structural analysis chapter 01

Structural Analysis 7Structural Analysis 7thth Edition in SI Units Edition in SI UnitsRussell C. HibbelerRussell C. Hibbeler

Chapter 1: Chapter 1: Types of Structures and LoadsTypes of Structures and Loads

Introduction

• Structures refer to a system of connected Structures refer to a system of connected parts used to support a loadparts used to support a load

• Factors to consider:Factors to consider:• SafetySafety• EstheticsEsthetics• ServiceabilityServiceability• Economic & environmental constraintsEconomic & environmental constraints

© 2009 Pearson Education South Asia Pte Ltd

Structural Analysis 7th EditionChapter 1: Types of Structure and Loads

Classification of Structures

• Structural elementsStructural elements• Tie rodsTie rods• BeamsBeams• ColumnsColumns

• Types of structuresTypes of structures• TrussesTrusses• Cables & ArchesCables & Arches• Surface StructuresSurface Structures



Loads

LoadsLoads

Structural formsStructural forms

Elements carrying primary loadsElements carrying primary loads

Various supporting membersVarious supporting members

Foundation Foundation © 2009 Pearson Education South Asia Pte Ltd


• Design loading for a structure is often Design loading for a structure is often specified in codesspecified in codes• General building codesGeneral building codes• Design codesDesign codes

Loads



• Types of loadTypes of load• Dead loadsDead loads

•Weights of various structural membersWeights of various structural members•Weights of any objects that are attached to Weights of any objects that are attached to

the structurethe structure

Loads



The floor beam is used to support the 1.83m width of The floor beam is used to support the 1.83m width of lightweight plain concrete slab having a thickness of lightweight plain concrete slab having a thickness of 102mm. The slab serves as a portion of the ceiling for the 102mm. The slab serves as a portion of the ceiling for the floor below & its bottom coated with plaster. A 2.44m floor below & its bottom coated with plaster. A 2.44m high, 305mm thick lightweight solid concrete block wall is high, 305mm thick lightweight solid concrete block wall is directly over the top flange of the beam. Determine the directly over the top flange of the beam. Determine the loading on the beam measured per m length of the beam.loading on the beam measured per m length of the beam.

Example 1.1Example 1.1



Using the data provided from the table,Using the data provided from the table,

SolutionSolution



mkNTotal

mkNmmmkN

mkNmmkN

mkNmmmmmmkN

/50.1526.1244.080.2

/26.12)305.0)(44.2)(/5.16( :block wall

/44.0)83.1)(/24.0( :ceilingplaster

/80.2)83.1)(102)(./015.0( :slab concrete

3

2

2

• Live loads Live loads •Varies in magnitude & locationVaries in magnitude & location•Building loads Building loads

• Depends on the purpose for which the building Depends on the purpose for which the building is designedis designed

• These loadings are generally tabulated in local, These loadings are generally tabulated in local, state or national codestate or national code

Loads



• Live loads Live loads •Building LoadsBuilding Loads

• Uniform, concentrated loadsUniform, concentrated loads

Loads



2

2

2

min areatributary

4column interior For factor.element load live

member by the supported area of load/m livedesign unreduced

member by the supported area of load/m livedesign reduced

where

units) (SI 57.4

25.0

T

LLLL

o

TLL

o

A

KK

L

L

AKLL

• Live loads Live loads •Building LoadsBuilding Loads

• Uniform, concentrated loadsUniform, concentrated loads

Loads



roof.or garage assembly, publicfor used structuresfor or

/79.4 loadsfor allowed isreduction No

floor one than more supporting membersfor 4.0

floor one supporting membersfor 5.0

2mkN

LL

LL

o

o

A 2-storey office building has interior columns that are A 2-storey office building has interior columns that are spaced 6.71m apart in 2 perpendicular directions. If the spaced 6.71m apart in 2 perpendicular directions. If the (flat) roof loading is 0.96kN/m(flat) roof loading is 0.96kN/m22, determine the reduced , determine the reduced live load supported by a typical interior column located at live load supported by a typical interior column located at ground level.ground level.




SolutionSolution



kNkNkNFFF

kNmmkNF

mkNL

mmmAKmkNL

kNmmkNFR

mmmA

FR

F

TLLo

T

0.1079.631.43

9.63)0.45)(/42.1(

50%59.1%100%(1.42/2.4) isreduction load The

/1.42180

57.425.04.2

2.37180)0.45(44 ,4 ,/4.2

floor, secondFor

1.43)0.45)(/96.0(

0.45)71.6)(71.6(

22

2

2222

22

2

• Highway Bridge loadsHighway Bridge loads•Primary live loads are those due to trafficPrimary live loads are those due to traffic•Specifications for truck loadings are reported Specifications for truck loadings are reported

in AASHTOin AASHTO•For 2-axle truck, these loads are designated For 2-axle truck, these loads are designated

with H followed by the weight of truck in tons with H followed by the weight of truck in tons and another no. gives the year of the and another no. gives the year of the specifications that the load was reportedspecifications that the load was reported

Loads



• Railway Bridge loadsRailway Bridge loads•Loadings are specified in AREALoadings are specified in AREA•A modern train having a 320kN (72k) loading A modern train having a 320kN (72k) loading

on the driving axle of the engine is designated on the driving axle of the engine is designated as an E-72 loadingas an E-72 loading

Loads



• Impact loadsImpact loads•Due to moving vehicles Due to moving vehicles •The % increase of the live loads due to impact The % increase of the live loads due to impact

is called the impact factor, Iis called the impact factor, I

Loads



load live the tosubjected is that min span theoflength

3.01.38

24.15

L

LI

• Wind loadsWind loads•Kinetic energy of the wind is converted into Kinetic energy of the wind is converted into

potential energy of pressure when structures potential energy of pressure when structures block the flow of windblock the flow of wind

•Effects of wind depends on density & flow of Effects of wind depends on density & flow of air, angle of incidence, shape & stiffness of the air, angle of incidence, shape & stiffness of the structure & roughness of surfacestructure & roughness of surface

•For design, wind loadings can be treated as For design, wind loadings can be treated as static or dynamic approachstatic or dynamic approach

Loads



• Wind loadsWind loads

Loads



1 alone, acting For wind

loads. ofn combinatio tosubjected is structure theonly when used isIt

wind. theofdirection for the accountst factor tha a

1 groundflat For s.escarpment % hills todue increases speed for wind accountst factor tha a

1.5. Table See

terrain.ground upon the depends andheight offunction A t.coefficien exposure pressure velocity the

occupancy. building theof nature upon the dependst factor tha importance the

map. winda from obtained are Values

period. recurrence50year a during ground theabove 10m measured windofgust 3s a of m/sin velocity

where

)2/(2613.0

dK

dK

ztKztK

zK

I

V

mNIVd

KztKzKzq

• Wind loadsWind loads•Once qOnce qzz is obtained, the design pressure can is obtained, the design pressure can

be obtained from a list of relevant equationsbe obtained from a list of relevant equations

Loads



)( pihp GCqqGCp

18.0 building, enclosedfully For

building. in the openings of type

upon the dependst which coefficien pressure internal the

surface. thefromaway acting pressure indicate valuesNegative

t coefficien pressure roofor wall

0.85 G structure, rigidFor

exposure.on depending factor,effect gust - winda

roof theofheight mean ,hz where wallleeward for the

ground theabove zheight at wall windwardfor the

pi

pi

p

h

z

GC

GC

C

G

q

qq

The enclosed building is used for agricultural purposes and is located outside of Chicago, Illinois on flat terrain. When the wind is directed as shown, determine the design wind pressure acting on the roof and sides of the building using the ASCE 7-02 Specifications.




SolutionSolution



mh

h

KIVKKKq zdztzz

63.92/03.462.7

03.410tan6.22'

3.853613.0

1K is loading Wind

1 K in,flat terraFor

0.87 I 40m/s, V speed, windBasic

0

2

d

zt

SolutionSolution



15285.0)18.0(845)85.0(

)(

18.0)( ,85.0

845990038539900

63921204119212980041

h zfor

ion interpolatlinear by determined wasK of value theNote

below. tablein the listed are profile pressure of

valuescalculated 1.5, Tablein K of valuesUsing

2

z

z

pp

pihp

pi

hh

h

qCCq

GCqqGCp

GCG

N/m).(., q.K

).-.)/(-K.().-.)/(.-.(

SolutionSolution



z (m)z (m) KKzz QQzz (N/m (N/m22))

0 – 4.60 – 4.6 0.850.85 733733

6.16.1 0.900.90 776776

7.67.6 0.940.94 814814

h = 9.6h = 9.6 0.9900.990 856856

SolutionSolution



22

226.7

221.6

226.40

/211 /517

5.0 1,5.722(22.86)/4

wallLeeward

/709 /400

/680 /374

/651 /344

8.0 , allFor

zheight with variesPressure

wallWindward

mNormNp

CL/B

mNormNp

mNormNp

mNormNp

CL/B

p

p

SolutionSolution



22

22

/356 /666

and 7.0 that so

,25.0211.086.22/63.9 Here

roofs Windward

/356 /666

7.0 , of valuesallFor

wallsSide

mNormNp

qqC

h/L

mNormNp

CL/B

hp

p

SolutionSolution



22 /65 /356

and 3.0 case, In this

roofs Leeward

mNormNp

qqC hp

• Wind loadsWind loads• If the structure represents an above-ground If the structure represents an above-ground

sign, the wind will produce a resultant force on sign, the wind will produce a resultant force on the face of the sign which is determined from:the face of the sign which is determined from:

Loads



ffz AGCqF

wind theinto projectedsign theof face theof area the

1.6 Tablein listed are Values

N.dimension small thesign to theof Mdimension large

theof ratio upon the dependst which coefficien force a

previously definedfactor t coefficiengust - windthe

of centroid

theof zheight at the evaluated pressure velocity the

where

f

f

f

z

A

C

G

A

q

• Snow loadsSnow loads•Design loadings depend on building’s general Design loadings depend on building’s general

shape & roof geometry, wind exposure, shape & roof geometry, wind exposure, location and its importancelocation and its importance

•Snow loads are determined from a zone map Snow loads are determined from a zone map reporting 50-year recurrence intervalreporting 50-year recurrence interval

Loads



• Snow loadsSnow loads•For flat roof (slope < 5%):For flat roof (slope < 5%):

Loads



hospitalfor 1.2 and facilities storage & eagriculturfor 0.8 e.g,For occupancy. torelatesit asfactor importance the

1.0. then structure, heatednormally a supporting is roof theif whereas1.2,

freezing belowkept structure unheatedFor building. within the re temperatuaverage the torefersch factor whi thermala

1.3 city large a of centre in the located & sheltered is roof theIf

0.8. area edunobstructan in roof exposedfully A terrain.upon the dependingfactor exposurean

where

1.5eqn 7.0

III

tCtC

tCeC

eCeC

gtef IpCCp

• Snow loadsSnow loads

Loads



)/96.0( use

,/96.0 If

or 1.5eqn from computedeither ,for luelargest va theuse

,/96.0 If

2

2

2

mkNIp

mkNp

Ippp

mkNp

f

g

gf

f

g

The unheated storage facility is located on flat open The unheated storage facility is located on flat open terrain near Cario, Illinois where the ground snow load is terrain near Cario, Illinois where the ground snow load is 0.72kN/m0.72kN/m2.2. Determine the design snow load on the roof. Determine the design snow load on the roof.




SolutionSolution



2

2

22

2

/58.0choose ,comparisonBy

/58.0)72.0)(8.0(

/96.0/72.0 Since

/39.0)72.0)(8.0)(2.1)(8.0(7.0

7.0

8.0 ,2.1 ,8.01.5eqn use flat, is roof theSince

mkNp

mkNIpp

mkNmkNp

mkNp

IpCCp

ICC

f

gf

g

f

gtef

te

• Earthquake loadsEarthquake loads•Earthquake produce loadings through its Earthquake produce loadings through its

interaction with the ground & its response interaction with the ground & its response characteristicscharacteristics

•Their magnitude depends on amount & type of Their magnitude depends on amount & type of ground acceleration, mass & stiffness of ground acceleration, mass & stiffness of structurestructure

•Top block is the lumped mass of the roofTop block is the lumped mass of the roof•Middle block is the lumped Middle block is the lumped

stiffness of all the building’s columnsstiffness of all the building’s columns•During earthquake, the ground During earthquake, the ground

vibrates both horizontally & verticallyvibrates both horizontally & vertically

Loads



• Earthquake loadsEarthquake loads•Horizontal accel -> shear forces in the columnHorizontal accel -> shear forces in the column• If the column is stiff & the block has a small If the column is stiff & the block has a small

mass, the period of vibration of the block will mass, the period of vibration of the block will be short, the block will acceleration with the be short, the block will acceleration with the same motion as the ground & undergo slight same motion as the ground & undergo slight relative displacementsrelative displacements

• If the column is very flexible & the block has a If the column is very flexible & the block has a large mass, induced motion will cause small large mass, induced motion will cause small accelerations of the block & large relative accelerations of the block & large relative displacementdisplacement

Loads



• Earthquake loadsEarthquake loads•The effects of a structure’s response can be The effects of a structure’s response can be

determined & represented as an earthquake determined & represented as an earthquake response spectrumresponse spectrum

• For small structure, static analysis is For small structure, static analysis is satisfactorysatisfactory

Loads



/ IR

SC DS

s

building theof use on the dependst factor tha importance

structure theofductility upon the dependst factor thaon modificati response

vibrationof periodsshort for accel response spectral

I

R

SDS

• Hydrostatic & Soil PressureHydrostatic & Soil Pressure•The pressure developed by these loadings The pressure developed by these loadings

when the structures are used to retain water when the structures are used to retain water or soil or granular materialsor soil or granular materials

•E.g. tanks, dams, ships, bulkheads & retaining E.g. tanks, dams, ships, bulkheads & retaining wallswalls

• Other natural loadsOther natural loads•Effect of blastEffect of blast•Temperature changesTemperature changes•Differential settlement of foundationDifferential settlement of foundation

Loads



• Material uncertainties occur due toMaterial uncertainties occur due to•variability in material propertiesvariability in material properties•residual stress in materialsresidual stress in materials•intended measurements being different from intended measurements being different from

fabricated sizesfabricated sizes•material corrosion or decaymaterial corrosion or decay

• Many types of loads can occur Many types of loads can occur simultaneously on a structuresimultaneously on a structure

Structural Design



• In working-stress design, the computed In working-stress design, the computed elastic stress in the material must not elastic stress in the material must not exceed the allowable stress along with the exceed the allowable stress along with the following typical load combinations as following typical load combinations as specified by the ASCE 7-02 Standardspecified by the ASCE 7-02 Standard

•Dead loadDead load•0.6 (dead load) + wind load0.6 (dead load) + wind load•0.6 (dead load) + 0.7(earthquake load)0.6 (dead load) + 0.7(earthquake load)

Structural Design



• Ultimate strength design is based on Ultimate strength design is based on designing the ultimate strength of critical designing the ultimate strength of critical sectionssections

• This method uses load factors to the loads or This method uses load factors to the loads or combination of loadscombination of loads

• 1.4 (Dead load)1.4 (Dead load)• 1.2 (dead load) + 1.6 (live load) + 0.5 (snow 1.2 (dead load) + 1.6 (live load) + 0.5 (snow

load)load)• 1.2 (dead load) + 1.5(earthquake load)+ 0.5 1.2 (dead load) + 1.5(earthquake load)+ 0.5

(live load)(live load)

Structural Design



structural analysis chapter 01

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