BPD20403 STRUCTURAL ANALYSIS

By:Associate Professor Dr. Narimah Kasim

IntroductionClassification of StructureTypes of StructureStructural DesignWhat is structural analysis?Idealization of StructureStructural ProblemsStability & Determinacy

What is STRUCTURE?

A structure is refers to a system of connected parts used to support a load. (Hibbeler, 2009)

Structure related to civil engineering includes:Buildings, Bridges, Tower, Tunnel, and etc.

Structure related to other branches of engineering includes:Ship, Aircraft frames, Tanks, Pressure vessels, Mechanical systems, Electrical supporting structures and etc.

The following elements should be considered by engineers who are involved in civil engineering works when designing a structure, includes:SafetyAestheticsServiceabilityEconomicEnvironmentalMaterials availability

Definition of structure

structure is a part of construction which has one or more element is subjected to various loads that it must resist without either collapsing or deforming excessively (Bambang Prihartanto et. al, 2008)

RafterSupportColumnBeam

Structural Elements:(a) Tie Rods(b) Beams(c) Columns

(a) Tie RodsTie Rods or Bracing struts are structural members pointed to a tensile force.

These elements are slender and are often chosen from rods, bars, angels or channels.

Typical Cross SectionsTie RodAngleChannelRodBar

(b) BeamsBeams are usually straight horizontal members used primarily to carry vertical loads. Materials commonly used for beams structure such as:SteelAluminiumConcreteTimberBeams can be classified according the way they are supported (Figure 1.2-2)

(b) BeamsBeams are primarily designed to oppose bending moment and large internal shear force (when beams are short and carry large loads). Beam cross section for metal materials such as steel and aluminium (Figure 1.2-3) . The forces developed in the top and bottom flanges of the beam form the necessary couple used to resist the applied moment M, while the web is effective in resisting the applied shear V.

The beam cross section normally a single unit in rolling mill in lengths up to 23m. If long span beams required and loads applied are rather large, the cross section may take the form of a plate girder (Picture 1). 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 together at points where the girder carries a small internal moment.

Picture 1: Typical Splice Plate Joints Used to Connect the Steel Girders of a Highway Bridge (source: Hibbeler, 2009)

Concrete beams generally have rectangular cross sections, since it is easy to construct this form directly in the field. Concrete with reinforcing steel are combined/cast together to resist tension. Precast concrete beams and girders are fabricated at yard and then transported to the construction site.

Prestressed Concrete Girders are Simply Supported for Highway Bridge (source: Hibbeler, 2009)

Steel Reinforcement for Concrete Beams (source: Hibbeler, 2009)

Timber beams are made from sawn timber from a solid of wood or laminated. Laminated beams are constructed from solid sections of wood, which are fastened together using high-strength glues.

Columns are members that generally vertical and resist axial compressive loads.Tubes and wide-flange cross sections are normally used for metal columns. Circular and square cross sections with reinforcing rods are used for concrete columns. Beam columns are subjected to both an axial load and a bending moment.

Columns (source: Hibbeler, 2009) Beam Columns (source: Hibbeler, 2009)

Types of Structure:TrussesCables and ArchesFramesSurface Structures

Structural FormsTension & Compression StructureFlexural Beam & Frame StructureSurface Structures

The combination of structural elements and the materials from which they are composed is referred to as a structural system. The structural systems are constructed of one or more of four basic types of structures such as trusses, cables and arches, frames, and surface structures.

Truss is a span of a structure which required being large and its depth is not an important criterion for design and consist of slender element with triangular fashion arrangement. Trusses are supported compression and tension forces in the members. One of the advantages of using truss compared to beam is that it uses less material to support a given load. Trusses are constructed from long and slender elements which can be arranged in various methods to support load. The truss spans are economically ranging from 9m to 122m and greater lengths.

Types of trusses:

Planar trusses Planar trusses are composed of members that lie in the same plane. Commonly used for bridge and roof support.

Space trussesSpace trusses are composed of members extending in three dimensions and are suitable for derricks and towers.

Compression and Tension in Truss Members (source: Hibbeler, 2009)

Cables are one of the structures usually flexible and carry their loads in tension and can be used to span long distances (greater than 46 m). Cables are regularly used to support bridges and building roofs. Cables will not become unstable and suddenly collapse, because they are always in tension. However, using of cables can reduced their sag, weight, and methods of anchorage for the purposes of truss construction which required added costs and increased depth as the span increases.

Cables (support loads in tension) (source: Hibbeler, 2009)

Arch is rigid and reverse curvature form, which can achieve compression strength.In order to maintain the shape of the arches, shear and moment loadings should be considered in the design process. Arches are regularly used in bridge structures, dome roofs, and for opening in masonry walls.

Arches (support loads in compression) (source: Hibbeler, 2009)

Frames are composed of beams and columns that are either pin or fixed connected and often used in buildings. The strength of the frames is derived from the moment interactions between the beams and the columns at the rigid joints. For the economic purposes the construction of frames must using smaller beams sizes and increasing the size of the columns due to the beam-column action caused by bending at the joints.

Frame Members (source: Hibbeler, 2009) Example of Steel Frame (source: Hibbeler, 2009)

A surface structure is made from rigid materials such as reinforced concrete, folded plates, cylinders, or hyperbolic paraboloids, and is referred to as thin plates or shells. It is act like cables or arches which support tension or compression loads and very little bending.

Surface Structures Georgia Dome, Atlanta(source: Hibbeler, 2009)

Tension & Compression StructureColumn, strut (compression)Cable-supported structure (tension)Arch (compression)Truss (compression & tension)

Flexural Beam & Frame StructureBeamFrameCombination (bridges, building)

Surface StructuresSlabsFolded platesShellsDomesSkin-type structuresInflatable members

Structural design is required to give consideration to both materials and load uncertainties. Materials uncertainties involved; Variability in materials properties, Residual stress in materials, Measurement being different from fabricated sizes, Accidental loadings due to vibration or impact,Material corrosion or decay.

Typical load combinations (ASCE 7-05 Standard) :Dead Load0.6 (Dead Load) + Wind Load0.6 (Dead Load) + 0.7 (Earthquake Load)

Load combinations to account uncertainty loads (ASCE 7-05 Standard) : 1.4 (Dead Load)1.2 (Dead Load) + 1.6 (Live Load) + 0.5 (Snow Load)1.2 (Dead Load) + 1.5 (Earthquake Load) + 0.5 (Live Load)

Specific structures should be analysed in order to ensure its strength and rigidity after preliminary design of a structure is proposed. Structural analysis

is a process in determining the reaction of the structure under the specified loads or actions (Bambang Prihartanto et. al, 2008)

The reaction can be measured by establishing the forces and deformations throughout the structure. The results from structural analysis can be used to; redesign the structure, determine accurate weight of the members, andaccount size of the members.

In order to analyse a structure properly, the following steps must be follow:Identify the structuresIdealization of the structuresLoading determination (codes and local specifications)Structure members forces and displacements (using theory of structural analysis)

Cables (source: Bambang et. al, 2008)

Trusses (source: Bambang et. al, 2008)

Arches (source: Bambang et. al, 2008)

Supports (source: Bambang et. al, 2008)

Compression & Tension (source: Bambang et. al, 2008)

Surface Structures (Curved Surface, Flat Plate) (source: Bambang et. al, 2008)

Idealization of Structures is idealizing model from actual structure in line diagram in order to perform structural analysis of the members.

Usually, structure can be idealized in 2 dimensional from 3 dimensional.

Idealization of Structures Beam Actual Beam (b) Idealized Beam (source: Bambang et. al, 2008)

Idealization of Structures Frames Actual Structure (b) Idealized Structure(source: Bambang et. al, 2008)

Idealization of Structures Supports(a) Roller support (b) Hinged support (source: Bambang et. al, 2008)

Idealization of Structures Supports (c) Fixed support (d) Link support (e) Ball and socket (f) Rigid support in space (source: Bambang et. al, 2008)

Idealization of Structures Connection (a) Idealized hinge (b) Idealized rigid joint (source: Bambang et. al, 2008)

Structure analysis should considered structural problems of structure members in order to improve the stability of the structures. The method of analysis can be divided to traditional (educational process) or modern matrix methods (practice of structural engineering).

STRUCTUREStableUnstableDeterminateIndeterminateStaticGeometryExternalInternal

There are two types of structural un-stability:(i) Kinematics Unstable (Partial Constraints)Number of reaction at the support or number of the member is less than the minimum requirement.One of structure members may have fewer reactive forces than equations of equilibrium that must be satisfied and the structure then becomes only partially constrained.(ii) Geometry Unstable (Improper Constraints)The location or the arrangement of the support or member is improper.

(i) Beam

r < n + 3: Statically unstabler = n + 3: Determinate (only if geometrically stable)r > n + 3: Indeterminate

(ii) Frame

3m + r < 3j + n : Statically unstable3m + r < 3j + n : Determinate (only if geometrically stable)3m + r > 3j + n : Indeterminate

(iii) Plane Truss

m < 2j r : Statically unstablem = 2j r : Determinate (only if geometrically stable)m > 2j r: Indeterminate

(iv) Space Truss

m < 3j r: Statically unstablem = 3j r: Determinate (only if geometrically stable)m > 3j r: Indeterminate

Where,

n= number of internal hinger= number of reactionm= number of memberj= number of joint

Bambang Prihartanto, Sharul Niza Mokhatar, Nurazuwa Md Noor, Noorli Ismail and Norhafizah Saleh (2008). Structural Analysis, Penerbit UTHM: Parit Raja, Batu Pahat, Johor.Hibbeler, R.C. (2009). Structural Analysis, 7th Edition, Prentice Hall: SingaporeNoorli Ismail (2008). Mechanics of Materials, Penerbit UTHM: Parit Raja, Batu Pahat, Johor.Yusof Ahmad (2001). Mekanik Bahan dan Struktur, Penerbit UTM: Skudai, Johor.Yusof Ahmad (2004). Teori Struktur, Penerbit UTM: Skudai, Johor.

Determinacy and Stability