STRUCTURE ANALYSIS-1 structural elements.pptx

STRUCTURAL ANALYSIS 1
Structural system (Classification, types
of structures), support conditions,
determinacy, stability
Instructor: Engr. Hajrah Nosheen

Week Contents Relevance w
Weekly Break Up Field Application CLO
1. Introduction to structural supports, types of beam redundancy
and stability of structure Structural safety
CLO1
2. Shear force and bending moment diagram of VDL beam Structural design CLO2
3. Determination of Member forces of truss by method of joint Truss analysis for structures CLO1,2 P
4. Determination of Member forces of truss by method of
section
CLO1,2 P
5. Axial force, shear force and bending moment diagram of
frame
Structural Frame design CLO1,2 P
6. Axial force, shear force and bending moment diagram of
frame
CLO2
7. Influence line Diagram for reactions and shear of beam under
moving loads
Bridge design, design of beams & trusses used
in crane rails, conveyor belts, floor girders, etc.
CLO1,2 P
8. Influence line Diagram for shear and bending of beam
under moving loads
CLO2
9.
Analysis of cables
Analyzing suspension bridges, transmission
lines and power cables
CLO1,2 P
10. Analysis of Arches Force and deformation analysis of arches CLO1,2 P
11. Rotation and deflection by conjugate Beam method (Simply
supported Beam)
Analysis of beam for any type of structure,
buckling, rotation and deformation behavior
CLO1,2 P
12. Rotation and deflection by conjugate Beam method
(Cantilever Beam)
CLO1,2 P
13. Rotation and deflection by moment area method (Simply
supported Beam)
CLO1,2 P
14. Rotation and deflection by moment area method (Cantilever
Beam)
CLO1,2 P
15. Rotation and deflection by principle of virtual work method
(Simply supported Beam)
CLO1,2 P
16. Rotation and deflection by principle of virtual work method
(Cantilever Beam)
CLO1,2 P

Structural system
• The combination of structural elements and the materials from which they are composed
is referred to as a structural system.
• A structure refers to a system of connected parts used to support a load. Important
examples related to civil engineering include buildings, bridges, and towers; and in other
branches of engineering, ship and aircraft frames, tanks, pressure vessels, mechanical
systems, and electrical supporting structures are important.
• When designing a structure to serve a specified function for public use, the engineer
must account for its safety, esthetics, and serviceability, while taking into consideration
economic and environmental constraints. Often this requires several independent studies
of different solutions before final judgment can be made as to which structural form is
most appropriate.
• This design process is both creative and technical and requires a fundamental knowledge
of material properties and the laws of mechanics which govern material response. Once a
preliminary design of a structure is proposed, the structure must then be analyzed to
ensure that it has its required stiffness and strength.
• To analyze a structure properly, certain idealizations must be made as to how the
members are supported and connected together

Classification of Structures
• It is important for a structural engineer to
recognize the various types of elements
composing a structure and to be able to
classify structures as to their form and
function.
• Structural Elements. Some of the more
common elements from which structures are
composed are as follows.
• Tie Rods. Structural members subjected to a
tensile force are often referred to as tie rods
or bracing struts. Due to the nature of this
load, these members are rather slender, and
are often chosen from rods, bars, angles, or
channels, Fig. 1–1.

Beams.
• Beams are usually straight horizontal members used primarily to carry vertical loads.
• Quite often they are classified according to the way they are supported, as indicated in Fig. 1–2.
• In particular, when the cross section varies the beam is referred to as tapered or haunched.
• Beam cross sections may also be “built up” by adding plates to their top and bottom.
• Beams are primarily designed to resist bending moment; however, if they are short and carry
large loads, the internal shear force may become quite large and this force may govern their
design.
• When the material used for a beam is a metal such as steel or aluminum, the cross section is
most efficient when it is shaped as shown in Fig. 1–3. This cross section is commonly referred to
as a “wide flange,” and it is normally formed as a single unit in a rolling mill in lengths up to 75 ft
(23 m).
• When the beam is required to have a very large span and the loads applied are rather large, the
cross section may take the form of a plate girder. This member is fabricated by using a large
plate for the web and welding or bolting plates to its ends for flanges.
• The girder is often transported to the field in segments, and the segments are designed to be
spliced or joined togetherat points where the girder carries a small internal moment.
• Concrete beams generally have rectangular cross sections, since it is easy to construct this form
directly in the field. Because concrete is rather weak in resisting tension, steel “reinforcing rods”
are cast into the beam within regions of the cross section subjected to tension.
• Precast concrete beams or girders are fabricated at a shop or yard in the same manner and then
transported to the job site.
• Beams made from timber may be sawn from a solid piece of wood or laminated. Laminated
beams are constructed from solid sections of wood, which are fastened together using high-
strength glues.

• Columns.
• Members that are generally vertical
and resist axial compressive loads are
referred to as columns, Fig. 1–4.
• Tubes and wide-flange cross sections
are often used for metal columns, and
circular and square cross sections
with reinforcing rods are used for
those made of concrete.
• Occasionally, columns are subjected
to both an axial load and a bending
moment as shown in the figure.

Types of Structures
• Trusses. When the span of a structure is required to be large and its depth is not an important
criterion for design, a truss may be selected. Trusses consist of slender elements, usually
arranged in triangular fashion.
• Planar trusses are composed of members that lie in the same plane and are frequently used
for bridge and roof support, whereas space trusses have members extending in three
dimensions and are suitable for towers.
• Due to the geometric arrangement of its members, loads that cause the entire truss to bend
are converted into tensile or compressive forces in the members. Because of this, one of the
primary advantages of a truss, compared to a beam, is that it uses less material to support a
given load.
• Economically feasible to use a truss to cover spans ranging from 30 ft(9 m) to 400 ft (122 m).

• Cables and Arches.
• Cables are usually flexible and carry their loads in tension. They are commonly used to
support bridges, Fig. 1–6a, and building roofs.
• When used for these purposes, the cable has an advantage over the beam and the truss,
especially for spans that are greater than 150 ft (46 m). Because they are always in tension,
cables will not become unstable and suddenly collapse, as may happen with beams or
trusses.
• The arch achieves its strength in compression, since it has a reverse curvature to that of the
cable. The arch must be rigid, however, in order to maintain its shape, and this results in
secondary loadings involving shear and moment, which must be considered in its design.
• Arches are frequently used in bridge structures, Fig. 1–6b, dome roofs, and for openings in
masonry walls.

• Frames.
• Frames are often used in buildings and are composed of beams and
columns that are either pin or fixed connected, Fig. 1–7.
• Like trusses, frames extend in two or three dimensions. The loading on a
frame causes bending of its members, and if it has rigid joint connections,
this structure is generally “indeterminate” from a standpoint of analysis.

Surface Structures
• A surface structure is made from a material having a very small thickness compared to
its other dimensions.
• Sometimes this material is very flexible and can take the form of a tent or air-inflated
structure. In both cases the material acts as a membrane that is subjected to pure
tension.
• Surface structures may also be made of rigid material such as reinforced concrete. As
such they may be shaped as folded plates, cylinders, or hyperbolic paraboloids, and are
referred to as thin plates or shells.
• These structures act like cables or arches since they support loads primarily in tension
or compression, with very little bending. In spite of this, plate or shell structures are
generally very difficult to analyze, due to the three-dimensional geometry of their
surface.

Loads
• Loads are specified in codes such as the ASCE 7-10 code.
• Dead loads are fixed and refer to the weights of members and
materials.
• Live loads are movable and consist of uniform building floor loads,
traffic and train loads on bridges, impact loads due to vehicles and
machines, wind loads, snow loads, earthquake loads, and hydrostatic
and soil pressure.

Support Connections
• Structural members are joined together
in various ways depending on the intent
of the designer.
• The three types of joints most often
specified are the pin connection, the
roller support, and the fixed joint.
• A pin-connected joint and a roller
support allow some freedom for slight
rotation, whereas a fixed joint allows no
relative rotation between the connected
members and is consequently more
expensive to fabricate.
• Examples of these joints, fashioned in
metal and concrete, are shown in Figs.
2–1 and 2–2, respectively

Principle of superposition
• The principle of superposition forms the basis for much of the theory of
structural analysis. It may be stated as follows: The total displacement or
internal loadings (stress) at a point in a structure subjected to several external
loadings can be determined by adding together the displacements or internal
loadings (stress) caused by each of the external loads acting separately.
• For this statement to be valid it is necessary that a linear relationship exist
among the loads, stresses, and displacements.
• Two requirements must be imposed for the principle of superposition to apply:
1. The material must behave in a linear-elastic manner, so that Hooke’s law is
valid, and therefore the load will be proportional to displacement.
2. The geometry of the structure must not undergo significant change when the
loads are applied, i.e., small displacement theory applies.

Determinacy
• The equilibrium equations provide both the necessarymand sufficient conditions
for equilibrium.
• When all the forces in a structure can be determined strictly from these
equations, the structure is referred to as statically determinate.
• Structures having more unknown forces than available equilibrium equations are
called statically indeterminate.
• As a general rule, a structure can be identified as being either statically
determinate or statically indeterminate by drawing free-body diagrams of all its
members, or selective parts of its members, and then comparing the total
number of unknown reactive force and moment components with the total
number of available equilibrium equations.
• For a coplanar structure there are at most three equilibrium equations for each
part, so that if there is a total of n parts and r force and moment reaction
components, we have

• Stability. To ensure the equilibrium of a structure or its members, it is not only
necessary to satisfy the equations of equilibrium, but the members must also
be properly held or constrained by their supports. Two situations may occur
where the conditions for proper constraint have not been met.
• Partial Constraints. In some cases a structure or one of its members may have
fewer reactive forces than equations of equilibrium that must be satisfied. The
structure then becomes only partially constrained. For example, consider the
member shown in Fig. 2–22 with its corresponding free-body diagram. Here
the equation will not be satisfied for the loading conditions and therefore the
member will be unstable.
• Improper Constraints. In some cases there may be as many unknown forces as
there are equations of equilibrium; however, instability or movement of a
structure or its members can develop because of improper constraining by the
supports. This can occur if all the support reactions are concurrent at a point.
Another way in which improper constraining leads to instability occurs when
the reactive forces are all parallel

Shear force and bending moment diagrams of beams
Field application:
Used in structural design to find maximum loads so that we can optimize the
design to prevent failure and reduce weight and cost of overall structure.
Shear on a member allow the ripping of a member in opposite direction. Force
V is resisting shear.
Bending moment is a reaction induced in a structural member when an external
force or moment is applied to member, causing it to bend. Couple M is resisting
or applied moment.

Types of Loading
• Loads applied to the beam may consist of a concentrated
load (load applied at a point), uniform load, uniformly
varying load, or an applied couple or moment. These
loads are shown in the following figures.

STRUCTURE ANALYSIS-1 structural elements.pptx

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