Structural Analysis and Design Tcm4-118204

8/11/2019 Structural Analysis and Design Tcm4-118204

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NATIONAL QUALIFICATIONS CURRICULUM SUPPORT

Civil Engineering

Structural Analysis and Design

AD!ANCED "I#"ER$

%a&es Dun'ar


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THERMOCHEMISTRY

Acknowledgements

Learning and Teac(ing Sc)tland grate*ully ac+n),ledge t(is c)ntri'uti)n t) t(e Nati)nal

Quali*icati)ns su--)rt -r)gra&&e *)r Civil Engineering. In -articular/ t(e assistance )* 0illMc1en2ie/ Mi+e Scully and C(arlie S&it( in t(e -re-arati)n )* t(is &aterial is

ac+n),ledged ,it( t(an+s.

Electr)nic versi)n 3443

5 Learning and Teac(ing Sc)tland 3443

T(is -u'licati)n &ay 'e re-r)duced in ,()le )r in -art *)r educati)nal -ur-)ses 'y

educati)nal esta'lis(&ents in Sc)tland -r)vided t(at n) -r)*it accrues at any stage.

ECONOMICS6 MICROECONOMICS 7A"8 III


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CONTENTS

Overview 9

Tutor Guide :

Student Guide ;

Study Guide 1 Analysis )* statically deter&inate -in


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THERMOCHEMISTRY

ECONOMICS6 MICROECONOMICS 7A"8 %


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OVERVIEW

T(ese su--)rt &aterials are -r)vided t) assist t eac(erslecturers in delivery )*

t(e Advanced "ig(er Civil Engineering c)urse unit Structural Analysis and

Design. T(ey ,ill als) (el- t) -re-are students *)r assess&ent.

T(e Tut)r #uide )**ers 'rie* advice )n t(e entry reuire&ents *)r t(e unit/ )n

t(e design d)cu&ents t) 'e issued t) candidates ,it( eac( )* t(e Study

#uides and t(e design -r)cedures t) 'e ad)-ted.

T(e Student #uide -r)vides a 'rie* intr)ducti)n t) t(e unit/ e-lains t(e

c)ntent )* eac( Study #uide and )**ers advice )n -re-arati)n *)r assess&ent.

Student su--)rt &aterials are -r)vided in t(e *)r& )* *ive Study #uides/ eac(

c)vering )ne )r t,) )utc)&es )* t(e unit.

T(e Nati)nal Assess&ent 0an+ su--)rt &aterial *)r t(is unit c)ntains *ive

assess&ent instru&ents t(at ta+e t(e *)r& )* end )* t)-ic> tests. T(ese &ay

'e used t) -r)vide *eed'ac+ )n candidates> -r)gress as ,ell as 'eing used *)r

su&&ative unit assess&ent.

T(e Study #uides in t(is -ac+ -r)vide t(e su--)rt n)tes reuired *)r t(e

)utc)&es c)vered 'y eac( instru&ent )* assess&ent. End )* Study #uide>

tests are als) -r)vided/ and t(ese are )* a si&ilar standard t) t(e instru&ents

)* assess&ent )* t(e Nati)nal Assess&ent 0an+.

T(e Study #uides are as *)ll),s6

Study Guide 1 An&lysis o' st&tic&lly determin&te (in)*ointed 'r&mes

T(is c)vers all t(e -er*)r&ance criteria )* Outc)&e 9.

Outc)&e 96 Analyse/ 'y &at(e&atical &eans/ statically deter&inate -in as t(e design

re*erence. T(e use )* any )t(er -u'licati)n &ay lead t) ans,ers t(at di**er t)

t()se given in t(e ea&-les. Study #uide 3 s()uld 'e underta+en 'e*)re t(e

design Study #uides/ as t(e standard case de*lecti)n *)r&ulae are ,idely used

in t(ese design guides.

Study Guide " ,esign o' rein'orced concrete elements

Eac( centre s()uld -r)vide candidates ,it( Ta'les )* areas )* rein*)rce&ent>

,(en issuing t(e Study #uide. T(e design &et()ds are 'ased )n 0SH994 Part

96 9; and t(e n)tes c)ncentrate )n t(e design euati)ns rat(er t(an t(e

design c(arts. At t(e ti&e )* -u'licati)n )* t(e Study #uide t(e design c(arts

in PP ;:93 ,ere etracted *r)& 0S H994 Part :6 9H@. As t(e c(arts ,ere

devel)-ed using a &aterials *act)r *)r steel g &)* 9.9@ and n)t 9.4@ as used

in t(e 9; versi)n )* t(e c)de/ t(ere is n), an in(erent err)r in t(e c(arts.

Areas )* rein*)rce&ent derived using t(e c(arts &ust t(ere*)re 'e &ulti-lied

'y t(e *act)r [email protected]@/ as il lustrated )n -age @9.

STRUCTURA L ANALBSIS AND DESI#N 7A"8 III


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T3TOR G3I,E

Study Guide # ,esign o' structur&l steelwork elements

Eac( centre s()uld -r)vide candidates ,it( t(e *)ll),ing d)cu&ents ,(enissuing t(e Study #uide6

t(e Structural Steel secti)n ta'les *)r U0 and UC secti)ns

t(e sa*e l)ad ta'les *)r UC and U0 su'=ect t) aial l)ad

t(e sa*e l)ad ta'les *)r ,e' 'earing and 'uc+ling )* U0 secti)ns.

C)-ies )* t(e &)st u-


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4 STRUCTUR AL ANALBSIS AND DESI#N 7A"8


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STUDENT GUIDE

Introduction

T(e unit Structural Analysis and Design ,ill a--eal t) y)u i* y)u are

interested in -r)'le& s)lving. It ,ill 'r)aden y)ur s+ills in t(e a--licati)n )*

scienti*ic and tec(n)l)gical -rinci-les t) t(e area )* structural design.

#aining t(is a,ard ,ill ena'le y)u t) c)ntinue devel)-&ent )* t(e

c)&-etences reuired )* t(e Inc)r-)rated Engineer. It ,ill -r)vide a str)ng

'ase *)r *urt(er study at "ND and Degree level. B)u ,il l ac(ieve a level )*

c)&-etence reuired )* a -ers)n in a design )**ice ,() (as t(e res-)nsi'ility

*)r t(e design )* 'asic structural ele&ents.

3nit content

T(e unit stresses t(e i&-)rtance )* structural engineering in t(e creative and

sa*e devel)-&ent )* t(e 'uilt envir)n&ent. It is designed t) 'ring t)get(er

t(e study )* structural &ec(anics/ -revi)usly studied and n), *urt(er

devel)-ed/ ,it( t(e -r)cesses )* structural design. It ,ill intr)duce y)u t)

t(e 0ritis( Standard C)des )* Practice used in t(e design )* rein*)rced

c)ncrete/ steel,)r+/ &as)nry and ti&'er structures K all -r)'le& tests.

T(e teac(ing and learning &aterials (ave 'een -re-ared as *ive Study #uides/

,(ic( -r)vide t(e su--)rt n)tes *)r t(e )utc)&es c)vered 'y eac( instru&ent

)* assess&ent. At t(e end )* eac( Study #uide y)u ,ill *ind an End )* Study

#uide> test t(at c)ntains uesti)ns t(at are )* a standard si&ilar t) t(at ,(ic(

y)u can e-ect in t(e assess&ent.

Study Guide 1 An&lysis o' st&tic&lly determin&te (in)*ointed 'r&mes

T(is c)vers Outc)&e 9. It ,ill intr)duce y)u t) t(e analytical &et()ds usedt) deter&ine t(e *)rces in -in


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Study Guide ! ,etermin&tion o' -e&m de'lections -y st&nd&rd 'ormul&e

&nd M&c&ul&y.s met/od

T(is c)vers Outc)&e 3. It ,ill ena'le y)u t) deter&ine t(e de*lecti)ns )*

'ea&s under standard and n)n


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ST3,E7T G3I,E

Part )* t(e classr))& ti&e ,ill 'e all)cated t) assess&ent. "),ever/ y)u ,ill

(ave t) s-end additi)nal ti&e in -re-aring y)ursel* *)r assess&ent. Learn

(), t) use t(e design c)des6 ,(at clauses 7)r -age nu&'ers8 d) y)u (ave t)l))+ u- *)r 7say8 'ending &)&ents a--lied t) 'ea&s ,(at ta'les are

a--lica'le d) t(e values *r)& t(e ta'les (ave t) 'e &)di*ied in s)&e ,ay

T(e assess&ent ,ill 'e carried )ut under t(e su-ervisi)n )* an invigilat)r

7n)r&ally y)ur teac(erlecturer8/ under strict ti&e c)nstraints. T(ese ,ill 'e

)utlined t) y)u -ri)r t) underta+ing t(e assess&ent. B)u &ust learn t) use

t(e design c)des uic+ly. Use t(e End )* Study #uide> tests as a guide t)

y)ur -re-aredness *)r *inal assess&ent.

Core skills

T(e assess&ent tas+s )* t(e unit ,ill als) 'e tail)red t) all), y)u t) devel)-

a nu&'er )* c)re s+ills/ including -r)'le& s)lving. C)&-leti)n )* t(e unit

&ay result in aut)&atic certi*icati)n )* certain c)re s+ills c)&-)nents.

Success*ul c)&-leti)n )* t(e Advanced "ig(er C)urse in Civil Engineering

,ill result in aut)&atic certi*icati)n )* )t(er c)&-)nents. B)u s()uld 'e

a,are )* t(e evidence y)u &ust gat(er t) de&)nstrate attain&ent )* c)re

s+ills and y)ur tut)r ,ill guide y)u in t(is area.

STRUCTUR AL ANALBSIS AND DESI#N 7A"8 8


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ST3,Y G3I,E 1

STUDY GUIDE 1

An&lysis o' st&tic&lly determin&te (in)*ointed 'r&mes

Introduction

T(is study guide c)vers Outc)&e 9 )* t(e unit.

Outcome 1

Analyse/ 'y &at(e&atical &eans/ statically deter&inate -in


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ST3,Y G3I,E 1

+/&t does t/e term :st&tic&lly determin&te (in)*ointed 'r&mes. me&n;

J(at ,ill 'e c)nsidered ,ill 'e t(e analysis )* trusses ,(ere t(e eternall)ads are a--lied at t(e n)de -)ints )nly 7intersecti)n )* t(e individual

ele&ents )* t(e *ra&e8/ suc( t(at n) 'ending e**ects can 'e devel)-ed in t(e

&e&'ers. As )nly aial c)&-ressive and tensile *)rces are devel)-ed in t(e

*ra&e &e&'ers t(e *ra&e is re*erred t) as -in K at a -in )nly direct

*)rces can 'e carried and n) 'ending e**ects can 'e devel)-ed.

Statically deter&inate> K t(e *ra&e can 'e s)lved using t(e t(ree c)nditi)ns

)* euili'riu& )nly.

T(e c)nditi)ns are6

Alge'raic su& )* &)&ents )* *)rces &ust eual 2er)

M < 9

Alge'raic su& )* vertical )* *)rces &ust eual 2er) % < 9

Alge'raic su& )* ()ri2)ntal )* *)rces &ust eual 2er) H < 9

J(en c)nsidering t(e *ra&e and its reacti)ns t(ere are t(ree c)nditi)ns )*

euili'riu& t) s)lve t(e reacti)ns/ t(us t(ere can 'e n) &)re t(an t(ree

un+n),ns.

In t(e *ra&e s(),n6

T(e su--)rt at t(e le*t.

I* t(e *ra&e is -r)vided ,it( t,) (inges as su--)rts/ as s(),n 'el),/

1! STRUCTUR AL ANALBSIS AND DESI#N 7A"8


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ST3,Y G3I,E 1

t(ere are *)ur un+n),ns and )nly t(ree c)nditi)ns )* euili'riu& ,it( ,(ic(

t) s)lve t(e& K t(e *ra&e reacti)ns are statically indeter&inate> and cann)t

'e s)lved 'y using t(e c)ndit i)ns )* euili'riu& )nly.

In a si&ilar &anner t(e ele&ents )* t(e *ra&e &ust c)n*)r& t) t(e euati)n

s(),n 'el), i* t(e *ra&e is statically deter&inate6

n


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ST3,Y G3I,E 1

Redra,ing *ra&e

Only n)des A and C are suita'le. 0 (as *ive un+n),n *)rces. D/ E and F all

(ave t(ree un+n),n *)rces.

Using )nly ! 4 and " 4/ *irstly n)de A t(en n)de C

Node A

! 4As t(e reacti)n is 9H +N u-,ards/ a 'alancing *)rce )* 9H +N d),n,ards is

reuired.

T(is can )nly )ccur in a vertical ele&ent/ t(us *)rce AF is 9H +N " 4As t(e reacti)n is 93 +N t) t(e le*t/ a 'alancing *)rce )* 9H +N t) t(e rig(t is

reuired.

T(is can )nly )ccur in a ()ri2)ntal ele&ent/ t(us *)rce A0 is 93 +N

Node C

! 4As t(e reacti)n is :4 +N u-,ards/ a 'alancing *)rce )* :4 +N d),n,ards is

reuired.

T(is can )nly )ccur in a vertical ele&ent/ t(us *)rce CD is 9H +N " 4As t(ere is )nly )ne ()ri2)ntal ele&ent at n)de C and n) eternal ()ri2)ntal

*)rces/ t(e *)rce in t(e single ele&ent &ust 'e 4. F)rce C0 4.

Ste( # su(erim(ose t/e known 'orces on t/e 'r&me

Re&e&'er t(e alge'raic su& )* *)rces in an ele&ent &ust 'alance. F)r

ea&-le i* t(e *)rce at )ne end 7n)de8 )* an ele&ent is 9H +N d),n,ards/ *)r

euili'riu& at t(e )t(er end 7n)de8 it &ust 'e 9H +N u-,ards.

STRUCTURA L ANALBSIS AND DESI#N 7A"8 1$


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ST3,Y G3I,E 1

Redra,ing t(e *ra&e

Ste( $ re(e&t ste(s " &nd # wit/ t/e rem&ining nodes o' t/e 'r&me

T(ere are n), )nly t,) un+n),ns at n)des F and D n)de E still (as t(ree

un+n),ns.

C)nsidering n)de F t(en n)de D

T(e inclined *)rces F0 and D0 can 'e s-lit )nt) ()ri2)ntal and vertical

c)&-)nents )* *)rce/ eit(er 'y +n),ing t(e rati) )* t(e sides )r 'y +n),ing

t(e values )* t(e angles.

Node F

! 4As t(e *)rce *r)& &e&'er AF is 9H +N u-,ards/ a 'alancing *)rce )* 9H +N

d),n,ards is reuired.

T(is can )nly )ccur in t(e vertical c)&-)nent )* ele&ent F0/ t(us t(e vertical

c)&-)nent )* F0 is 9H +N. "),ever/ F0 is an inclined &e&'er s) t(e actual

directi)n )* t(e *)rce al)ng t(e lengt( )* t(e &e&'er &ust 'e d),n and t) t(e

rig(t. T(e &agnitude is

9Hc)s ?@ 3@.?@ +N )r 9H3 3@.?@ +N

" 4At t(is n)de t(ere are t(ree ()ri2)ntal *)rces FE/ t(e ()ri2)ntal

c)&-)nent )* F0 and t(e eternal 93 +N *)rce.

I* t(e *)rce in F0 is acting d),n and t) t(e rig(t/ t(e ()ri2)ntal



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ST3,Y G3I,E 1

c)&-)nent is acting t) t(e rig(t. F0( 3@.?@ sin?@ )r 3@.?@ 3 9H +NFE F0( 93 4 *)rces t) rig(t -)sitive

FE 9H 93 4FE K:4 +N :4 +N acting t) t(e le*t

Node D

As &e&'er D0 is inclined/ it can s-lit int) its ()ri2)ntal and vertical

c)&-)nents

D0v D0 sin ?@ )r D03D0( D0 c)s ?@ )r D03C)nsidering t(e n)de/ t(ere is a vertical *)rce )* :4 +N acting u-,ards in

ele&ent DC.

T(is &ust 'e 'alanced 'y a d),n,ards *)rce )* :4 1N. T(is can )nly )ccur

in D0v.

D0v :4 +N T(e *)rce in D0 &ust t(ere*)re 'e acting d),nand t) t(e le*t.

D0v D0 sin ?@ )r D03 D0 ?3.? +N

" 4DE is un+n),n/ 'ut &ust 'alance D0( as t(ere are n) )t(er ()ri2)ntal

ele&ents at t(is n)de. D0( is acting t) t(e le*t K DE &ust act t) t(e rig(t.

DE D0( ?3.? c)s ?@ )r ?3.?3 :4 +N

Re(e&t Ste( # su(erim(ose t/e known 'orces on t/e 'r&me

N), c)nsider n)de E

T(e vertical *)rce EA is t(e )nly un+n),n

T(is &ust 'alance t(e eternal ?H +N *)rce

EA ?H +N

Finis(ed *ra&e

STRUCTURA L ANALBSIS AND DESI#N 7A"8 15


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ST3,Y G3I,E 1

Met/od o' sections

T(e &et()d *)r analysis )* t(e *)rces in *ra&es 'y secti)ns is used ,(en )nlyt(e *)rces in s-eci*ic ele&ents are reuired. T(e t(ree c)nditi)ns )*

euili'riu& are availa'le *)r use/ s) t(e secti)n s()uld cut acr)ss n) &)re

t(an t(ree ele&ents in ,(ic( t(e *)rces are un+n),n.

C)nsider t(e *ra&e used in t(e =)int res)luti)n ea&-le.

T(e *irst ste- 7as 'e*)re8 is t) calculate t(e reacti)ns/ giving t(e result6

T(e secti)n c)nsidered t) cut t(e *ra&e s(),s t(at t(e *)rces in ED/ 0D and

0C are t) 'e *)und.

T(e eternal euili'riu& )* t(e -art )* t(e *ra&e t) t(e le*t


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ST3,Y G3I,E 1

Ta+e &)&ents a')ut D

Cl)c+,ise &)&ents -)sitive

79H G8 793 :8 K 7?H :8 70C :8 494H ?H K 9?? :.0C 4

4 :0C 4 0C 4

! 4 'ec)&es Ta+ing u-,ards *)rces as -)sitive9H K ?H 0Dv 4

K:4 0Dv 4

0Dv :4 +N t),ards n)de D

F)rce in 0D acts al)ng t(e line )* t(e ele&ent/ t(e directi)n is u- and t) t(e

rig(t.

Magnitude )* *)rce 0D :4 c)s ?@ )r :43 ?3.? +N

" 4 Ta+ing *)rces acting t) t(e rig(t as -)sitive93 K 93 0D( ED 0C 4

93 K93 ?3.?sin ?@ ED 4

:4 ED 4

ED K:4 +N Fr)& D t(e *)rce acts t) t(e le*t.

Su-eri&-)se t(e results )n t(e *ra&e.

Re&e&'er t(e alge'raic su& )* *)rces in an ele&ent &ust eual 2er).

Ans,ers agree ,it( t()se *)und 'y &et()d )* =)int res)luti)n.



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ST3,Y G3I,E 1

Study Guide 1 End Test

T(e *igure 'el), s(),s in )utline a -in


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ST3,Y G3I,E !

STUDY GUIDE 2

,etermin&tion o' -e&m de'lections -y st&nd&rd 'ormul&e

&nd -y M&c&ul&y.s met/od

Introduction

T(is study guide c)vers Outc)&e 3 )* t(e unit.

Outcome !

Deter&ine t(e de*lecti)ns )* statically deter&inate 'ea&s usingstandard *)r&ulae and Macaulay>s &et()d.

On c)&-leti)n )* t(e Study #uide y)u s()uld 'e a'le t)6

calculate t(e &ai&u& de*lecti)ns )* statically deter&inate 'ea&s using

standard *)r&ulae

calculate critical de*lecti)ns in 'ea&s su'=ect t) n)ns &et()d.

STRUCTUR AL ANALBSIS AND DESI#N 7A"8 !1


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ST3,Y G3I,E !

M&c&ul&y.s met/od

T(is is a &et()d )* analysis t(at all),s t(e sl)-e and de*lecti)n )* a 'ea& t)'e deter&ined.

Fr)& t(e euati)n )* si&-le 'endingM E

I R

,(ere6 M 'ending &)&ent at a secti)n

E &)dulus )* elas tici ty

I sec)nd &)&ent )* area )* t(e secti)n

R radius )* curvature

J(en ')t( E and I are c)nstant *)r a given secti)n/ M and R are t(e )nly

varia'les.

T(e e-ressi)n *)r M is t(enEI

M R

I* t(e de*lecti)n )* t(e &e&'er is y/ and as de*lecti)n is a *uncti)n )* t(e

radius )* curvature R/ t(en6

3

3

d y I

d R 7R is t(e sec)nd derivative )* de*lecti)n8

t(en63

3

d yM EI

d

,(ere = distance al)ng t(e lengt( )* t(e 'ea& t) -)siti)n )* 'ending

&)&ent M.

T) )'tain de*lecti)n6

3

3

d y M

d EI

0ending &)&ent e-ressi)n

dy M Ad EI Sl)-e e-ressi)n

My A 0

EI De*lecti)n e-ressi)n

STRUCTUR AL ANALBSIS AND DESI#N 7A"8 !!


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ST3,Y G3I,E !

J(ere A and 0 are c)nstants )* integrat i)n. T(ey are deter&ined 'y

c)nsidering t(e ')undary c)nditi)ns relating t) t(e 'ea& 7i.e. t(e +n),n

values )* sl)-e and de*lecti)n8.

It is t(ere*)re -)ssi'le t) *ind t(e sl)-e and de*lecti)n at any -)int al)ng a

'ea& 'y -r)viding a general e-ressi)n *)r 'ending &)&ent at any secti)n in

ter&s )* = and integrating t(e euati)n t,ice.

T(e -r)cedure *)r deter&ining t(e 'ending &)&ent e-ressi)n is as *)ll),s6

9. Assu&e )ne end )* t(e 'ea& t) 'e t(e )rigin 7generally t(e le*t


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ST3,Y G3I,E !

Example 1: Poit load!

A 'ea& is si&-ly su--)rted as s(),n. F)r t(e illustrated l)ading syste&/

deter&ine6

7a8 t(e sl)-e and de*lecti)n under t(e 344 +N l)ad

7'8 t(e &agnitude and -)siti)n )* t(e &ai&u& de*lecti)n.

E 34@ +N&&3

I 44 94G&&?

Find t(e value )* t(e reacti)ns

Ta+e &)&ents a')ut Ra

M 4/ cl)c+,ise &)&ents are -)sitive7344 3 8 7:@4 @ 8 K 7R

'; 8 4

R' :4;.9 +N

! 4/ u-,ards *)rces are -)sitiveR

a 344 :@4 K :4;.9 3?3. +N

A--ly Macaulay>s &et()d at a secti)n K 'ey)nd t(e last a--lied l)ad

Ta+e &)&ents a')ut K

Distance t) l)ad *r)& M)&ent F)rce distance

secti)n K

7&8

Ra

3?3.

344 +N K3 344K3$

:@4 +N K@ :@4K@$

!# STRUCTUR AL ANALBSIS AND DESI#N 7A"8

X


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ST3,Y G3I,E !

T(e t)tal &)&ent at =&ay 'e ,ritten as6

3

3d yM EI 3?3.$ K 344 K3$ K :@4 K@$d

Integrate ,it( res-ect t) >

3

3

d yEI 3?3.$ K 344 K3$ K :@4 K@$

d&)&ent 7+N&8

3 3 3dy $ K3$ K@$EI 3?3. K 344 K :@4 A

d 3 3 3

sl)-e euati)n

7+N& & +N& 38

: : :$ K3$ K@$EI y 3?3. K 344 K :@4 A 0

G G G

de*lecti)n euati)n

7+N&3 & +N&:8

N), de*lecti)ns are 2er) at t(e su--)rts t(us6

J(en 4/ y 4 and ;/ y 4

Su'stituting in t(e de*lecti)n en. *)r 4/ y 4

: : :4$ 4K3$ 4K@$

EI 4 3?3. K 344 K :@4 A4 0G G G

Note: J(en deter&ining uantities/ )&it any ter& inside a 'rac+et t(at is

negative )r 2er).

T(us6

4 748 K 7ign)re8 K 7ign)re8 748 0

T(us c)nstant )* integrati)n 0 4

Su'stituting in t(e de*lecti)n en. *)r ;/ y 4

: : :; ;K@ ;K@

EI 4 3?3. K 344 K :@4 A ;$G G G

4 9:HHG K ?GG; K ?G; ;A

A K 93@4

STRUCTURA L ANALBSIS AND DESI#N 7A"8 !$


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ST3,Y G3I,E !

T(us general euati)ns *)r sl)-e and de*lecti)n at any -)int al)ng t(e lengt(

)* t(e 'ea& are

3 3 3dy $ K3$ K@$EI 3?3. K 344 K :@4 K 93@4

d 3 3 3sl)-e

: : :$ K3$ K@$EI y 3?3. K 344 K :@4 K 93@4$

G G Gde*lecti)n

T) *ind t(e sl)-e and de*lecti)n at t(e 344 +N l)ad su'stitute *)r 3

3 3 3dy 3$ 3K3$ 3K@$EI 3?3. K 344 K :@4 K 93@4

d 3 3 3

?HG K 748 K 7ign)re8 K 93@4 +N&3

dy K;G?

d EI

9 +N&3 94 N&&

9 +N&&3 94 :N&&3

Units are n), c)nsistent

A

G

:

;G? 94 44 94

34@ 94

K4.44?9 radians

: : :3$ 3K3$ 3K@$EI y 3?3. K 344 K :@4 K 93@43$

G G G

:3? K 4 K 4 K 3@44 +N&:

K39;Gy

EI

A

G

:

K39;G 94 44 94

34@ 94

3 ?N&&

&&N&& &&

K99.H && 799.H && d),n,ards8

T) deter&ine t(e -)siti)n )* t(e &ai&u& de*lecti)n euate sl)-e euati)n t)

2er).

3 3 3dy $ K3$ K@$EI 3?3. K 344 K :@4 K 93@4

d 3 3 3

4 939.@$3K 944 3K ?. ?$ K 9;@ 3K 94. 3@$ K 93@4

4 K9@:.@3

39@4 K G43@ &=!

> -= >c

!4 STRUCTUR AL ANALBSIS AND DESI#N 7A"8


32/141

ST3,Y G3I,E !

S)lving *)r / 3

K39@4 739@4 K ? 9@:.: G43@8

3 9@:.@

= < 0-

-!#&c2?!&

94.: & )r :.HH &.

*)r :.HH & de*lecti)n y K 3;4GEI K 9G.; &&

Example 2: Ui"o#ml$ di!t#i%&ted load!

A si&-ly su--)rted 'ea& is L& l)ng and is reuired t) carry a uni*)r&ly

distri'uted l)ad )* , +N&. In general ter&s/ deter&ine t(e &ai&u&

de*lecti)n )* t(e 'ea&6

Find value )* reacti)ns6

As 'ea& is sy&&etrically l)aded/ Ra R

' , L3 ,L3

A--ly Macaulay>s &et()d at a secti)n K 'ey)nd t(e last a--lied l)ad

In t(is ea&-le c)nsider t(e secti)n K i&&ediately t) t(e le*t )* reacti)n R'


!alue )* l)ad Distance t) centre )* M)&ent F)rce distance

l)ad *r)& secti)n K 7&8

Ra

,L3 ,L.3

, +N& ,. 3 ,..3

STRUCTURA L ANALBSIS AND DESI#N 7A"8 !5


33/141

ST3,Y G3I,E !

T(is &ay 'e ,ritten as6

3 3

3,L , d yM K EI

3 3 d


3 :

: ?

dy ,L ,EI O K Q A sl)-e eDuati)n

d ? G

,L ,EI y O K Q A Q 0 de*lecti)n eDuati)n

93 3?

In )rder t) *ind t(e c)nstants )* integrati)n A and 0 a--ly t(e ')undaryc)nditi)ns.

F)r a si&-ly su--)rted 'ea& ,it( sy&&etrical l)ading6

De*lecti)n at su--)rts is 2er).

De*lecti)n at &id


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ST3,Y G3I,E !

T) deter&ine &ai&u& de*lecti)n/ su'stitute in de*lecti)n euati)n *)r

L3 as t(e 'ea& is sy&&etrically l)aded.

: ? :

: ? :

? ? ?

? ? ?

?

,L7L38 ,7L38 ,L 7L38EI y K K

93 3? 3?

,L.L ,L ,L .LEI y K K

93 3? ?H

,L ,L ,LEI y K K

G :H? ?H

?,L ,L H,LEI y K K

:H? :H? :H?

K@,L

y :H?EI

8 16/ /

Example ': Catile(e#

A cantilever 'ea& is 3& l)ng and is reuired t) carry a uni*)r&ly distri'uted

l)ad )* 34 +N& and a -)int l)ad )* G? +N at t(e ti-.

7a8 Using Macaulay>s &et()d/ deter&ine t(e &ai&u& de*lecti)n )* t(e

'ea& in ter&s )* EI.

7'8 C(ec+ t(e ans,er )'tained in 7a8 'y a--lying t(e standard euati)ns *)r

de*lecti)n

Additi)nal in*)r&ati)n

Standard de*lecti)n *)r&ulae *)r cantilevers6

Uni*)r&ly distri'uted l)ad ,L ?HEIP)int l)ad at ti- JL::EI

STRUCTURA L ANALBSIS AND DESI#N 7A"8 !8


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ST3,Y G3I,E !

Find value )* reacti)ns6

Reacti)n &ust 'alance d),n,ards *)rces/ as ! 4

Ra 34 3 G? 94? +NTa+ing &)&ents a')ut R

a/

M 4/ cl)c+,ise &)&ents are -)sitiveKM

a 734 3 98 G? 3 4

Ma 9GH +N& 7anticl)c+,ise8

A--ly Macaulay>s &et()d/ at a secti)n K as *ar al)ng t(e 'ea& as -)ssi'le.


!alue )* l)ad Distance t) centre )* M)&ent F)rce distancel)ad *r)& secti)n K 7&8

94? 94?

34. 3 34..3

C)nsidering als) t(e &)&ent at t(e su--)rt/ t(is &ay 'e ,ritten as6

3 3

3

d y 34M EI K 9GH 94? K

d 3


3

: ?

dy 94? 34EI K 9GH K A sl)-e euati)n

d 3 G

K9GH 94? 34EI y K A 0 de*lecti)n euati)n

3 G 3?

In )rder t) *ind t(e c)nstants )* integrati)n A and 0 a--ly t(e ')undary

c)nditi)ns.

F)r a cantilever 'ea&/ de*lecti)n at t(e su--)rt is 2er)/ and sl)-e is 2er) at a

'uilt< in su--)rt.

"9 STRUCTUR AL ANALBSIS AND DESI#N 7A"8


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ST3,Y G3I,E !

A--lying t(e de*lecti)n euati)n at su--)rt/ ,(en 4 y 4

3 : ?

K9GH4$ 94?4$ 344$EI 4 K A4$ 03 G 3?

T(ere*)re 0 4

A--lying t(e sl)-e euati)n at t(e 'uilt


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ST3,Y G3I,E !

7'8 C)&-are ,it( standard euati)ns6

Standard de*lecti)n *)r&ulae *)r cantilevers6

Uni*)r&ly distri'uted l)ad ,L ?HEIP)int l)ad at ti- JL ::EI

?

:

34.3 ?4F)r udl

HEI EI

G?.3 9;4.G;*)r a -)int l)ad

:EI EI

394.G;t)tal de*lecti)n

EI

Ans,ers are eactly t(e sa&e.

Note: Standard euati)ns assu&e de*lecti)n is d),n,ards and negative sign

is )&itted.

Example ): Simpl$ !&ppo#ted %eam *it+ a o(e#+a,

N)te )n dealing ,it( variat i)n )* uni*)r&ly distri'uted l)ad 'et,een s-ans.

C)nsider a si&-ly su--)rted 'ea& ,it( an )ver(ang. T(ree c)nditi)ns )*

uni*)r&ly distri'uted l)ad ,ill 'e ea&ined and t(e general e-ressi)n *)r

&)&ent derived.

1. C)nstant udl al)ng t(e lengt( )* t(e 'ea&

C)nsidering a secti)n K t) t),ards t(e end )* t(e 'ea&

"! STRUCTUR AL ANALBSIS AND DESI#N 7A"8


38/141

ST3,Y G3I,E !


M Ra. K ,..3 K R'.Ka$ Ra. K,.3

3 K R'.Ka$

!@ udl )n t(e &ain s-an and a larger udl )n t(e )ver(ang

F)r analysis -ur-)ses t(is is treated as a c)nstant udl )ver t(e entire

'ea& and an additi)nal l)ad )* 72K, +N&8 )n t(e )ver(ang. As in 798/

&)&ents are ta+en a')ut t(e secti)n K.


7sa&e as c)nditi)n 98 7additi)nal ter&8

M

Ra. K,..3 K R

'.Ka$ K 72K,8.Ka$.Ka$3

Ra. K,.33 K R

'.Ka$ K 72K,8.Ka$33

"@ udl )n t(e &ain s-an and a s&aller udl )n t(e )ver(ang

F)r analysis -ur-)ses t(is is treated as a c)nstant udl )ver t(e entire

'ea& lessan additi)nal l)ad )* 7,K2 +N&8 )n t(e )ver(ang. L)ad ,K2

acts u(w&rdsand gives a -)sitive &)&ent a')ut secti)n K. As in t(e

)t(er cases &)&ents are ta+en a')ut t(e secti)n K.

STRUCTURA L ANALBSIS AND DESI#N 7A"8 ""


39/141


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ST3,Y G3I,E !

Ta+e &)&ents a')ut K/ c)nsidering a uni*)r& l)ad )* :4+N& )ver t(e

entire lengt( )* 'ea& and a negative 7u-,ard8 l)ad )* 34+N& )n t(e

)ver(ang.

!alue )* l)ad Distance t) centre )* M)&ent F)rce distance

l)ad *r)& secti)n K 7&8

99;.@ +N 99;.@

:4 +N&. 3 :4..3

9?3.@ +N KH 9?3.@7KH8

34 +N&.7KH8 7KH83 34.7KH833

T(is &ay 'e ,ritten as6

3 3 3

3

dy :4 34KH$M EI 99;.@ K 9?3.@KH$

d 3 3


3 : 3 :

: ? : ?

dy 99;.@ :4 9?3.@KH$ 34KH$EI K A sl)-e euati)n

d 3 G 3 G

99;.@ :4 9?3.@KH$ 34KH$EI y K A 0 de*lecti)n euati)n

G 3? G 3?

In )rder t) *ind t(e c)nstants )* integrati)n A and 0 a--ly t(e standard

c)nditi)ns.

F)r a si&-ly su--)rted 'ea& de*lecti)n is 2er) at t(e su--)rts.

J(en 4 / y 4 K a--ly t) de*lecti)n euati)n

: ? : ?99;[email protected] :4.4 9?3.@4KH$ 344KH$EI 4 K A 0

G 3? G 3?

4 748 K 748 7ign)re ter&8 7ign)re ter&8 748 0

0 4

STRUCTURA L ANALBSIS AND DESI#N 7A"8 "$


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ST3,Y G3I,E !

Als) ,(en H/ y 4 K a--ly t) de*lecti)n euati)n

: ? : ?

99;[email protected] :4.H 9?3.@HKH$ 34HKH$EI 4 K AG 3? G 3?

4 9443; K @934 748 748 A.H

A K79443;K@9348H KG9:.?

Standard euati)ns 'ec)&e6

3 : 3 :

: ? : ?

dy 99;.@ :4 9?3.@KH$ 34KH$EI K K G9:.? sl)-e euati)n

d 3 G 3 G99;.@ :4 9?3.@KH$ 34KH$

EI y K K G9:.? de*lecti)n euati)nG 3? G 3?

Actu&l de'lections

At centre )* &ain s-an/ ?&

: ? : ?99;.@.? :4.? 9?3.@?KH$ 34?KH$EI y K K G9:.?.?

G 3? G 3?

EI y 93@:.: K :34 7ign)re8 7ign)re8 K 3?@:.G

In ter&s )* EI/ y K9@34.:EI

Actual de*lecti)n/ y K9@34.: 9493 734@ 94:@@::4 94?8y K9:.? && 7d),n,ards de*lecti)n8

De*lecti)n at ti- )* 'ea&/ 94&

: ? : ?99;[email protected] :4.94 9?3.@94KH$ 3494KH$

EI y K K G9:.? 94G 3? G 3?

EI y 9@H:.: K 93@44 94 9:.: K G9:?

In ter&s )* EI/ y [email protected] EI

Actual de*lecti)n/ y [email protected] 9493 734@ 94:@@::4 94?8

y 94.3 && 7u-,ards de*lecti)n8



42/141

ST3,Y G3I,E !

Study Guide ! End Test

St&nd&rd lo&d c&se 'ormul&e

9. A series )* ti&'er 'ea&s *)r& -art )* a 'alc)ny )* a 'uilding. T(e

'ea&s are cantilevered )ver a 3.?& lengt( as s(),n in Figure 9. T(e

'ea&s are at 9.3& centres and are reuired t) su--)rt a uni*)r&ly

distri'uted l)ad )ver t(e entire lengt( and a -)int l)ad at t(e ti-. Using

t(e design *)r&ulae and t(e additi)nal data/ deter&ine t(e de*lecti)n at

t(e ti- )* t(e 'ea&.

Fi,e 1

Additi)nal data6

Uni*)r&ly distri'uted l)ad )n *l))r 'eing carried'y 'ea&s 3.? +N&

P)int l)ad at cantilever ti- 9 +N

M)dulus )* elasticity )* ti&'er secti)n 7E8 HH44 N&&3

De*lecti)n *)r&ulae6

Due t) udl ,L?HEIDue t) -)int l)ad at ti- JL::EI

3. F)r t(e ?@; 99 H3 U0 'ea& l)aded as s(),n 'el),/ use t(estandard case de*lecti)n *)r&ulae given in t(e design data t) deter&ine

t(e &id


43/141

ST3,Y G3I,E !

Design data6

M)dulus )* elasticity 7E8 34@ +N&&3

Sec)nd &)&ent )* area :;4@4 c&?

De*lecti)n *)r&ulae6

Due t) udl @,L?:H?EIDue t) -)int l)ad at &ids &et()d/ -r)ve t(at t(e standard *)r&ula *)r a si&-ly

su--)rted 'ea& carrying a -)int l)ad at &id *r)& Ra.

7c8 Derive t(e euati)ns *)r sl)-e and de*lecti)n.

7d8 Deter&ine t(e actual de*lecti)n )* t(e 'ea& ,(en :&.

Fi,e )

E 94H44 N&&3

I :@; 94G&&?



44/141

ST3,Y G3I,E !

Answers

9. ud l

@.4: && -) in t

3.:: && t)tal

;.:G &&

3. ud l

@.:: && -) in t

:.@G && t)tal

H.H &&

?. Ra .H +N R' ;.: +N

M .H K 333 ;.:7KG8 K97KG833

Sl)-e euati)n6 .H33 K 3:G ;.:7KG833 K 7KG8:G K ?4.H

De*lecti)n euati)n6 .H :G K 3?3? ;.:7KG8:G K 7KG8?3? K ?4.H

De*lecti)n6 33&&

STRUCTURA L ANALBSIS AND DESI#N 7A"8 "8


45/141

#9 STRUCTUR AL ANALBSIS AND DESI#N 7A"8


46/141


47/141

ST3,Y G3I,E "

In t(e design -r)cess t(e *)ll),ing &aterial strengt(s ,ill 'e used

t(r)ug()ut6

C(aracteristic strengt( )* c)ncrete/ *cu

?4 N&&3

C(aracteristic strengt( )* &ain rein*)rce&ent/ *y

?G4 N&&3

C(aracteristic strengt( )* s(ear rein*)rce&ent/ *yv

3@4 N&&3

Unit ,eig(t )* c)ncrete 3? +N&:

In additi)n t) t(e study guide y)u ,ill reuire a c)-y )* Reinforced Concrete

Design-Details of Reinforcing Steel.

Sym-ols &nd terms used in rein'orced concrete design

F)r a si&-ly su--)rted 'ea& ,it( tensi)n )n t(e ')tt)& sur*ace due t)

'ending.

' K 'readt( )* t(e secti)n( K )verall de-t( )* t(e secti)n

d K e**ective de-t( )* secti)n 7t(is is t(e de-t( *r)& t(e c)&-ressi)n

sur*ace t) t(e centre )* t(e tensi)n rein*)rce&ent8

AsK area )* &ain tensi)n rein*)rce&ent

Asv

K area )* lin+ 7s(ear8 rein*)rce&ent

STRUCTUR AL ANALBSIS AND DESI#N 7A"8 #!


48/141


49/141


50/141

ST3,Y G3I,E "

(b) here none of the conditions (*), (+) or (3) apply, the bar spacing

should be limited to the "alues gi"en in table 3+ for slabs here the

percentage of reinforcement e!ceeds *1 or the "alues gi"en in table3+ di"ided by the reinforcement percentage for lesser amounts4

Example

I* a sla' is :44 && dee- and *r)& design calculati)ns 4.?@ )* (ig( yield

rein*)rce&ent is reuired/ t(en t(e &ai&u& distance 'et,een 'ars can 'e

deter&ined as *)ll),s6

Fr)& Ta'le :.3H &a. s-acing 9@@ &&

"),ever t(is *igure is 'ased )n 9 )r &)re )* rein*)rce&ent 'eing -r)vided

Fr)& Cl :.93.99.3.; &ai&u& s-acing 9@@4.?@ :?? &&

Minimum &re& o' rein'orcement "@1!@$

En)ug( rein*)rce&ent s()uld 'e -r)vided t) c)ntr)l t(e crac+ ,idt(s in t(e

tensi)n *ace regardless )* any )t(er design c)nsiderati)ns. Fr)& Ta'le :.3@6

Situati)n De*initi)n )* Mini&u& -ercentage

-ercentage *y 3@4N&&3

Tensi)n rein*)rce&ent7c8 Rectangular secti)ns 944 A

sA

c4.3? 4.9:

7in s)lid sla's t(is &ini&u&

s()uld 'e -r)vided in ')t(

directi)ns8

F)r (ig( yield rein*)rce&ent &ini&u& -er&issi'le area is 4.9: )* gr)ss

secti)n/

t(ere*)re &ini&u& As 4.449:'(

Distri'uti)n )r sec)ndary steel is reuired in sla's. T(is rein*)rce&ent runs atrig(t angles t) t(e &ain tensi)n rein*)rce&ent and is tied t) it. T(e -ur-)se

)* t(e sec)ndary steel is t) tie t(e sla' t)get(er and t) assist in distri'uting

t(e l)ading t(r)ug( t(e sla'. T(e area )* t(is steel &ust 'e &t le&steual t)

t(e &ini&u& area )* steel *)und *r)& Ta'le :.3@

T(e distri'uti)n steel is al,ays -laced inside t(e &ain steel t(us giving t(e

tensi)n rein*)rce&ent t(e greatest e**ective de-t(.

STRUCTURA L ANALBSIS AND DESI#N 7A"8 #$


51/141

ST3,Y G3I,E "

M&=imum &re& o' rein'orcement "@1!@4

P(ysically in )rder t) c)&-act t(e c)ncrete -r)-erly and ensure adeuate')nd devel)-s 'et,een t(e c)ncrete and t(e steel rein*)rcing 'ars a &ai&u&

&ust 'e -ut )n t(e a&)unt )* rein*)rce&ent all),ed in ele&ents

0ea&s and sla's Neit(er t(e area )* tensi)n rein*)rce&ent n)r area )*

c)&-ressi)n s()uld eceed ? )* t(e gr)ss cr)ss *)r u--er *l))rs

C(aracteristic i&-)sed l)ad 9344+N

C(aracteristic dead l)ad H34+N

E-)sure c)nditi)ns &)derate

Fire resistance : ()urs

C)lu&n cr)ss


79/141

ST3,Y G3I,E "

A!*e#!

Sl&- ,esign

Ans,ers ,(ere a--r)-riate K -er &etre ,idt( )* sla'6

Design l)ading 9G.HG +N& M ?G.@@ +N& ! :.G +N

1 4.4:9

AS @;@ &&3&

v 4.3 N&& 3 vc 4.?; N&&3

Actual s-ande-t( rati) 3?.9 -er&iss i'le s-ande-t( rati) 3?.?

e&m design

Results *r)& analysis )* all t(ree l)ad cases6

Reacti)n

A7+N8

Reacti)n 0

7+N8

&)&ent

Mai&u&

sagging

&)&ent 7+N&8

Mai&u&

()gging

&)&ent 7+N&8

L)ad case 9 3::.3 @[email protected] :;.H 3;H.:

L)ad case 3 3@@.? :G3.3 ?@ 94

L)ad case : ;4.3 :?9.: HH.? 3;H.:

Mai&u& sagging &)&ent ?@ +N&

Mai&u& ()gging &)&ent 3;H.: +N&

Mai&u& s(ear at A 3@@.? +N

7'8 Sagging rein*)rce&ent ")gging rein*)rce&ent

1 4.94H 1 4.4GG

2 4.HG d 2 4.3 d

As 34@: &&3 A

s 99G? && 3

7c8 v 4.@H N&&3 vc 4.G9 N&&3

R93>s 344 && centres )r euivalent

7d8 Actual s-ande-t( rati) ?.; Per&issi'le s-ande-t( rati)

G.3

5# STRUCTUR AL ANALBSIS AND DESI#N 7A"8


80/141

ST3,Y G3I,E "

Column design

Dead l)ad *r)& *l))r :;:.? +NI&-)sed l)ad *r)& *l))r 3?4 +N Design l)ad/ N :GH +N

Asc

G?:H &&3

Main rein*)rce&ent HT:3 7G?:4 && 38

Lin+s RH>s :@4 && centres/ )r alternatives

STRUCTURA L ANALBSIS AND DESI#N 7A"8 5$


81/141

ST3,Y G3I,E #

STUDY GUIDE )

,esign o' structur&l steelwork elements

Introduction

T(is study guide c)vers Outc)&es @ and G )* t(e unit.

Outcome $

Design statically deter&inate structural steel 'ea&s.

Outcome 4

Design aially l)aded/ single


82/141

ST3,Y G3I,E #

Structur&l steel struts su-*ect to &=i&l lo&d S $8$911889

Com(ression mem-ers cl&use #@5

C)&-ressi)n &e&'ers are classed as eit(er6

798 >lastic

Compact in eac( case t(e secti)n can resist t(e *ull l)ad

Semi-compact 7suas( l)ad8

It is )nly necessary *)r strut design t(at t(e secti)n 'e classi*ied as n)t

slender.

T(is is n)t related t) t(e Euler t(e)ry de*initi)n )* slender> 'ut relates t) t(e

a'ility )* t(e cr)ss


83/141

ST3,Y G3I,E #

T(us *)r a ?@; 9@3 ;? U0 in #rade ?: steel6,e' t(ic+ness t . &&

*lange t(ic+ness T 9;.4 &&Design strengt( -

y 3G@ N&& 3

Note: T(e design strengt( de-ends )n t(e greater &aterial t(ic+ness.

F)r slender secti)ns -yis &)di*ied 'y a stress reducti)n *act)r as given in

Ta'le H 7n)t a--lica'le t) UC secti)ns8.

T(e cl&ssi'ic&tion o' t/e sectionis *)und using T&-le 5)* 0S@@4 and is a

&easure )* t(e ease ,it( ,(ic( t(e cr)ss


84/141

ST3,Y G3I,E #

T(e slenderness is a &easure )* t(e ease ,it( ,(ic( t(e strut ,ill 'uc+le

)ver its lengt( and is *)und using6

SlendernessELE**ective lengt(O O

Radius )* gyrati)n r

E**ective lengt( is de*ined as t(e lengt( 'et,een -)ints )* e**ective restraint

)* a &e&'er &ulti-lied 'y a *act)r t) ta+e acc)unt )* t(e end c)nditi)ns and

l)ading

LE 1L

,(ere L actual lengt(1 e**ective lengt( rati)

1 is deter&ined *r)& t(e c)nditi)ns )* end restraint.

In t(is c)urse E< 1@9 or 9@6$

T(e value y)u s()uld use ,ill 'e given in eac( uesti)n.

Note:Universal c)lu&n secti)ns (ave two&a=)r aes K and yKy/ t(us t(ere

are t,) values )* s lenderness6

EyE

y

LL and

r r

0)t( values (ave t) 'e calculated in )rder t) deter&ine t(e c)&-ressive

strengt( (c@

T) decide ,(ic( )* t(e T&-les !50&2 0d2 are t) 'e used in deter&ining (c

re*erence &ust *irst 'e &ade t) T&-le !$.

F)r UC secti)ns/ etracting *r)& Ta'le 3@ gives6

Ty(e o' section T/ickness == &=is yy &=is

R)lled "


85/141

ST3,Y G3I,E #

All UC secti)ns are "


86/141


87/141


88/141


89/141

ST3,Y G3I,E #

St&nc/ions restr&ined &t &n intermedi&te (osition

Alt()ug( t(ey are n)t as e**icient as UC secti)ns/ Universal 0ea& secti)nsare *reuently used t) carry aial l)ads. T(e y


90/141

ST3,Y G3I,E #

Example Sta-+io *it+ ite#mediate #e!t#ait!

T(e diagra& 'el), s(),s t(e elevati)n )* a c)lu&n t(at is t) 'e -r)vided

,it( inter&ediate ties -r)viding restraint a')ut t(e yKy ais )nly. T(ec)lu&n is t) carry aial un*act)red l)ads )* @H4+N dead and ;G4+N i&-)sed.

T(e -r)-)sed secti)n *)r t(e c)lu&n is @:: 394 949 U0. C(ec+ t(esuita'ility )* t(e -r)-)sed secti)n/ using t(e s&'e lo&d t&-les 'or 3

sections / LE

9.4L

Design l)ad 9.? dead 9.G i&-)sed 9.? @H4 9.G ;G4 343H+N

E**ective lengt( yKy ais LEB

:.G&

E**ective lengt( K ais LEV

G.H&

Fr)& t(e sa*e l)ad ta'les6

LEBF)r L

EB :.@& P

CB 34G4 +N

F)r LEB

?.4& PCB

9H@4 +N

F)r LEB

:.G& PCB

34G4 K9@ 734G4K9H@48 349H+NL

EV

F)r LEV

G.@& PCV

3;G4 +N

F)r LEV

;.4& PCV

3;@4 +N

F)r LEV

G.H& PCV

3;G4 K:@ 94 3;@? +N

C)&-ressive resistance )* stanc(i)n/ PC349H +N



91/141

ST3,Y G3I,E #

,esign o' mem-ers su-*ect to -ending S $8$911889

T(e rules *)r t(e design )* &e&'ers in 'ending are given in sections #@! &nd#@")* 0S @@46 Part 9. T(e design )* suc( ele&ents is -ri&arily c)ncerned

,it( 'ending strengt(/ 'ut since 'ending &)&ent is su'=ect t) variati)n al)ng

t(e lengt( )* t(e &e&'er and is acc)&-anied 'y s(ear acti)n/ t(e

c)&'inati)n )* 'ending and s(ear &ust 'e ta+en int) acc)unt. In additi)n/ t(e

degree )* restraint a--lied t) t(e 'ea& ends and al)ng its lengt( greatly

in*luence t(e 'ending ca-acity. I* t(e 'ea& is *ully restrained al)ng its

c)&-ressi)n *lange as de*ined in clause ?.3.3/ t(ere is n) need t) &a+e any

all),ance *)r lateral t)rsi)nal 'uc+ling.

All 'ea&s &ust (ave an adeuate resistance t) 'ending and s(ear/ and 'ea&s

t(at are n)t *ully restrained laterally &ust 'e c(ec+ed *)r a reduced 'ending

ca-acity due t) lateral t)rsi)nal insta'ility/ in acc)rdance ,it( secti)n ?.:.

Dully restr&ined -e&ms

A -ractical situati)n ,(ere t(e 'ea& &ay 'e c)nsidered as (aving its

c)&-ressi)n *lange *ully restrained is ,(ere it is reuired t) carry a c)ncrete

*l))r 7eit(er in-situ)r *)r&ed *r)& -re


92/141


93/141


94/141

ST3,Y G3I,E #

+e- -uckling &nd -e&ring

uckling #@$@!@1

At -)ints )* c)ncentrated l)ad suc( as t(e c)nditi)n s(),n 'el),/ ,(ere t(e

'ea& is su--)rted/ it is -)ss i'le t(at t(e 'ea& ,e' can 'uc+le. T(e

reuire&ents )* clause [email protected] &ust 'e &et.

T(e 'uc+ling resistance Bw< 0-

1> n

12 t (

c

Ty-ical values )* 'earing lengt( are6

*)r a 'ea& resting )n 'ric+ su--)rts '9944 &&

*)r a 'ea& resting )n seating cleats '9 39 &&

n9

l)ad dis-ersal lengt( K *)r su--)rts t(is is eual t) (al* t(e de-t(

)* t(e 'ea&

t 'ea& ,e' t(ic+ness-

c c)&-ressive strengt( )* t(e ,e' K *)und using Ta'le 3;7c8 )* t(e

c)de *)r a slenderness/ 3.@dt



95/141

ST3,Y G3I,E #

e&ring

It is als) -)ssi'le t(at t(e =uncti)n 'et,een t(e 'ea& *lange and ,e' &ay 'esu'=ect t) a 'earing *ailure.

T(e l)cal ca-acity )* t(e inter*ace 'et,een t(e ,e' and t(e 'ea& is given 'y6

Bcri(

< 0-1> n

!2 t (

yw

,(ere n3 t(e lengt( )'tained 'y dis-ersi)n t(r)ug( t(e *lange t) t(e

*lange


96/141

ST3,Y G3I,E #

Sol&tio

Section (ro(ertiesSecti)n si2e G94 33 99: Universal 0ea&De-t( )* steel secti)n D G4;.G &&

Jidt( )* steel secti)n 0 33H.3 &&

T(ic+ness )* *lange T 9;.: &&

T(ic+ness )* ,e' t 99.9 &&

R))t radius r 93.; &&

Inertia a')ut &a=)r ais I H;:34 c&?

Plastic &)dulus a')ut &a=)r ais S :3H9 c&:

Elastic &)dulus X 3H;? c&:

Area )* secti)n A 9?? c&3

Strengt/ o' steel Cl&use "@1@1

F)r &aterial t(ic+ness )* 9;.: &&/ *r)& Ta'le G

Design strengt( 7#rade ?:8 -y 3G@ N&&3

B)ung>s &)dulus E 34@ +N&&3

D&ctored lo&ding

Distri'uted l)ad , 9.? dead 9.G i&-)sed

9.? 3? 9.G :4 H9.G +N&

P)int l)ad J 9.? 93? 9.G H? :4H +N

Reacti)ns ,L3 J3

H9.G G3 :4H3 :H.H +N

T(is is als) t(e &ai&u& s(ear

Mai&u& &)&ent ,L3H JL?

H9.G G 3H :4H G? H3.3 +N&

Section cl&ssi'ic&tion

Rati)s *)r l)cal 'uc+ling 'T G.G4 H.@e

dt ?.: ;e

T(ere*)re secti)n is (l&stic

S/e&r #@!@"

S(ear area Av tD 99.9 G4;.G G;??.?

&& 3

S(ear ca-acity Pv 4.G -

yA

v

4.G 3G@ G;??.?94: 94;3.? +N

Design s(ear *)rce Fv :H.H +N

Since Fv 4.G P

vl), s(ear l)ad c)nditi)n a--lies Cl&use #@!@$



97/141

ST3,Y G3I,E #

Note:t(is is t(e ,)rst arrange&ent )* s(ear *)rce.

T(e 'ea& s()uld 'e c(ec+ed *)r t,) c)nditi)ns6

798 &ai&u& s(ear *)rce and c)eistent &)&ent

738 &ai&u& &)&ent and c)eistent s(ear *)rce

I* t(e l), s(ear l)ad c)nditi)n a--lies at t(e reacti)ns/ ,(ere t(e s(ear *)rce

is t(e (ig(est/ it a--lies al)ng t(e lengt( )* t(e 'ea&. T(us t(e 'ea& needs

)nly t) 'e c(ec+ed *)r &ai&u& &)&ent.

Moment c&(&city #@!@$

M)&ent ca-aci ty *)r -las tic sect i)n Mc -

yS

-

yX

Mc

-y

S

3G@ :3H994:

HG.@ +N&

)r Mc 9.3-

yX

9.3 3G@ 3H;?94: 9? +N&

Critical value is t(e lesser )* t(e t,)

Since M Mc7H3.3 +N& HG.@ +N&8 a--lied &)&ent is ,it(in &)&ent

ca-acity.

,e'lection

.pply imposed loads only

Uni*)r& l)ad :4 +N&

Mai&u& de*lecti)n *)r a uni*)r&ly distri'uted l)ad

@,L?:H?EI @ :4 G444?:H? 34@ 94: H;:34 94?

3.H: &&

Mai&u& de*lecti)n *)r a -)int l)ad at &id


98/141

ST3,Y G3I,E #

+e- -e&ring &nd -uckling

e&ring on t/e we- #@$@"L)cal ca-acity )* ,e' P

crit 7'

9n

38t.-

y,

,(ere6

Sti** 'earing lengt( '9

;@ &&

S-read t) *illet n3 3.@ 7rT8

3.@ 793.;9;.:8 ;@ &&

F)r 'ea& ,e' t(ic+ness )* 99.9 &&

Design strengt( )* ,e' -y,

3;@ N&&3

L)cal ca-acity )* ,e' Pc

7'9n

38t.-

y,

7;@;@899.9 3;@94:

?@H +N

F)rce a--lied t(r)ug( *lange Fv

:H.H +N

Since value )* reacti)n is less t(an t(e ca-acity )* t(e ,e'/ n) 'earing

sti**ener is reuired.

uckling o' t/e we- #@$@!

0uc+ling ca-acity )* ,e' P,

7'9

n98t.-

c

,(ere6

Sti** 'earing lengt( '9 ;@ &&

S-read t) centre )* secti)n n9 D3 G4;.G3 :4:.H &&-

cis t(e c)&-ressive strengt( 'ased )n -

y*)r t(e ,e' 7t 99.9 && *r)&

Ta'le G6 3;@ N&& 38

and slenderness rati) 3.@ dtdis t(e de-t( 'et,een t(e *illets )'tained *r)& t(e Secti)n Ta'les.

Alternatively dt is t(e rati) *)r l)cal 'uc+ling )'tained ,(en c(ec+ing t(e

'ea& classi*icati)n 7dt ?.:8.

3.@ @?;.G99.9 93:.:)r 3.@ ?.: 93:.:

Fr)& Ta'le 3;7c8C)&-ressive strengt( -c ? N&& 3

0uc+ling ca-acity )* ,e' P, 7'

9 n

98t.-

c

7;@ :4:.H899.9 ?94:

:@.3 +N

Since t(e reacti)n *)rce is greater t(an t(e ca-acity 7:H.H +N :@.3 +N8 a

l)ad carrying sti**ener ,ill 'e reuired t) -revent t(e ,e' *r)& 'uc+ling.

6his is not a failure condition and ill not change the suitability of the beam

to carry the loads @oe"er stiffeners ill ha"e to be designed to help

distribute the end reaction from the beam eb to the support

8# STRUCTUR AL ANALBSIS AND DESI#N 7A"8


99/141

ST3,Y G3I,E #

Example 2 U!e o" t+e momet -apa-it$ ta%le ad %ea#i, ad %&-3li,

(al&e! "o# &!ti""eed *e%!4 ta%le!5

A series )* 'ea&s at :& centres are reuired t) carry -re


100/141


101/141

ST3,Y G3I,E #

Je' 'uc+ling ca-acity 9@3 ?4 4.;@: 9@3 :4.9 9H3.9 +N [email protected] +N

0ea& ,e' d)es n)t reuire a 'uc+ling sti**ener

T(e end c)lu&n )* t(e ta'le als) gives t(e s(ear ca-acity )* t(e secti)n *)und

using

S(ear ca-acity Pv 4.G -y A

v Fr)& ta'le P

v @4@ +N



102/141

ST3,Y G3I,E #

3nivers&l -e&ms su-*ect to -ending moment c&(&city 'or gr&de #" steel

,esign&tion ,esign&tion

Seri&l

SiFe

mm

M&ss?

metre

kg

Moment

C&(&city

k7m

Seri&l

SiFe

mm

M&ss?

metre

kg

Moment

C&(&city

k7m

9? ?9

9? :4@

H:H 33

;G3 3G;

GHG 3@?

G94 :4@

G94 33

@:: 394

?@; 99

?@; 9@3

:HH

:?:

3H3@:33?349

33G

9?9;G

9;

9;:9?;

9;49@39?4

93@

3:H

9;9?

9?493@99:949

933949493H3

HHH3;?G;

H3;?G;G4@3

?G4

?994

::?43H43@343334

3?:4

34:49H44

944

9G?49:;4

9?49:349394

94G4

9H4

9?G49394

9944;@H;3;3

H?H;?;G?G@3@GG

@9@::@4:?@G?4?

?;;?3:G:@3:44

?4G 9;H

?4G 9?4

:@G 9;9

:@G 93;

:4@ 9G@

:4@ 93;

:4@ 943

3@? 9?G

3@? 943

34: 9::

34: 943

9;H 9439@3 H

93; ;G

;?

G;G4@?

?G:

G;

@;@9?@

:::

@??G?4

?H?3

:;

::3H3@

?::;

:9

3H3@33

:43@

3:

99G

9:

?93

:;9:3;3H

3??9H

:::

3;H3?G39:

9H49?H

3:399;3

9?9GH

9?H

9:39933

9@G9::

94

;H?;3

HG;9

G:

?;:?

3:



103/141

ST3,Y G3I,E #

Study Guide # End Test

Figure 9 s(),s t(e -art lay)ut )* &ulti


104/141

ST3,Y G3I,E #

7'8 In additi)n t) t(e *l))r l)ading t(e stanc(i)n is reuired t) carry a

design aial l)ad )* :9G4+N *r)& u--er *l))rs. Using t(e a--r)-riate

clauses )* 0S H994K9/ c(ec+ t(e suita'ility )* a :4@ :4@ 9@H UCsecti)n i* t(e lengt( 'et,een restraints is ?& and t(e e**ective lengt( LE

4.H@L.

7c8 I* t(e UC ,ere t) 'e re-laced 'y a U0 secti)n/ *r)& t(e sa*e l)ad ta'les

select a suita'le secti)n i* side rails ,ere used t) restrain t(e yKy ais at

&id


105/141

ST3,Y G3I,E #

Answers

Ty(e A -e&m

7a8 Design l)ad ?.H +N&

7'8 Mai&u& &)&ent M :H.? +N&

Mai&u& s(ear *)rce Fv 9.3 +N

7c 8 Mc ?93 +N&/ P

v G?; +N De*lecti)n 9;.9 s-an:G4

Ty(e -e&m

7a8 C)ncentrated l)ad :H.? +N

7'8 Mai&u& &)&ent M 99@ +N&

7c8 Secti)n G94 :4@ 9? U0 )r GHG 3@? 9?4 U0 *)r ')t(M

c 9394 +N&

7d8 F)r G94 :4@ 9? UC Pv 99? +Nde*lecti)n 9?.? s-an:G4

7e8 Je' 'earing ca-acity ?@G +N

Je' 'uc+ling ca-acity ?:9 +N

Column

Aial design l)ad ?3@@ +N

Pc ?@3G +N

U0 secti)n6 GHG 3@? 9;4 )r alternative Pcy

?;44 +N/ Pc

@4?4 +N

STRUCTUR AL ANALBSIS AND DESI#N 7A"8 191


106/141

ST3,Y G3I,E $

STUDY GUIDE 6

,esign o' m&sonry &nd tim-er elements

Introduction

T(is study guide c)vers Outc)&es ; and H )* t(e unit.

Outcome 5

Design vertically l)aded singleart *' Structural use of unreinforced masonry

Tim-er

AS 5+2+'*77 Structural use of timber

>art +' Code of practice for permissible stress design, materials and

or$manship

STRUCTURA L ANALBSIS AND DESI#N 7A"8 19"


107/141

ST3,Y G3I,E $

,esign o' m&sonry to S $4!61 188!

M&teri&ls

Mas)nry is t(e na&e given t) t(e c)nstructi)n c)nsisting )* 'ric+,)r+ 7)r

'l)c+,)r+8 and &)rtar. T(e *inal strengt( )* t(e structural ele&ents *)r&ed

is de-endent )n6

T(e strengt( )* t(e 'ric+ 7)'tained *r)& t(e &anu*acturer>s data s(eets8

T(e strengt( )* t(e &)rtar 7de-endent )n &)rtar c)nstituents and

-r)-)rti)ns8

0ric+s &ay 'e divided int) t(e categ)ries6

Clay K ,(ic( &ay 'e *urt(er su'divided int) c)&&)n/ *acing and

engineering

Calc iu& si licate

C)ncre te 'ric+s

Standard 'ric+ *)r&at is 39@ && l)ng 943.@ && ,ide G@ && (ig(

0l)c+s &ay 'e de*ined as6

Clay 'l)c+s

Dense c)ncrete 'l)c+s

Aerated 7)r lig(t,eig(t8 c)ncrete 'l)c+s

Si2es can vary *r)& 944 t) 344 && ,ide/ u- t) :44 && (ig( and ??4 &&

l)ng.

M)rtar varieties are6

Ce&ent6 l i&e6 sand

Mas)nry ce&ent and sand

Ce&ent6 sand ,it( -lasticiser

M)rtars are as s-eci*ied 'y t(eir &i -r)-)rti)ns as a rati) )* ce&ent t) li&e

t) sand/ e.g. 9636H 7ce&ent6 li&e6 sand8. Ce&ent sand &)rtars (ave strengt(

'ut acc)&&)date &)ve&ent -))rly. Intr)ducing varying a&)unts )* li&e

all),s t(e &)rtar t) acc)&&)date settle&ent/ te&-erature and &)isture

c(anges t) ,(ic( t(e *inal structure &ay 'e su'=ect/ 'ut (as t(e disadvantage

)* reducing t(e *inal strengt( )* t(e &)rtar. Ta'le 9 )* 0S @G3H designates

*)ur ranges )* &)rtars assigned 7i8/ 7ii8/ 7iii8 and 7iv8.

STRUCTURA L ANALBSIS AND DESI#N 7A"8 19#


108/141

ST3,Y G3I,E $

7i8 indicates a &)rtar ,it( (ig( strengt( 'ut -))r at acc)&&)dating

&)ve&ent.

7iv8 indicates a &)rtar g))d at acc)&&)dating &)ve&ent 'ut (aving l),strengt(.

Ta'le 9 *urt(er s-eci*ies t(e c)nditi)ns )* use 'et,een t(e t(ree &ain &)rtar

ty-es6

Ce&ent6 li&e6 sand &)rtars (ave g))d ')nding -r)-erties and (ence (ig(

resistance t) rain -enetrati)n 'ut l), resistance t) *r)st attac+. C)nversely

ce&ent6 sand ,it( -lasticiser &)rtars (ave a (ig( resistance t) *r)st attac+

'ut d) n)t ')nd ,ell ,it( t(e 'ric+s )r 'l)c+s and &ay 'e su'=ect t) rain

-enetrati)n. Mas)nry &)r tars atte&-t t) -r)vide a &ediu& 'et,een t(e )t(er

t,) &)rtar ty-es 'y (aving 'etter ')nding -r)-erties t(an ce&ents ,it(

-lasticisers and an increased resistance t) *r)st attac+ )ver ce&ent6 li&e6 sand

&)rtars.

,esign consider&tions S $4!61

o&ds

In deter&ining t(e l)ads )n ele&ents )* t(e structure t(e *)ll),ing

c(aracteristic l)ads and t(eir c)&'inati)ns are c)nsidered in t(is c)urse.

,e&d

T(e c(aracteristic dead l)ad 7#+8 is t(e ,eig(t )* t(e structure c)&-lete ,it(

*inis(es/ *itures and -artiti)ns.

Im(osed

T(e c(aracteristic i&-)sed l)ad 7Q+8 is calculated in acc)rdance ,it( 0S

G:6 Part 9/ 'ased )n t(e activity)ccu-ancy *)r ,(ic( t(e *l))r area ,ill 'e

used/ )r in acc)rdance ,it( 0S G:6 Part : *)r r))* l)ads.

C)&'inati)ns )* t(e a')ve l)ads *)r& t(e 'asis )* t(e design l)ads used in

t(e analysis )* t(e structural ele&ents. Clause 33 )* t(e c)de )utlines/ *)r

c)&'inati)ns )* l)ad/ t(e design l)ads ta+en as t(e su& )* t(e -r)ducts )* t(e

c)&-)nent l)ads &ulti-lied 'y t(e a--r)-riate -artial sa*ety *act)r.

F)r ea&-le/ t(e c)&'inati)n )* dead and i&-)sed l)ad used *)r t(e design

l)ad is ta+en as t(e &)st severe c)nditi)n )*6

Design dead l)ad 4. #+)r 9.? #

+

Design i&-)sed l)ad 9.G Q+

STRUCTUR AL ANALBSIS AND DESI#N 7A"8 19$


109/141

ST3,Y G3I,E $

C/&r&cteristic strengt/ o' m&sonry Cl&use !"

T(e c(aracteristic strengt( *+)* any &as)nry ,all )r c)lu&n &ust ta+e int)c)nsiderati)n t(e *)ll),ing *act)rs6

9. M)r tar ty-e and -r)-)rt i)ns K T&-le 1 @

3. T(e 'ric+ ty-e and s trengt( K T&-le ! 0&2 to 0d2de-endent )n t(e 'ric+

)r 'l)c+ unit used and rati) )* 'l)c+ di&ensi)ns K see clause !"@1@

:. T(e ()ri2)ntal cr)ss


110/141

ST3,Y G3I,E $

It is a narr), 'ric+ ,all s) clause 3:.9.3 d)es a--ly.

T(us t(e c(aracteristic strengt( )* t(e &as)nry *+93.3 9.9@ 9? N&&3.

B&rti&l s&'ety '&ctor 'or m&teri&l strengt/ !5

Clause 3; )* 0S @G3H


111/141

ST3,Y G3I,E $

'et,een lateral su--)rts and t(e resistance t) lateral &)ve&ent. T(is is

si&ilar t) t(e &et()ds given in t(e structural steel,)r+ and rein*)rced

c)ncrete c)des 7*)r ea&-le LE 9.4L in steel and l e l)in c)ncretedesign8.

F)r &as)nry design t(e e-lanati)n )* t(e ter&s lateral su--)rt and en(anced

resistance are given in clause !6@!.

&ter&l su((orts

T(e lateral su--)rt can 'e 'ased )n t(e ()ri2)ntal )r vertical di&ensi)n/

de-ending )n ,(et(er t(e su--)rt is -r)vided )n a ()ri2)ntal )r vertical line.

Ea&-les )* t(e ty-e )* su--)rt given are listed 'el),.

F)r t(is c)urse )nly dead and i&-)sed l)ad )n ,alls ,ill 'e c)nsidered/ t(us

)nly t(e e**ective (eig(t )* t(e structure need 'e calculated/ as ,alls reuired

t) carry ,ind l)ading are c)nsidered t) s-an vertically.

HoriFont&l l&ter&l su((orts

Sim(le resist&nce

F)r ()uses n)t eceeding t(ree st)reys/ ,it( ti&'er *l))rs and =)ists s-aced

n)t &)re t(an 9.3 & a-art/ and c)nnected 'y suita'le =)ist (angers.



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En/&nced resist&nce

7a8 Fl))rs )r r))*s )* any *)r& )* c)nstructi)n s-anning *r)& ')t( sides att(e sa&e level/ i.e. interi)r l)ad 'earing ,alls

7'8 In


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,esign (rocedure 'or lo&ding "!

T(e actual l)ad )n t(e ,all is c)&-ared ,it( t(e design vertical resistance )*t(e ,all. Clause "!@!@1gives t(e *)r&ula *)r calculating t(e design vertical

resistance )* a ,all -er unit lengt( and t(e de*initi)ns )* t(e ter&s.

.t.*+

&

K ca-acity reducti)n *act)r all),ing *)r t(e e**ects )* slenderness andeccentricity/ and is )'tained *r)& ta'le ;

t K t(ic+ness )* t(e ,all

*+ K c(aracteristic strengt( )* t(e &as)nry

&K -artial sa*ety *act)r *)r t(e &ater ial

Example

Single le&' w&ll

A single lea* internal 'ric+ ,all )* a traditi)nally 'uilt ()use is su'=ect t) t(e

l)ading given in t(e design data. It &ay 'e assu&ed t(at t(e *l))r c)nsists )*

ti&'er =)ists at ?@4&& centres s-anning acr)ss t(e ,all.

C(ec+ t(e suita'ility )* t(e ,all in c)&-ressi)n.

Design data

Aial design l)ad *r)& u--er *l))r ?H +N&

C(aracteristic i&-)sed l)ading )n *l))rs 9.@ +N&3

C(aracteristic dead l)ad inclusive )* sel*


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Dind eccentricity &t to( w&ll

T(e eccentricity *r)& t(e ti&'er *l))rs is assu&ed t) 'e a--lied at t:

A--lying RT.e

SR.t:

@.? e

G.@ t: K ?. t :

4.44t

Slenderness !6

Ti&'er *l))r s-anning acr)ss t(e ,all ,)uld 'e assu&ed t) give en(anced

resistance 7see 3H.3.3.37a88.

E**ective (eig(t 4.;@ clear (eig(t 4.;@ 3.; 343@ &&

Fr)& Figure : e**ective t(ic+ness )* c)lu&ns and ,alls e**ective t(ic+ness/ t

943.@ &&

e**ective (eig(t 343@Slenderness rati) 9.H 3; suita'le

e**ective t(ic+ness 943.@

Design vertical resistance )* a ,all -er unit lengt( "!@!

K *r)& Ta'le ; *)r slenderness 9.H and e 4.44 t

As e 4.4@ t/ eccentricity is ta+en as 4.4@ t

Slenderness 9H 4.;;

34 4.;4

Inter-)lating *)r 9.H 4.;4G

Material sa*ety *act)r *r)& Ta'le ? *)r n)r&al c)nditi)ns )* &anu*acture and

c)nstructi)n c)ntr)l &is "@$@

*+K c(aracteristic strengt( )* &as)nry !"

T(e c)&-ressive strengt( *r)& t(e &anu*acturer>s data 94 N&& 3and &)rtar

designati)n is 7iv8 *r)& Ta'le 3.

*+ :.@ N&&3



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T(is can 'e &ulti-lied 'y 9.9@/ as it is a single lea* 'ric+ ,all t (at is eual in

,idt( t) t(e ,idt( )* a standard *)r&at 'ric+ 7see cl.3:.9.38

*+ :.@ 9.9@ ?.4 N&& 3

Resistance )* ,all .t.*+

&

4.;4G 943.@ ?.4 H3.;N&& H3.;+N&

:.@

As t(is value eceeds t(e t)tal design l)ad )n ,all 7@.? +N&8/ ,all is

suita'le.

C&vity w&lls under com(ression

T(e design -r)cess is t(e sa&e as t(at *)r t(e single lea* ,all 'ut additi)nal

-)ints listed 'el), s()uld 'e c)nsidered6

Fl))r l)adings are n)r&ally )nly carried )n t(e inner lea*.

T(e ta'ulated values )* 'ric+ and 'l)c+ arrange&ents are acce-ta'le6

Outer le&' Inner le&'

-rick -rick

-rick -lock

-lock -lock

T(e t,) leaves )* &as)nry are c)nnected 'y ties in acc)rdance ,it( clause

!8@1and T&-le 4)* 0S @G3H.

As t(e ,alls are c)nnected 'y ties/ t(e e**ective (eig(t )* t(e )uter lea* is

ta+en as 'eing t(e sa&e as t(at )* t(e inner lea*.

T(e rules )* Digure "are used t) )'tain t(e e**ective t(ic+ness6

t(e greatest )* 3:7t9 t

38

)r t9

)r t3

In design/ eac( lea* is c)nsidered se-arately

T(e slenderness rati) calculati)ns are 'ased )n ')t( leaves.

T(e strengt( calculati)ns are 'ased )n a single lea*.

STRUCTUR AL ANALBSIS AND DESI#N 7A"8 11 "


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Example

C&vity w&ll

T(e eternal ,all )* a traditi)nally 'uilt l),


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Dind eccentricity &t to( w&ll

T(e eccentricity *r)& t(e *l))r &ay 'e ta+en as t:

A--lying R Te

R

9t:

94;.9 e 33.: t :

33.:te 4.4;t

94;.9 :

Slenderness !6

Pres data @ N&& 3 and &)rtar

designati)n is 7iii8.

STRUCTUR AL ANALBSIS AND DESI#N 7A"8 11 $


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J(ic( Ta'le 3 is t) 'e used

As s)lid c)ncrete 'l)c+s are used ,it( a (eig(t t) least ()ri2)ntal di&ensi)nrati) 33@9@4 9.@

Clause 3:.9.G states t(at t(e value )* *+s()uld 'e )'tained 'y inter-)lati)n

'et,een t(e values given in ta'les 3 7'8 and 37d8

Ta'le 37'8 * + 3.@ N&& 3

Ta'le 37d8 * + @.4 N&& 3

*+ :.;@ N&&3


&

4.HGG 9@4 :.;@ 9:.3N&& 9:.3+N&

:.@

As t(is value eceeds t(e t)tal design l)ad )n ,all 794;.9 +N&8/ ,all is

suita'le.

,esign o' m&sonry w&lls wit/ (iers !6@1

A -ier is a t(ic+ened secti)n *)r&ing an integral -art )* t(e &as)nry

c)nstructi)n. Piers are -laced at regular intervals al)ng t(e ,all and (ave t(e

advantage )* reducing t(e slenderness rati) )* t(e ,all and (ence increasing

its l)ad carrying ca-acity. Piers &ay 'e intr)duced int) single lea* )r cavity

,alls.

Plan vie, )* cavity ,all ,it( -iers at c)nstant centres

T(e design -r)cedure is t(e sa&e as t(at *)r a single lea* )r cavity ,all/ ,it(

an additi)nal c)nsiderati)n given in Ta'le @ ,(en deter&ining t(e e**ective

t(ic+ness )* t(e ,all.

Example

T(e diagra& 'el), s(),s t(e )utline )* a cavity ,all ,it( -iers at :&

centres. T(e ,all is t) 'e *)r&ed *r)& 'l)c+,)r+ 944 && t(ic+ *)r ')t(



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leaves ,it( t(e -iers 'eing an additi)nal 944 && t(ic+ and :44 && ,ide. T(e

cavity 'et,een t(e inner and )uter leaves &ay 'e assu&ed t) 'e @4 &&.

C(ec+ t(e suita'ility )* t(e inner lea* t) carry t(e l)ads given in t(e designdata. It &ay 'e assu&ed t(at t(e *l))r units 'ear )ver t(e entire ,idt( )* t(e

inner lea*. T(e (eig(t )* t(e ,all &ay 'e c)nsidered as 'eing ?.3&.

Design data'

Structural units6 c)ncrete 'l)c+

944 && t(ic+ 344 && (ig( :44 && l)ng ; N&&3

L)ads *r)& u--er *l))r6

Inner lea* K dead :4 +N&

i&-)sed 34 +N&

I&-)sed l)ading )n *l))r @ +N&3

Dead l)ad inclusive )* sel* ,eig(t )* *l))rs ? +N&3

S-an )* -re


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A--lying R T.e

SR.t:

;.H e

3:.H t :

3:.Hte O O 4.4Ht

AA.H :

Slenderness !6

Pre


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Material sa*ety *act)r *r)& Ta'le ? *)r n)r&al c)nditi)ns )* &anu*acture and

c)nstructi)n c)ntr)l & :.@

'k c/&r&cteristic strengt/ o' m&sonry !"

T(e c)&-ressive strengt( *r)& t(e &anu*acturer>s data ; N&& 3 and &)rtar

designati)n is 7ii8.

J(ic( Ta'le 3 is t) 'e used

As s)lid c)ncrete 'l)c+s are used ,it( a (eig(t t) least ()ri2)ntal di&ensi)n

rati) 344944 3

Use Ta'le 37d8 *)r unit strengt( ; N&& 3and &)rtar designati)n 7ii8

*+ G.? N&&3


&

4.G4 944 G.? 94.;N&& 94.;+N&

:.@

As t(is value eceeds t(e t)tal design l)ad )n ,all 7;.H +N&8/ ,all is

suita'le.

Structur&l design o' tim-er to S $!46!1884

T(e structural design )* ti&'er ele&ents is 'ased )n -er&issi'le stresses and

de*lecti)ns derived *r)& elastic t(e)ry.

Dle=ur&l mem-ers K &e&'ers su'=ect t) 'ending

Me&'ers su'=ect t) 'ending 7i.e. 'ea&s8 are assu&ed t) 'e(ave in acc)rdance

,it( elastic 'ending t(e)ry -r)vided t(at t(e -er&issi'le &aterial stresses are

n)t eceeded. T(e 'ending e-ressi)n can 'e a--lied t) ti&'er design6

MI *y ER

At any -)int acr)ss a secti)n )* a 'ea& ,(ic( is l)cated a distance y *r)& t(e

neutral ais )* a secti)n/ a stress ',ill 'e devel)-ed as a c)nseuence )*

a--lying a 'ending &)&ent Mt) t(e secti)n. T(e &agnitude )* t(e stress

devel)-ed ,ill vary ,it( t(e sec)nd &)&ent )* area )* t(e secti)n I.

STRUCTUR AL ANALBSIS AND DESI#N 7A"8 11 8


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In t(e ti&'er design c)de/ is t(e designati)n *)r stress/ (ence t(e a')veeuati)n &ay 'e ,ritten as6

B/I /y

In ti&'er design generally rectangular secti)ns are used/ t(ere*)re t(e

&ai&u& c)&-ressive and tensile 'ending stress ,ill )ccur at t(e etre&e

*i'res. T(us y is eual t) (al* t(e de-t( )* t(e secti)n.

As ')t( I and y are ge)&etric -r)-erties )* t(e secti)n it is c)nvenient t)

c)&'ine t(e t,) ter&s in a single -r)-erty ,(ic( is re*erred t) as t(e elastic

&)dulus and den)ted 'y t(e sy&')l L.

X Iy

Furt(er/ as rectangular secti)ns are 'eing c)nsidered/ i* ' is t(e ,idt( )* t(e

secti)n and /t(e de-t( t(en Iand y&ay 'e e-ressed as6

I '(:93 and y (3

"ence elastic &)dulus/ L 7'(:9387(38 -/!?4

C)nsidering/ *r)& t(e 'ending e-ressi)n/ MI y and c)&'ining ,it( t(e

de*initi)n )* elastic &)dulus t(en6

M < L

T(is can 'e rearranged t) deter&ine t(e &ai&u& 'ending stress in t(e 'ea&

and t(en c)&-ared ,it( t(e -er&issi'le stress t(at t(e 'ea& &ay carry.

Ot/er design reuirements

T(e )t(er c(ec+s reuired t) ti&'er 'ea&s are s(ear/ 'earing/ de*lecti)n and

t(e &ai&u& de-t( t) 'readt( rati).

As t(e 'ea&s are si&-ly su--)rted/ and generally carry uni*)r&ly distri'uted

l)ads/ s(ear ,ill 'e a &ai&u& at t(e su--)rts.

Mai&u& s(ear stress : L)ad

K3 Cr)ss


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Mai&u& 'earing stress L)ad L)ad

OC)ntact area ,idt( )* 'ea& 'earing lengt(

0)t( )* t(ese values can t(en 'e c)&-ared ,it( t(e -er&issi'le values

)'tained *r)& t(e design c)de.

,e'lection/ as ,it( )t(er structural &aterials/ is a servicea'ility reuire&ent.

Mai&u& de*lecti)ns are deter&ined using t(e standard de*lecti)n *)r&ulae

and c)&-ared ,it( t(e de*lecti)n li&its given in t(e design c)de.

Tim-er &s & structur&l m&teri&l

Unli+e )t(er c)nstructi)n &aterials/ ti&'er cann)t 'e &ied t) a -re

Documents

Structural Analysis and Design Tcm4-118204