Syllabus 9956001207 - ANÁLISIS DE ESTRUCTURAS




Ability to choose the right structure, tensions of isostatic and hyperstatic structures, calculation of tensions in iron, wood, concrete and brick. Software dimensioning







0 Summary of structural mechanics
• Recognize the Indeterminacy Degree of simple structures (simple frame structures and structures with
internal pins).
• Apply Basic Equilibrium Equations.
• Calculate reactions of (externally) isostatic solids, specially in-plane cases.
• Understand the difference between internal and external equilibrium of a structure, internal and external
• Calculate and draw internal force diagrams (N, M, V) of simple, plane, isostatic structures (specially
beams). Typical cases:
- Continuous load, point load and their combinations.
- Simply supported beams, cantilevers, beams with one or two cantilevers and beams with
internal pins.
- Isostatic plane frames.
- Trusses using joint and section method.
• Understand the relationships between q, V and M and apply these relationships to:
- Drawing intuitive diagrams.
- Finding location and value of maximum bending moment.
• Apply the superposition principle to solve structures with complex load combinations. Especially relevant is the case of beams with cantilevers, replacing the cantilevers by their effect on the beam.

1 Loads and Safety
• Understand and apply the principle of structural safety to actions and materials through Limit State Design.
• Understand the difference between Ultimate Limit States and Serviceability Limit States.
• Implement safety on your structural calculations through use of partial factors and combination factors for loads and materials.
• Estimate the self weight of different kind of structures. Solid slabs, waffle slabs, one-way slabs, composite floors, beams and columns, in steel, wood, masonry and concrete.
• Estimate the load due to finishing materials, using their constructive description and the code (EC1, CTE) tables.
• Classify the category of use for different buildings and determine the suitable live load and combination
factor given by european and spanish codes.
• Differentiate characteristic load from design load.
• Ultimate Limit States (Internal forces): Calculate design loads and determine design diagrams.
• Serviceability Limit States (deflections): Calculate short-term and long-term total and relative deflections and identify their allowable limits.
• Correct steel sections if deflections are not allowable.

2 Sectional Behaviour
• Calculate the Area, Centroid and (second moment of) Inertia of simple plane areas and compound areas, using Steiner’s (Parallel-axis) theorem.
• Calculate the elastic modulus of compound sections.
• Sectional elastic behaviour of steel and wood.
- Estimate the typical design strength and elastic modulus values for structural steel and solid wood.
- Understand the concept of service class for wood and its relevance on wood strength through suitable factors.
- Calculate maximum design stress values.
- Perform a resistance check for bending moment.
• Determine the plastic resistance of steel sections (both conventional and welded sections formed by steel plates).
• Sectional behaviour of reinforced concrete sections.
- Estimate the typical design strength for concrete and reinforcing steel.
- Know the usual layout of reinforcement in concrete sections.
- Verify the resistance of a section, given its reinforcement.
- Design the amount of steel required for a section, given its design bending moment.
• Determine the suitable height of concrete sections in order to avoid deflection calculations.

3 Deflections
• Understand the concepts and variables used on the standard tensile test: stress σ, strain ε, stress-strain diagram, yield stress fy, yield strain ε y, ultimate strength fu, elastic modulus Es, their units and relationships.
• Use fluently the basic relationships between stress, strain, elastic modulus, length, displacement, axial load and area in order to calculate displacements of cables under tensile load.
• Understand the (differential) relationship between M and curvature (C = 1/R), and between curvature and deflection.
• Use those relationships to draw intuitive bending moment and deflection diagrams.
• Acknowledge the relevance of different parameters on beam deflections: Inertia, Elastic modulus, load, support conditions.
• Calculate the value of E·I for different materials and kind of sections (see A4). Identify the relevant Inertia
to be used in the calculations.
• Understand the superposition and proportionality principles applied to deflection calculations.
• Calculate deflections for simple beams with continuous or point loads with or without cantilevers, using superposition principles and tables for canonic cases.
• Calculate and check relative deflections for beams and cantilevers, and correct unsuitable deflections by changing beam cross-section.

4 Elastic analysis of statically Indeterminate Structures
• Determine the redundancy degree of statically indeterminate (hyperestatic) beams.
• Use the compatibility method to solve hyperestatic simple or continuous beams with redundancy degree of 1 or 2.
• Understand the effect of continuity on beams and frames using calculation programs as an educational tool.

5 Plastic Analysis
• Understand the influence of the stress-strain diagram of steel on the behaviour of the section past the yielding limit, particularly the non-linear evolution of the section curvature (C = 1/R) as the bending moment moves from elastic to plastic.
• Understand the concepts of plastic hinge and collapse mechanism.
• Determine the number of plastic hinges necessary to develop a collapse mechanism for simple and continuous beams with different support conditions.
• Design steel beams (simple hyperestatic beams or continuous beams) using plastic analysis (lower bound analysis).
• Grasp the limits of plastic analysis and its advantages:
- Limits: only steel sections, only for resistance calculations (Ultimate Limit States), no superposition principle applies.
- Advantages: ease of use, economy.

6 Models: one-way floors.
• Understand the underlying concept of models as simplification of a physical reality.
• Calculate simple models by hand, using hierarchy of elements to assess loads.
• Use the concept of tributary area to get loads on different elements.
• Understand the basic differences between isostatic, elastic and plastic behaviour for joists and beams and its relevance on tributary loads and reactions.
• Calculate isostatic and hyperestatic one-way slabs through elastic analysis.

7 Models: Two-way floors
• Determine the indeterminacy degree of simple grids.
• Calculate simple grids with point and distributed loads using the compatibility method.
• Acknowledge the relevant parameters in the distribution of forces to elements of a grid: Stiffness (E·I) and length.
• Understand the differences, advantages and drawbacks of typical slab systems.
• Determine the suitable thickness of the slab.
• Reinforce slab elements to resist design bending moments (usually one-meter strip except in one-way slabs with ribs or two-way waffle slabs).
• Calculate design bending moments in rectangular slabs supported or fixed in their perimeter using tables.
• Calculate and reinforce two-way slabs on columns under gravity load using the equivalent frame method and compare results with program output.

8 Lateral Stability
• Understand the way frames deform and resist under lateral loads, acknowledging the contribution of both beams and columns and the importance of relative stiffness for the overall behaviour.
• Estimate the wind load on conventional buildings.
• Understand the difference between a rigid-framed building and a braced building. Acknowledge the reasons why one or other option is preferred for typical cases.
• Understand the way buildings resist wind (and lateral) loads, and the load path from façade elements to the foundation for:
- Buildings with floors.
- Buildings without floors (sheds).

Determine the minimum number of bracing planes necessary in a building with floors, which are the preferred dispositions for bracing, and which dispositions are to be avoided.
• Understand the basic difference between cross diagonals and other kind of bracing dispositions.
• Calculate forces on bracing elements manually (diagonals and columns that are part of bracing systems).
• Understand the difference between 1st and 2nd order analysis.
• Calculate forces on bracing elements with the program (particularly, calculate forces on bracing elements with cross diagonals not capable of carrying compression) using the 2nd order options if necessary.
• Determine the design diagram envelope on a frame considering all loads and their combinations with suitable partial factors.
• Determine the dimension necessary for bracing elements using the usual sections (UPN, LPN, SHS,cables).

9 Computer models
• Skills that must be mastered using a calculation program (tricalc) (not a exhaustive list):
- Be able to generate simple 2-D and 3-D models of structures using grids.
- Copy and modify structures.
- Input structures from Autocad 3D models.
- Move through horizontal planes. Create and store new planes and frames.
- Manage the graphical options of the program.
- Apply support conditions.
- Understand the difference between external and internal constraints and how to apply each.
- Understand the concept of hypothesis and the way the program manages the different hypothesis, including dead load, use load, wind and snow.
- Manage structure self-weight options.
- Activate and deactivate wind hypothesis.
- Apply continuous and point loads on bars and points.
- Apply surface loads creating one-way slabs.
- Apply wind loads generating wind panels.
- Change internal restraints of bars (pin-joints, rigid-joints).
- Use sets (groups) for ease of change.
- Apply sections to bars. Change section orientation.

- Create new sections using the program facilities.

- Understand the concept of ‘ties’ (tirantes).
- Analyze structures without ties.
- Analyze structures with ties (2nd order analysis).
- Print on screen and/or list the design diagrams (envelope with partial factors), as well as the simple diagrams (simple cases with no partial factors), of the whole structure, or a part, with or
without labels.
- List values of internal forces and reactions on structures.
- List deflections on the structure.




There are two Exams. 
The first exam is more theoretical and students are not allowed the use of the computer or notes (some specific summary tables are allowed).
The second exam is more practical. Use of the computer is encouraged, although it is possible to face the exam without it.


There are 10 scheduled exercises, although during the course this number might be adjusted. The exercises
are begun during class time and they should be finished by students working autonomously and delivered at
a given date.


A main activity of the course is the structural analysis of an existing building. This building will be assigned
by the teacher.
This activity will start at the 4th week of the course, once the group of students is settled. A series of class
sessions are devoted to tutorized work on this assignment. Deadline for this activity is the last class day.

Course book:
The reading of a book on structures is compulsory and should be done during the term. The title and
reference of the book will be provided on the first day of the course. Questions about the book will be
interspersed with the course theory in exams


Exams weight 40% on the course mark. Every exam weights 20%

There are 10 scheduled exercises. Weight of exercises on the course mark is 30%.

A main activity of the course is the structural analysis of an existing building. Weight of this assignment in the course mark is 30%.


Prerequisites: Structural mechanics.