This document provides an introduction to structural analysis. It discusses key concepts including structural idealizations, load classifications, and analytical models. Structural idealizations involve representing actual structural connections and supports as pinned or fixed connections in analytical models. Loads are classified as dead loads from structural materials and live loads from occupancy. Structural systems can be modeled as plane or space structures and represented through line diagrams. The role of structural analysis in engineering design projects is to predict structural performance under prescribed loads through analyzing stresses, deflections, and reactions.

1. Prof. Luis Eduardo Zapata Ordúz
Ing. Civil -UIS
M.Sc Ingeniería de Materiales
M.Eng Structures
Ph.D Materials & Structures
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2. Issues:
Part 1: basic concepts in structural analysis
Part 2: structural idealizations
Part 3: structural stability
Part 4: energy methods
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3. Issues:
Part 5: Alternative analysis methods*
*Depending on time considerations:
(i) Cross´method
(ii) Slope-deflection method
(iii) Bowman´s method
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4. PART A:
Structural
Analysis
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5. INTRODUCTION
 USCS  The United States Customary System of units uses FPS (foot-pound-
second) also called English or Imperial units.
 SI  The International System of units uses MKS (meter-kilogram-second).
However, CGS (centimeter-gram-second) units are often accepted as SI
units (especially in textbooks).
 The objective of this part is to develop an understanding of the basic
principles of structural analysis.
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6. INTRODUCTION
¿WHAT STRUCTURAL ANALYSIS IS?
 Structural analysis  is the prediction of the performance of a given
structure in static equilibrium under prescribed loads and/or other external
effects, such as support movements or temperatura changes.
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7. INTRODUCTION
 The performance characteristics commonly of interest in the design of
structures are:
(i) Stresses-Strains (axial forces, shear forces, bending moments, etc)
(ii) Deflections
(iii) Support reactions
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8. INTRODUCTION
BRIEF HISTORICAL BACKGROUND
 It was not until about the middle of XVII century that engineers began
applying the knowledge of mechanics in designing structures.
 Earlier engineering structures were designed by trial-and-error and by
using rules of thumb based on past experience.
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9. INTRODUCTION
BRIEF HISTORICAL BACKGROUND
 The fact that some structures from earlier eras such as Egyptian pyramids
(3000 B.C.) or Gothic cathedrals (A.D. 1000-1500) still stand today is a
testimonial to the _____________ of their builders.
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10. The fact that some structures from earlier eras (Egyptian pyramids or Gothic
cathedrals) still stand today is a testimonial to the INGENUITY of their builders..
Notre-Dame de Reims Egyptian pyramids Roman coliseum
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11. INTRODUCTION
 Galileo Galilei (1564-1642) is generally considered to be the originator of
the theory of structures, in which the analytical principles of mechanics
and strength of materials would have a major influence on the design of
structures.
 In his book “Two New Sciences” (1638) Galileo analyzed (only
approximate) the failure of some structures such as cantilever beams.
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12. INTRODUCTION
 The availabilty of computers in the 1950´s revolutionized structural analysis.
The computer could solve large systems of simultaneous equations in
seconds, in the precomputer era it takes days or weeks.
 The development of the current computer-oriented methods of structural
analysis can be attributed to, among others, J.H. Argyris, R.W. Clough, S.
Kelsey, R.K. Livesley, H.C. Martin, M.T. Turner, E.L. Wilson, and O.C.
Zienkiewicz.
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13. Role of structural
analysis in structural
engineering projects
Structural engineering 
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14. Role of structural
analysis in structural
engineering projects
Structural engineering  is the science and art
of planning, designing, and constructing safe
and economical structures that will serve their
intended purposes.
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The function of the structural analysis is the
prediction of the performance of the
proposed structure.

15. INTRODUCTION
PLANNING PHASE:
 The most crucial phase of the entire project
 General layout and dimensions of the structure
 Possible types of structures (e.g., rigid beams or truss, etc)
 Choosing of the materials (e.g., structural steel or RC)
 Nonstructural factors (e.g., aesthetics, environmental, etc)
 The outcome is usually a structural system that meets the functional safety
requirements and is expected to be the most economical.
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16. INTRODUCTION
PRELIMINARY STRUCTURAL DESIGN:
 The sizes of the members of the structural system are estimated based on
approximate analysis, past experience, and code requirements.
ESTIMATION OF LOADS:
 Determination of all the loads that can be expected to act on the
structure.
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17. INTRODUCTION
STRUCTURAL ANALYSIS:
 The loads are used to carry out an analysis of the structure to determine
stresses and strains in the members and deflections at various points of the
structure.
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18. INTRODUCTION
SAFETY AND SERVICEABILITY CHECKS:
 The results of the analysis are compared with the safety and serviceability
requirements of the design codes (e.g., NSR-10). This phase has two
options:
 If yes  the design drawings and the construction specifications are
prepared (the construction phase begins).
 If not  come back to previous steps (iterative process begins).
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19. INTRODUCTION
CLASSIFICATION OF STRUCTURES
 The most important decision made by a structural engineer in a project is
the selection of the type of structure to be used for suporting or
transmiting loads.
 Commonly used structures can be classified into five basic categories,
depending on the type of primary stresses that may develop under major
design loads.
 However, any two or more of the basic structural types may be combined
in a single one, to meet the structure’s functional requirements.
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20. INTRODUCTION
(I) TENSION STRUCTURES
 Tension structures composed of flexible steel cables are frequently
employed to support bridges (suspension bridges) and long-span roofs.
 Because of their flexibility, cables have negligible bending stiffness.
 Suspension bridges and other cable structures lack stiffness in lateral
directions  susceptible to wind-induced oscilations (bracing or stiffening
systems are required).
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21. 21

22. 22

23. INTRODUCTION
(ii) COMPRESSION STRUCTURES
 The most common examples are columns and arches.
 Column  straight member subjected to axially compressive loads and
moments.
 Arches  curved structures frequently used to support bridges and long-
span roofs. Are rigid elements and therefore susceptible to suffer bending
and shear stresses due to some loading conditions.
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25. 25

26. INTRODUCTION
(iii) TRUSSES STRUCTURES
 Composed of straight members connected at their ends by hinged
connections to form a stable configuration.
 When loads are applied only at the joints (ideal truss), its members either
elongate or shorten (ideal truss  uniform tension or uniform compression).
 Real trusses are constructed by connecting members to gisset plates by
bolted or welded connections.
 The rigid joints cause some bending under load, but in most cases such
secondary bending stresses are small, and the assumption of hinged joints
yields satisfactory designs.
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27. 27

28. INTRODUCTION
(iv) SHEAR STRUCTURES
 Shear structures develop mainly in plain shear, with relatively small
bending stresses under the action of external loads.
 The most commom example is reinforced concrete shear walls. RCSW are
used in multistory buildings to reduce lateral movements due to wind
and/or earthquake loads.
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31. 31

32. INTRODUCTION
(v) BENDING STRUCTURES
 Bending structures develop mainly bending stresses under the action of
external loads. However, in some structures the shear associated with the
changes in bending may also be significant (i.e., Eq. C.13–1 from NSR-10).
 The most commom examples of bending structures are:
o beams
o rigid frames
o plates
o slabs
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33. INTRODUCTION
ANALYTICAL MODELS
 Simplified or ideal representations for the purpose of analysis of a real
structure.
 In the model much of the detail about the members, connections, and so
on, that is expected to have little effect on the desired characteristics are
discarded.
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34. INTRODUCTION
Development of the analytical model generally involves consideration of the
following factors:
1. Determination of whether or not the structure can be treated as a plane
structure
2. Construction of the line diagram of the structure
3. Idealization of connections and supports
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35. INTRODUCTION
 Plane vs. Space structures
o Most of the actual 3D structures can be subdivided into plane structures
for analysis
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36. 36
Stringers are supported by floor beams.
Floor beams are connected at
Their ends to the joints of the trusses.
Dashed lines  Secondary bracing members to resit lateral loads and to provide stability.
Solid lines  Main members designed to suport vertical loads.

37. 37
¿Can trusses be treated
as plane structures?

38. 38
Floor beams  transmit the weight of traffic, deck, stringers
and s-w (floor beams) to the supporting trusses at their joints.
YES: Trusses can be treated as plane structures

39. 39
YES: Each frame can be analyzed as a plane structure.
The floor slab rests on floor beams, which transfer any load
applied to the floor, the weight of the slab, and their own
weight to the girders of the supporting frame.

40. INTRODUCTION
LINE DIAGRAM
 The analytical 2D or 3D model selected for analysis is represented by a line
diagram (centroidal axis).
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41. INTRODUCTION
 The dimensions of the members and the size of the connections are not
shown on the diagram.
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42. INTRODUCTION
CONNECTIONS/SUPPORTS
 Structural members are joined together in various ways depending on the
intent of the designer.
 In concrete and steel construction the three types of joints most often
specified are:
pin connection Freedom for slight rotation
roller (link)support
fixed joint
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43. INTRODUCTION
VIP INFORMATION
 It is important to be able to recognize the symbols for connections (or
supports) and the kinds of reactions they exert when idealizing structures.
 The connection/support will develop a force if it prevents translation.
 The connection/support will develop a moment if it prevents rotation.
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45. 45

46. 46

47. INTRODUCTION
STRUCTURAL SYSTEMS REPRESENTS BY IDEALIZED MODELS
 The idealized structure is shown as a line drawing.
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48. INTRODUCTION
STRUCTURAL SYSTEMS REPRESENTS BY IDEALIZED MODELS
 The idealized structure is shown as a line drawing.
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49. INTRODUCTION
 Girder  main load-carrying element of the building floor.
 Beams  smaller elements with shorter span are connected to the girders.
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Slab supported by floor joists, these in turn are supported by two side girders
Pin and/or roller connected to
the columns (do not touch)
Pin and/or roller connected
to the girders (do not touch)

50. INTRODUCTION
 If reinforced concrete construction is used, beams and girders are
represented by double lines. Also, the lines for the beams and girders
would touch the columns.
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51. INTRODUCTION
 Structural idealizations for timber structures are similar to those made of
metal.
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Joists are simply supported on the wall

52. INTRODUCTION
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Top view of steel beams

53. 53
In reality, all connections exhibit some stiffness
toward joint rotations, owing to friction and
material behavior.
If k = 0  the joint is a pin
If k  ∞ the joint is fixed

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55. 55
Pin support
Pin and rocker (roller)
Roller and bearing pad
Rocker bearing

56. INTRODUCTION
 For most timber structures, the members are assumed to be pin
connected, since bolting or nailing them will not sufficiently restrain them
from rotating with respect to each other.
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57. INTRODUCTION
SUMMARY
 Two types of connections are commonly used to joint members of
structures:
o Rigid (fixed) connections
o Flexible (hinged) connections
NOTE: Semirigid connections (recognized by structural steel design codes).
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58. LOADS ON
STRUCTURES
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59. LOADS ON STRUCTURES
 In designing a structure, an engineer must consider all the loads that can
realistically be expected to act on the structure during its planned life
span.
 The loads that act on common civil engineering structures can be
grouped according to their nature and source as:
(i) Dead loads  self-weight and any other material permanently attached.
(ii) Live loads  movable loads.
(iii) Environmental loads  wind, snow, earthquakes, etc…
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60. LOADS ON STRUCTURES
 An engineer must also consider the possibility that some of these loads
might act simultaneously on the structure.
 The structure is finally designed so that it will be able to withstand the most
unfovarable combination of loads that is likely to occur in its lifetime.
 Building codes (e.g. NSR-10)  specify the minimum design loads and
load combinations for which the structure must be designed.
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61. LOADS ON STRUCTURES
 Local building codes are usually legal documents enacted to safeguard
public welfare and safety  the engineer must become familiar with the
building code for the area in which the structure is to be built.
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63. LOADS ON STRUCTURES
DEAD LOADS
 Dead loads are gravity loads of constant magnitudes and fixed positions.
 Weights of the structural system itself and of all other material and equipment
permanently attached to the structural system.
 The actual weight of a structure is computed by using the member sizes and
the unit weights of materials (equipment  from the manufacturer).
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64. LOADS ON STRUCTURES
DEAD LOADS
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Usually 24

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66. 66

67. LOADS ON STRUCTURES
EXAMPLE
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68. LOADS ON STRUCTURES
TRIBUTARY LOADS
 It is necessary to determine how the load on surfaces is transmitted to the
various structural elements used for their support.
 There are generally two ways in which this can be done: 1D or 2D actions
 The choice depend on the geometry of the structural system, the material
from which it is made, and the method of its construction.
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69. LOADS ON STRUCTURES
 If the slab is RC with steel in only 1D, or the concrete is poured on a
corrugated metal deck  1D action can be assumed.
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Metal deck
Girder
Beam
1D or 2D???

70. LOADS ON STRUCTURES
 If the slab is flat on top and bottom and is reinforced in two directions 
consideration must be given to the possibility of load transmition in either
one or two directions.
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If L2/L1 > 2 which beams
are more important?
(i) AB, CD and EF
(ii) AE and BF
(iii) Equally important
(iv) Insufficient information
ACI 318/NSR-10 (C.13.1.6)

71. LOADS ON STRUCTURES
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72. LOADS ON STRUCTURES
TWO-WAY SYSTEMS
 One of the most typical cases is when L2/L1 ≤ 2 (ACI 318/NSR-10: C.13).
 However, the geometry is not the only parameter to be evaluated, should
be also analyzed :
o the structural system,
o the method of its construction, and
o the material from which it is made.
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73. 73
One-way or Two-way action?

74. LOADS ON STRUCTURES
 Find the tributated area for beam AB:
the beam AB is assumed to have the tributary area in a triangular form.
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w = (100 lb/ft2)*(5 ft)
w = 500 lb/ft

75. LOADS ON STRUCTURES
 Find the tributated area for beams AB and AC (p = 100 lb/ft2):
A case of two-way action but now L2/L1 = 1.5. In this case, trapezoidal (beam
AB) and triangular (beam AC) distributed loads can be formed.
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w = (100 lb/ft2)*(5 ft)
w = 500 lb/ft

76. LOADS ON STRUCTURES
LIVE LOADS
 Live loads are loads of varying magnitudes and/or positions caused by
the use of the structure.
 Building codes  specify the magnitudes of live loads.
 LL´s position may change  each member of the structure must be
designed for the position of the load that causes the maximum stress.
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77. LOADS ON STRUCTURES
 LL´s for buildings are ususally specified as uniformly distributed surface
loads.
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78. LOADS ON STRUCTURES
 LL´s for bridges are specified by codes (e.g. AASHTO).
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84. LOADS ON STRUCTURES
EXERCISE
 The roof of a classroom is to be supported by the joists shown. Each joist is
6.2 m long and they are spaced 0.80 m on centers. The roof itself is to be
made from simple concrete (23 kN/m3) 80 mm thick. Assuming that the
joist is formed for two L5 X 5 X ½ standars angles. Determine the reactions
on the joist.
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86. 86

87. 87
INCORRECTO