplified way, aiming at the acquisition by the student of basic knowledge in the field of Civil Engineering Structures, which will allow their further study in specialization course units.
Learning outcomes and competences
Knowledge: Know the fundamental concepts of Strength of Materials and the simplified models for determining the states of stress and strain in linear members, concerning shear and torsion effects (shear stress effects), combined effects of axial effort and bending moment (composed bending), present in isostatic or one time hyperstatic reticulated structures. Determine the states of stress and strain at a point in a continuous medium (solid mechanics). Know the fundamental concepts of elastic instability in axially compressed bars.
Understanding: Understand the structural behavior in service of three-dimensional reticulated systems. Understand the resistant behavior of linear members. Understand the implications, in terms of stresses and strains, of brittle materials in tension. Understand the determination of stresses and strains, and their principal directions, of plane stress and strain states. Understand the structural behavior of axially compressed bars exposed to elastic instability.
Application: Solve practical exercises directed towards the analysis of real problems in civil engineering.
Analysis: Analyze, discuss, and critically interpret the results, highlighting the models' potentialities and limitations.
Summary: Formulate simple solutions for practical applications in civil engineering.
Rating: Criticize the chosen solutions and methodologies used, demonstrating the capabilities of the models and their limitations.
Working method
PresencialPre-requirements (prior knowledge) and co-requirements (common knowledge)
PRIOR KNOWLEDGE:
Student should have attended, previously, the following Course Units: Mechanics 1, Mechanics 2 and Strength of Materials 1.
SIMULTANEOUS KNOWLEDGE:
As co-requisites, they must simultaneously attend the Mechanics 2 course unit.
SPECIAL RULES FOR MOBILITY STUDENTS:
Students must have previously attended the undergraduate Curricular Units introductory to the scientific theme dealt with in this subject. They must also fulfil the condition of Attendance in the current academic year.
Student should have attended, previously, the following Course Units: Mechanics 1, Mechanics 2 and Strength of Materials 1.
SIMULTANEOUS KNOWLEDGE:
As co-requisites, they must simultaneously attend the Mechanics 2 course unit.
SPECIAL RULES FOR MOBILITY STUDENTS:
Students must have previously attended the undergraduate Curricular Units introductory to the scientific theme dealt with in this subject. They must also fulfil the condition of Attendance in the current academic year.
Program
1. Shear force in bolted connections
1.1. Single shear.
1.2. Double shear.
1.3. Safety condition in ultimate limit state.
2. Shear flow and shear stress due to transverse shear
2.1. Shear flow.
2.2. Bolted connections subject to shear flow.
2.3 Shear stresses in member cross-section.
2.4. Shear stresses in open thin-walled sections.
2.5. Shear stresses in closed thin-walled sections.
2.6. The shear centre of the cross-section.
2.7. Deformation due to transversal shear.
2.8. Safety condition in ultimate limit state.
3. Stresses and strains due to torsional moment
3.1. Torque moment.
3.2. Shear stresses in solid or hollow circular cross-sections.
3.3. Twist of the cross-section caused by torsion.
3.4. Shear stress in rectangular cross-sections.
3.5. Membrane and hydrodynamic analogies.
3.6. Shear stress in open thin-walled sections.
3.7. Shear stress in closed thin-walled sections.
3.8. Safety condition in ultimate limit state.
3.9. Shear stress due to the combined effect of twist and transverse shear.
4. Composite bending and combined forces
4.1. Normal stresses in sections subjected to composite bending (N, Mx e My).
4.2. Concepts of pressure centre, neutral axis and central core.
4.3. Members of materials not resistant to normal tensile stresses.
4.4. Members subjected to centred or eccentric prestressing action.
4.5 Safety condition in ultimate limit state.
4.6. Members subjected to a general combination of stresses (N, M, V e T).
4.7. Stresses in the point neighbourhood (cube), in the cross-section plane and in the longitudinal shear plane.
5. State of stress and state of deformation at a point
5.1. Stress at a point. Von-Karman convention.
5.2. Characterisation of the state of stress at a point. Equilibrium conditions and analytical method.
5.3. Characterisation of the plane state of stress.
5.4. Plane stress transformation. Analytical method.
5.5. Plane stress transformation. Representation by Mohr's Circle.
5.6. Principal stresses and plans.
5.7. Three-dimensional analysis of the plane stress state. Absolute maximum stresses.
5.8. Stresses in thin-walled pressure vessels.
5.9. Hooke's Law Generalised.
5.10. Characterisation of the plane state of strain. Graphical representation.
5.11. Plane strain transformation. Analytical method.
5.12. Plane strain transformation. Representation by Mohr's Circle.
5.13. Principal stresses and directions.
5.14. Strain gauge rosettes.
6. Buckling of axially compressed members
6.1. Stable, indifferent, unstable equilibrium.
6.2. Critical load concept.
6.3. Euler's problem. Concepts of critical load, buckling length and slenderness coefficient.
6.4. Bars with different support conditions than Euler's problem.
6.5. Compressed members in trusses.
6.6. The most favourable orientation for the axially compressed member cross-section.
6.7. Safety check for axially compressed members.
DISTRIBUTION OF MATTERS:
Chap. 1: 5%; Chap. 2: 22%; Chap. 3: 15%; Chap. 4: 17%; Chap. 5: 24%; Chap. 6: 17%;Scientific Content – 70%
Technology Content – 30%
DEMONSTRATION OF THE SYLLABUS COHERENCE WITH THE CURRICULAR UNIT'S OBJECTIVES:
In this program, the study of Strength of Materials is based on the understanding of the classical simplified models that describe the behavior of materials and structures. The approach followed makes it possible to understand the necessary formulas, and to realize the conditions under which they can be safely applied in the analysis and design of real engineering structures.
1.1. Single shear.
1.2. Double shear.
1.3. Safety condition in ultimate limit state.
2. Shear flow and shear stress due to transverse shear
2.1. Shear flow.
2.2. Bolted connections subject to shear flow.
2.3 Shear stresses in member cross-section.
2.4. Shear stresses in open thin-walled sections.
2.5. Shear stresses in closed thin-walled sections.
2.6. The shear centre of the cross-section.
2.7. Deformation due to transversal shear.
2.8. Safety condition in ultimate limit state.
3. Stresses and strains due to torsional moment
3.1. Torque moment.
3.2. Shear stresses in solid or hollow circular cross-sections.
3.3. Twist of the cross-section caused by torsion.
3.4. Shear stress in rectangular cross-sections.
3.5. Membrane and hydrodynamic analogies.
3.6. Shear stress in open thin-walled sections.
3.7. Shear stress in closed thin-walled sections.
3.8. Safety condition in ultimate limit state.
3.9. Shear stress due to the combined effect of twist and transverse shear.
4. Composite bending and combined forces
4.1. Normal stresses in sections subjected to composite bending (N, Mx e My).
4.2. Concepts of pressure centre, neutral axis and central core.
4.3. Members of materials not resistant to normal tensile stresses.
4.4. Members subjected to centred or eccentric prestressing action.
4.5 Safety condition in ultimate limit state.
4.6. Members subjected to a general combination of stresses (N, M, V e T).
4.7. Stresses in the point neighbourhood (cube), in the cross-section plane and in the longitudinal shear plane.
5. State of stress and state of deformation at a point
5.1. Stress at a point. Von-Karman convention.
5.2. Characterisation of the state of stress at a point. Equilibrium conditions and analytical method.
5.3. Characterisation of the plane state of stress.
5.4. Plane stress transformation. Analytical method.
5.5. Plane stress transformation. Representation by Mohr's Circle.
5.6. Principal stresses and plans.
5.7. Three-dimensional analysis of the plane stress state. Absolute maximum stresses.
5.8. Stresses in thin-walled pressure vessels.
5.9. Hooke's Law Generalised.
5.10. Characterisation of the plane state of strain. Graphical representation.
5.11. Plane strain transformation. Analytical method.
5.12. Plane strain transformation. Representation by Mohr's Circle.
5.13. Principal stresses and directions.
5.14. Strain gauge rosettes.
6. Buckling of axially compressed members
6.1. Stable, indifferent, unstable equilibrium.
6.2. Critical load concept.
6.3. Euler's problem. Concepts of critical load, buckling length and slenderness coefficient.
6.4. Bars with different support conditions than Euler's problem.
6.5. Compressed members in trusses.
6.6. The most favourable orientation for the axially compressed member cross-section.
6.7. Safety check for axially compressed members.
DISTRIBUTION OF MATTERS:
Chap. 1: 5%; Chap. 2: 22%; Chap. 3: 15%; Chap. 4: 17%; Chap. 5: 24%; Chap. 6: 17%;Scientific Content – 70%
Technology Content – 30%
DEMONSTRATION OF THE SYLLABUS COHERENCE WITH THE CURRICULAR UNIT'S OBJECTIVES:
In this program, the study of Strength of Materials is based on the understanding of the classical simplified models that describe the behavior of materials and structures. The approach followed makes it possible to understand the necessary formulas, and to realize the conditions under which they can be safely applied in the analysis and design of real engineering structures.
Mandatory literature
Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David. F. Mazurek; Mecânica dos Materiais, MCGRAW-HILL, 2015. ISBN: 9788580554984Victor Dias da Silva; Mecânica e Resistência dos Materiais, Ediliber, 1995
Luís Filipe Pereira Juvandes; Resistência dos Materiais - Parte II, Efeitos Gráficos Unipessoal lda, 2023
Carlos Sousa, Miguel Ferraz e Castorina Vieira; Introdução às aulas teórico práticas de Resistência dos Materiais 2, 2024 (The document is available in the contents of the UC, in SIGARRA)
Complementary Bibliography
Russell C. Hibbeler; Mechanics of Materials in SI Units, 10/E. ISBN: 1292178205Comments from the literature
It is recommended to read the explanations about the topics covered in this course unit in at least one of the books indicated as "Compulsory Bibliography".Alternatively, the student may use the book indicated in the "Supplementary Bibliography".
Teaching methods and learning activities
Theoretical classes: contents exposition supported by multimedia resources; formulation and solution of typical problems at the end of each unit; Consultation of support worksheets available in the Sifeup’s webpage.
Theoretical-practical classes: distribution of worksheets with problems to solve, chapter by chapter; teacher’s support to the students, individually, throughout the solution; if the whole class has a common doubt, the teacher will clear it to the class, so that the problem can be surpassed.
DEMONSTRATION OF THE COHERENCE BETWEEN THE TEACHING METHODOLOGIES AND THE LEARNING OUTCOMES:
The used teaching methodologies allow to solve practical exercises directed to the analysis of real civil engineering problems, analysis, discussion and critical interpretation of results, emphasizing the potential of models and their limitations.
Theoretical-practical classes: distribution of worksheets with problems to solve, chapter by chapter; teacher’s support to the students, individually, throughout the solution; if the whole class has a common doubt, the teacher will clear it to the class, so that the problem can be surpassed.
DEMONSTRATION OF THE COHERENCE BETWEEN THE TEACHING METHODOLOGIES AND THE LEARNING OUTCOMES:
The used teaching methodologies allow to solve practical exercises directed to the analysis of real civil engineering problems, analysis, discussion and critical interpretation of results, emphasizing the potential of models and their limitations.
keywords
Technological sciences > Engineering > Civil engineering > Structural engineeringEvaluation Type
Distributed evaluation with final examAssessment Components
| Designation | Weight (%) |
|---|---|
| Teste | 25,00 |
| Exame | 75,00 |
| Total: | 100,00 |
Amount of time allocated to each course unit
| Designation | Time (hours) |
|---|---|
| Estudo autónomo | 97,00 |
| Frequência das aulas | 65,00 |
| Total: | 162,00 |
Eligibility for exams
Approval in the course unit implies compliance with the attendance requirement, considering that a student complies with this requirement if, having been regularly enrolled, the limit of 25% of absences for presential classes, of each type, is not exceeded. In addition to the cases identified in the FEUP rules, students who have obtained a final grade of 6 or higher in the course in the immediately preceding academic year are exempt from the attendance requirement.
This point refers only to the obligation of Frequency (Attendance). The information about grades and classifications is provided in a specific part of this document. It is emphasized that the student's classification in all the assessment components is always obtained in the school year in progress.
This point refers only to the obligation of Frequency (Attendance). The information about grades and classifications is provided in a specific part of this document. It is emphasized that the student's classification in all the assessment components is always obtained in the school year in progress.
Calculation formula of final grade
1. GENERAL ASPECTSThe Final Grade (CF) is defined based on a Distributed Assessment and a Final Exam in the Regular Season and/or in the Appeal Season. The Distributed Assessment is compulsory and it is not counted in the case of Exam for Improvement of Classification. . Students who do not succed in the Regular Season are admitted to the exam in the Appeal Season. All assessment components are expressed on a scale of 0 to 20.
2. DISTRIBUTED ASSESSMENT (AD)
The Distributed Assessment is compulsory and is always done for the school year in progress. It consists in two tests (AD1 and AD2), with equal quotations, and a total weight of 25%. These tests consist of a written test, without consultation, on dates to be announced. The material to be assessed in the 2 tests (AD1 and AD2), in terms of worksheets, will be announced after the publication of the timetable for distributed assessment tests defined by the Director of the L.EC. The student's classification in the Distributed Assessment tests, AD1 and AD2, is rounded to the nearest tenth, and is designated as CAD1 and CAD2. A student who does not take any of the tests will have a zero in that component.
3. REGULAR SEASON (EN)
The final exam, to be made in the Regular Season, is a written test without consultation, about all of the Course Unit's programme. The Normal Season Classification (N) is determined by the formula:
N = 0.125 CAD1 + 0.125 CAD2 + 0.75 CEN
where CEN represents the student's mark in the final exam of the regular examination period, rounded to the nearest tenth. The grade N is rounded to the nearest integer.
If the student misses one of the Distributed Assessment tests and their absence is considered justified by the L.EC secretary, the weight of that component is carried over to the final exam. In other words:
- if you miss test AD1, N = 0.125 CAD2 + 0.875 CEN
- if you miss test AD2, N = 0.125 CAD1 + 0.875 CEN
- if you miss both tests, N = CEN
4. APPEAL SEASON (ER)
The final exam, to be made in the Appeal Season, is a written test without consultation, about all of the Course Unit's programme. The Appeal Season Classification (R) is given by:
R = 0,125 CAD1 + 0,125 CAD2 + 0,75 CER
where CER represents the student's mark in the final exam of the Appeal Season, rounded to the nearest tenth. The grade R is rounded to the nearest integer.
If the student misses one of the Distributed Assessment tests and their absence is considered justified by the L.EC secretary, the weight of that component is carried over to the final exam. In other words:
- if you miss test AD1, R = 0.125 CAD2 + 0.875 CER
- if you miss test AD2, R = 0.125 CAD1 + 0.875 CER
- if you miss both tests, R = CER
5. CALCULATION OF FINAL GRADE (CF)
The Final Grade (CF) is given by the following formula:
CF = max {N ; R}
The maximum Final Grade CF obtained under the conditions described before is limited to 17 values. To obtain higher classification is necessary to conduct a complementary oral test in conditions to be agreed with the regents of UC (no need to register with FEUP's Central Secretariat).
Examinations or Special Assignments
Not applicable.Internship work/project
Not applicable.Special assessment (TE, DA, ...)
The knowledge assessment for Students who require Special Exams, under the FEUP Evaluation Rules, will be carried out exclusively at a single moment by performing a written exam on all the subjects taught at UC, without consultation. The Special Exam classification, between 0 and 20 points, is rounded to the unit.
The maximum final grade obtained in the written exam is limited to 17 values. To obtain higher classification is necessary to conduct a complementary Oral Test in conditions to be agreed with the regents of UC (no need to register with FEUP's Central Secretariat).
SPECIAL RULES FOR MOBILITY STUDENTS:
The assessment of students in these conditions is performed according to the criteria described in the fields "Calculation formula of final grade" and "Classification improvement".
The maximum final grade obtained in the written exam is limited to 17 values. To obtain higher classification is necessary to conduct a complementary Oral Test in conditions to be agreed with the regents of UC (no need to register with FEUP's Central Secretariat).
SPECIAL RULES FOR MOBILITY STUDENTS:
The assessment of students in these conditions is performed according to the criteria described in the fields "Calculation formula of final grade" and "Classification improvement".
Classification improvement
Access to the Exam for improvement of Final Grade (CF) is only granted to students who already have approval to the UC and are properly registered for that purpose in FEUP's Central Secretariat.
The Classification Improvement is based on a written test in the Grade Improvement Season (FEUP's Specific Regulation for Student Assessment). The student's classification in that final exam is denoted by CM, between 0 and 20 points. The student's Final Grade is given by:
CM = CEN (ou CER) (rounded to the nearest integer)
CF = max {CA; CM}
where CA represents the student's Approval grade previous.
The maximum Final Grade CF obtained under the conditions described before is limited to 17 values. To obtain higher classification is necessary to conduct a complementary oral test in conditions to be agreed with the regents of UC (no need to register with FEUP's Central Secretariat).
The Classification Improvement is based on a written test in the Grade Improvement Season (FEUP's Specific Regulation for Student Assessment). The student's classification in that final exam is denoted by CM, between 0 and 20 points. The student's Final Grade is given by:
CM = CEN (ou CER) (rounded to the nearest integer)
CF = max {CA; CM}
where CA represents the student's Approval grade previous.
The maximum Final Grade CF obtained under the conditions described before is limited to 17 values. To obtain higher classification is necessary to conduct a complementary oral test in conditions to be agreed with the regents of UC (no need to register with FEUP's Central Secretariat).
Observations
During any test or exam, the possession of any electronic device (e.g. mobile phone, tablet, headphones, smartwatch, etc.) is strictly prohibited, with the exception of those expressly indicated by the teaching staff (e.g. calculators). It is the student's responsibility to anticipate this situation before the start of the test or exam.Complementary study material is available in the SIGARRA Contents.
Working time estimated out of classes: 5 hours/week
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