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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 9.4@9.9@/ 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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19 STRUCTUR AL ANALBSIS AND DESI#N 7A"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
14 STRUCTUR AL ANALBSIS AND DESI#N 7A"8
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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.
STRUCTURA L ANALBSIS AND DESI#N 7A"8 18
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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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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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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
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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'
Ta+e &)&ents a')ut K
!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
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T(is &ay 'e ,ritten as6
3 3
3,L , d yM K EI
3 3 d
Integrate ,it( res-ect t) >
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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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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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.
Ta+e &)&ents a')ut K
!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
Integrate ,it( res-ect t) >
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.
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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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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&
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ST3,Y G3I,E !
Ta+e &)&ents a')ut K
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.
Ta+e &)&ents a')ut 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$33
"@ udl )n t(e &ain s-an and a s&aller udl )n t(e )ver(ang
F)r analysis -ur-)ses t(is is treated as a c)nstant udl )ver t(e entire
'ea& lessan additi)nal l)ad )* 7,K2 +N&8 )n t(e )ver(ang. L)ad ,K2
acts u(w&rdsand gives a -)sitive &)&ent a')ut secti)n K. As in t(e
)t(er cases &)&ents are ta+en a')ut t(e secti)n K.
STRUCTURA L ANALBSIS AND DESI#N 7A"8 ""
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Ta+e &)&ents a')ut K/ c)nsidering a uni*)r& l)ad )* :4+N& )ver t(e
entire lengt( )* 'ea& and a negative 7u-,ard8 l)ad )* 34+N& )n t(e
)ver(ang.
!alue )* l)ad Distance t) centre )* M)&ent F)rce distance
l)ad *r)& secti)n K 7&8
99;.@ +N 99;.@
:4 +N&. 3 :4..3
9?3.@ +N KH 9?3.@7KH8
34 +N&.7KH8 7KH83 34.7KH833
T(is &ay 'e ,ritten as6
3 3 3
3
dy :4 34KH$M EI 99;.@ K 9?3.@KH$
d 3 3
Integrate ,it( res-ect t) >
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$EI y K A 0 de*lecti)n euati)n
G 3? G 3?
In )rder t) *ind t(e c)nstants )* integrati)n A and 0 a--ly t(e standard
c)nditi)ns.
F)r a si&-ly su--)rted 'ea& de*lecti)n is 2er) at t(e su--)rts.
J(en 4 / y 4 K a--ly t) de*lecti)n euati)n
: ? : ?99;.@.4 :4.4 9?3.@4KH$ 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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Als) ,(en H/ y 4 K a--ly t) de*lecti)n euati)n
: ? : ?
99;.@.H :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$EI y K K G9:.?.?
G 3? G 3?
EI y 93@:.: K :34 7ign)re8 7ign)re8 K 3?@:.G
In ter&s )* EI/ y K9@34.:EI
Actual de*lecti)n/ y K9@34.: 9493 734@ 94:@@::4 94?8y K9:.? && 7d),n,ards de*lecti)n8
De*lecti)n at ti- )* 'ea&/ 94&
: ? : ?99;.@.94 :4.94 9?3.@94KH$ 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 99@3.G EI
Actual de*lecti)n/ y 99@3.G 9493 734@ 94:@@::4 94?8
y 94.3 && 7u-,ards de*lecti)n8
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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
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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&&?
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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&&
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#9 STRUCTUR AL ANALBSIS AND DESI#N 7A"8
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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 #!
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(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 #$
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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
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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 @4@.3 :;.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
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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$
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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
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Structur&l steel struts su-*ect to &=i&l lo&d S $8$911889
Com(ression mem-ers cl&use #@5
C)&-ressi)n &e&'ers are classed as eit(er6
798 >lastic
Compact in eac( case t(e secti)n can resist t(e *ull l)ad
Semi-compact 7suas( l)ad8
It is )nly necessary *)r strut design t(at t(e secti)n 'e classi*ied as n)t
slender.
T(is is n)t related t) t(e Euler t(e)ry de*initi)n )* slender> 'ut relates t) t(e
a'ility )* t(e cr)ss
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T(us *)r a ?@; 9@3 ;? U0 in #rade ?: steel6,e' t(ic+ness t . &&
*lange t(ic+ness T 9;.4 &&Design strengt( -
y 3G@ N&& 3
Note: T(e design strengt( de-ends )n t(e greater &aterial t(ic+ness.
F)r slender secti)ns -yis &)di*ied 'y a stress reducti)n *act)r as given in
Ta'le H 7n)t a--lica'le t) UC secti)ns8.
T(e cl&ssi'ic&tion o' t/e sectionis *)und using T&-le 5)* 0S@@4 and is a
&easure )* t(e ease ,it( ,(ic( t(e cr)ss
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T(e slenderness is a &easure )* t(e ease ,it( ,(ic( t(e strut ,ill 'uc+le
)ver its lengt( and is *)und using6
SlendernessELE**ective lengt(O O
Radius )* gyrati)n r
E**ective lengt( is de*ined as t(e lengt( 'et,een -)ints )* e**ective restraint
)* a &e&'er &ulti-lied 'y a *act)r t) ta+e acc)unt )* t(e end c)nditi)ns and
l)ading
LE 1L
,(ere L actual lengt(1 e**ective lengt( rati)
1 is deter&ined *r)& t(e c)nditi)ns )* end restraint.
In t(is c)urse E< 1@9 or 9@6$
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 "
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All UC secti)ns are "
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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
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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
64 STRUCTUR AL ANALBSIS AND DESI#N 7A"8
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,esign o' mem-ers su-*ect to -ending S $8$911889
T(e rules *)r t(e design )* &e&'ers in 'ending are given in sections #@! &nd#@")* 0S @@46 Part 9. T(e design )* suc( ele&ents is -ri&arily c)ncerned
,it( 'ending strengt(/ 'ut since 'ending &)&ent is su'=ect t) variati)n al)ng
t(e lengt( )* t(e &e&'er and is acc)&-anied 'y s(ear acti)n/ t(e
c)&'inati)n )* 'ending and s(ear &ust 'e ta+en int) acc)unt. In additi)n/ t(e
degree )* restraint a--lied t) t(e 'ea& ends and al)ng its lengt( greatly
in*luence t(e 'ending ca-acity. I* t(e 'ea& is *ully restrained al)ng its
c)&-ressi)n *lange as de*ined in clause ?.3.3/ t(ere is n) need t) &a+e any
all),ance *)r lateral t)rsi)nal 'uc+ling.
All 'ea&s &ust (ave an adeuate resistance t) 'ending and s(ear/ and 'ea&s
t(at are n)t *ully restrained laterally &ust 'e c(ec+ed *)r a reduced 'ending
ca-acity due t) lateral t)rsi)nal insta'ility/ in acc)rdance ,it( secti)n ?.:.
Dully restr&ined -e&ms
A -ractical situati)n ,(ere t(e 'ea& &ay 'e c)nsidered as (aving its
c)&-ressi)n *lange *ully restrained is ,(ere it is reuired t) carry a c)ncrete
*l))r 7eit(er in-situ)r *)r&ed *r)& -re
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+e- -uckling &nd -e&ring
uckling #@$@!@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 ?.@.3.9 &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
89 STRUCTUR AL ANALBSIS AND DESI#N 7A"8
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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
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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 #@!@$
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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
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+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
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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
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Je' 'uc+ling ca-acity 9@3 ?4 4.;@: 9@3 :4.9 9H3.9 +N 9@.G +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
STRUCTURA L ANALBSIS AND DESI#N 7A"8 85
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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:
86 STRUCTUR AL ANALBSIS AND DESI#N 7A"8
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Study Guide # End Test
Figure 9 s(),s t(e -art lay)ut )* &ulti
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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
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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
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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"
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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.
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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+
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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
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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
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'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
11! STRUCTUR AL ANALBSIS AND DESI#N 7A"8
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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*.
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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.
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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
Resistance )* ,all .t.*+
&
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
Resistance )* ,all .t.*+
&
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.
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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
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