DESIGN PRINCIPLES FOR ROOF STEEL TRUSS

INTRODUCTION:
Steel trusses are being used for both buildings and bridges. But the design
principles are different for different uses. Many books are course oriented and
not with a practical principles. Now an attempt has been made to gather
information on the design principles from various references ON TH !"#O$T
"N% OTH& %S'(N )&'N*')!S.
Steel roof trusses are used for mainly for the 'ndustrial buildings where free
space re+uirement are essential for more working areas. The span of truss varies
from ,-./-0 to 1--./-0 depending on the type of re+uirement and the available
spaces.
The following steps should be considered when designing a truss2
,. Select the general layout of truss members and truss spacing.
3. stimate e4ternal loads to be applied including self weight of truss5 purlins
and roof covering together with wind loads.
1. %etermine critical 6worst combination7 loading. 't is usual to consider %ead
loads alone and then %ead and 'mposed loads combined.
8. "naly9e the frame work to find forces in all members.
:. Select material and section to produce in each member a stress value
which does not e4ceed the permissible value. )articular care must be
taken with compression members 6struts7 or members normally in tension
but sub;ect to stress reversal due to wind uplift.
<or span up to about 3-.-- m5 the spacing of steel trusses is likely to be about
8.--m i.e. ,=: of span.
" slope of 33(degree) is common for corrugated steel and asbestos roofing
sheets.
<or economic spacing of roof trusses5 the cost of truss should be e+ual to twice
the cost of purlins >the cost of roof covering. "s a guide the spacing of the roof
trusses can be kept 2
a. ? of span upto ,:.-m.
b. ,=: of span upto ,:m to 1-m.
Trusses with parallel chords are often referred to as !"TT'* ('&%&S.
DIFFERENT SHAPES OF TRUSSES FOR DIFFERENT SPANS .
1
7.0M TO 11.0m
Belgium truss
<7.0M
2
*ON<'($&"T'ONS2
The pitch of roof truss depends on the roofing materials.
a7 Min. recommended for (' sheet@,in A.i.e h=lB,=A hBl=A
b7 <or ".* sheet /, in ,3i.e hBl=,3.
)arallel chord trusses2 The economical span to depth ratio B,3 to 38.
Trape9oidal trusses2
The configuration shown below reduces the a4ial forces in the chord members
ad;acent to supports.
TENSION CHORD
COMPRESSION CHORD COMPRESSION CHORD
TENSION CHORD
N-GIRDER/PRATT
TRUSS
WARREN GIRDER

!"SPAN
#
conomical span to depth ratio is around ,-. The slope is ,=:. Spacing of
trusses should be in the region of ,=8 to ,=: of span.
<an trusses are used when the &after members of the roof trusses have to be
subdivided into O%% number of panels.
)itch B!=hB8 to ,-
hB!=8 to !=,-
$


The mass per s+.m of 2
a7 <ink trusses is lowest for spans from ,:m upwards.
b7 )ratt trusses from ,- m to 3-m.
c7 "nd of )ortal frames from ,-m to 3-m.
The roof slope is normally chosen to ,2,A or ,2,- depending on type of roofing. "
slope less than ,2,A should be used with caution since the deflection decreases
the inclination and if the actual roof slope becomes too small trouble with water
run/off can give problems with water accumulation6)onding7. The smallest
possible slope depends on the si9e of the snow load.
" rough estimate of section height for a gabled truss is that for roof slope ,2,A5
HB!=3: to !=1-.
<or slope ,2,-5 HB!=1: to !=8- where H is the depth at support.
%
<or parallel trusses the relation is appro4imately HB!=3-.
The most advantageous angle between the diagonals and the bottom chord is
8:/:- in a triangular lattice and 1: /8:in a diagonal one.

'n the practice of designing industrial and residential buildings5 the most fre+uent
case is use of support diagonals upwards.
Triangular trusses are employed only in roofs with steep pitches.
Loadings:
<alse ceiling/////////////////////////////////////////////3-- N=s+.m
%uct ///////////////////////////////////////////////////// 8- N=s+.m
(.'.Sheet/-.A1mm thick to ,5A mm thick///////////:: to ,8- N=s+.m
"sbestos sheet /////////////////////////////////////////,C, N=s+.m.
&oofing tiles /////////////////////////////////////////////1:- to D:- N=s+.m
Bracings //////////////////////////////////////////////////,3/,: N=s+.m
)urlins ////////////////////////////////////////////////////3-- to 8-- N=s+.m
Mangalore tiles with battens //////////////////////////A:-N=s+.m.
Sl! wig"t o! truss:
Earious Handbooks and te4t book furnish different formulae for the self weight of
steel truss. One has to make use of it ;udiciously and with engineering ;udement.
Felded sheeted roof trusses is given appro4imately as2
". F B,=,--6:.1C>-.-:18"7Gn=s+.m where " is the plan area in s+.m.
&
<rom the HB for Building ngineers in Metric system5
a7 <ink type roof truss6<rom Getchum.s structural engineers HB7
FB-.-333).".!6,>-.1A33!=H"7in Gg where
)B capacity of truss in Gg=s+.m in hori9ontal pro;ection of
roof6,:-/ 8--Gg=s+.m7
"B spacing c=c of truss in m.
!B span of truss in m.
b7 for steel truss in general
FB o.868.83E!>!7 Gg=s+.m of hori9ontal covered area.
!B span in m.
B. %! of trussB6Span=1>:7I,- N=s+.m
&efering to page 3C1 of %esign of Metal Structures by k.Mukhanov/M'&
publication.
The Minimum weight of truss is appro4imately obtained when the weight of the
chords e+ual to that of the lattice6including the gusset plate7 which will be the
case with comparatively large truss depth to span ratio.6h=!J,=:7.
The weight of standard trusses g in kg=s+.m area covered depending up on the
design load +6in Gg=s+.m7 is2
Span g6Gg=s+.m7
! B,D.-m gB3.3>+=,3:
! B38.-m gB3.CD>+=:8.3
! B1-.-m gB8.88>+=18.C
! B1A.-m gB:.3C>+=3,

&ef2)1K,%esign of Metal structures by G.Mukhanov.
"ppro4imate weights of elements of steel 'ndustrial building framework in
Gg=s+.m of building area2
Sl.L lement of steel frame
work
(roup of shops
!ight Medium Heavy
,. &oof2
&oof trusses ,A/3: ,D/1- 3-/8-
Secondary trusses -/A 8/C D/3-
)urlins ,-/,3 ,3/,D ,3/,A
Skylights -/,- D/,3 D/,3
Ties 1/8 1/: D/,:
Total #$%&$ &'%($ '$%)$
3. *olumns with tie M
platforms
,-/,D ,D/8- C-/,3-
*rane girder with bracing -/,8 ,8/8- :-/,:-
'
beams
Fall frame work -/1 :/,8 ,3/3-
Miscellaneous / -/,- 1/,3
(rand total #'%)$ ('%*($ +$$%&$$
&ef2 Table 3"/&eynold.s handbook on &* %esign2
&oof Trusses2
Span of trusses
Feights6appr47 of steel roof trusses. !bs=sft or
Gg=s+.m
Spacing of truss
,-. ,:. 1m 8.:m
Feights6appr47 of steel roof trusses. !bs=sft or
Gg=s+.m
3:.-0 C.:m 3 ,.: ,- C.:
1-.-0 K.-m 3.: ,.: ,,.: C.:
8-.-0 ,3.-m 3.C: ,.C: ,8.- K.-
:-.-0 ,:.-m 1.- 3.3: ,:.- ,,.-
A-.-0 ,D.-m 8.3: 1.- 3,.- ,:.-
D-.-0 3:.- :.- 1.: 3:.- ,C.:
GRA,IT- LOADS:
(ravity loading about ,kpa6including !! but e4cluding the self weight of purlins
and roof principals7 and basic wind speed 8Am=s.
Fhere the ma4imum gravity loading6%!>!!7 e4ceeds the net uplift
loading6%!>F!7 as usual in roofs of buildings5 the web compression members
under gravity loading attract higher forces because of their slope.
LI,E LOADS:
&oof slope "ccess load
N,- provided ,:--N=s+.m of plan area
N,- not provided C:-N=s+.m of plan area.
,- C:-N=s.m reduced by ,-N=s+.m for every
degree increase upto M including 3-.
&educed by 3-N=s+.m for each one
degree increase above 3-.
But not less than 8--N=s+.m.
T" loads on truss .an / ta0n +1# as pr IS .od )('. This reduction is not
for the design of )urlins.

2IND LOADS:
(
On roof trusses5 unless the roof slope is too high5 would be usually uplift force
perpendicular to the roof 5 due to suction effect of the wind blowing over the roof.
Hence wind load on roof truss usually acts opposite to the gravity load and its
magnitude can be larger than gravity loads5 causing reversal of forces in truss
members. 6&ef2 Teaching resources on structural steel design/chapter/3C7.
<or buildings up to ,-.-m in height5 the intensity of wind pressure may be
reduced by 3:O for stability calculations and for the design of frame work.
EARTH3UA4E LOADS:
Since arth+uake load on a building depends on the mass of the building5
earth+uake loads usually does not govern the design of !'(HT 'N%$ST&'"!
ST! B$'!%'N(S. Find loads usually govern.6&ef2 Teaching resource on
structural %esign/*hapter 3C7.
DESIGN PRINCIPLES:
The spacing of purlins ad;acent to the eaves and the ridge of a roof may be
reduced to give a more uniform moment distribution in the roof sheets.
<or fully continuous purlin configurations the larger B.Ms and the truss loadings
in the end span and at the penultimate trusses can be reduced by making the
end spans6i.e. at the end bays of the building7smaller than the interior.
'f the purlins are placed at intermediate points i.e. between the ;oints of the top
chord5 the chord will be sub;ected to moments.
)
5E56ER SI7ES:
*ommon practice is to specify a minimum angle si9e :-4:-4Amm in the case of
trusses.
Single angle tension member having twisting tendency and produce eccentric
forces in the ;oints. Therefore double angle cross sections are provided.
The width of the members should be kept minimum as far as possible because
wide members have greater secondary sresses.
Two angles back to back or a structural tee form the most common section for
members of a roof truss. Fhen the load is light and the span is short5 a single
angel section will often suffice and may be used in spite of its lack of symmetry.
This is true for web members to carry only nominal stresses
SU6DI,ISION OF THE 5AIN PANELS:
SECONDAR- STRESSES:
Normally the secondary stresses in roof trusses may be disregarded if
,. the slenderness ratio of the chord member is greater than :-.6l=rP:-7
3. that of the web member is greater than ,--.6l=rP,--7.
1.
"ll the members of the roof truss usually do not reach their limit state of collapse
simultaneously.
&*OMMN%% TH'*GNSS O< &OO< T&$SS ($SSTS
5a89dsign
!or.s in
support
1diagonals:tons;
$pto 3- 3-/8: 8:/C: C:/,,: ,,:/,A: ,A:/33: 33:/1--
T"i.0nss o!
gussts%<<
D ,- ,3 ,8 ,A ,D 3-
1*
The design code suggest an effective length factor between -.C and ,.- for the
in/plane buckling of member depending upon this restraint and ,.- for the out of
plane buckling. Qin the case of roof trusses5 a member normally $N%&
TNS'ON due to gravity loads6%!>!!7 may e4perience stress reversal into
compression due to %!>F! combination.
SLENDERNESS RATIO:
The design standard 6'SD--7 imposes restrictions on the ma4.slenderness ratio
as given below2
Sl.n
o
Member type Ma4 l=r limit
,. Member under *OM)&SS'ON under loads other than
Find=Rload
,D-
3. TNS'ON members undergoing reversal due to loads other
than F!
,D-
1. Members normally under TNS'ON but may have to resist
*OM)&SS'ON under Find load
3:-
8. Members designed only for TNS'ON even though they
may e4perience stress reversal
1:-
:. Members always under TNS'ON 8--
<or smaller or where there is net uplift loading a F"&&N truss will be lighter
than )&"TT/truss.
&ef2 %esign of Metal Structures by G.Mukhanov.
Sl.tion o! s.tions and t=p o! s.tions:
The top chord if une+ual angle section is chosen then the short leg should pro;ect
downwards as shown to have more r
44.
6outstanding leg is smller from the
plane of the truss7
!+"2!,
E-u.l ./gle se0ti1/ is
2re3erre45
11
'f each ;oint of the top chord is fi4ed in someway by ties or roof slab6!yB!47 e+ual
stability of the chord is ensured by section formed of une+ual leg angles installed
with their short legs outstanding from the plane of the truss.
The remaining compression diagonals and verticals between whose effective
lengths there is insignificant differences6!4B-.D!5!yB!7 are most fre+uently
designed of e+ual leg angles.
<or tension members the type and arrangements of the angles is not so
importance since here the determining factor is the net sectional area.
Other types of sections than angle are seldom employed and only if there are
specific re+uirements for design. Thus for e4ample5 chord made from channels
are employed when they are sub;ected not only to an a4ial force but also to a
considerable local moments originated by a load applied between panel points of
the trusses.
The verticals of trusses are designed with a T section formed of t+o e+ual leg
angles.
EFFECTI,E LENGTH OF CO5PRESSION ELE5ENTS:
The effective length of a compression top chord in the plane of truss is e+ual to
its geometrical length6between panel point centres7 !eB!.
<or diagonals6e4cept for the support one which is considered as a continuation of
chord7 and verticals the effective length in the plane of truss is taken e+ual to
!eB-.D!.
Fhen selecting angle sections for compression elements5 the tendency should
be to use angles of the smallest possible thickness since their radii of gyration
have the relatively greatest value.
!imiting slenderness ratio S for compression and tension elements
N"M O< !MNT
*OM)&S
S'ON
!MNT
S
TNS'ON !MNTS
$N%&
%'&*T
"*T'ON O<
%#N"M'*
!O"%S
ST"T'
*
!O"%
'N B$'!%'N(
F'TH H"E#
S&E'*
*ON%'T'ONS
*hords5 support diagonals M verticals
of trusses5 transmitting support
reactions
,3- 3:- 8-- 3:-
Other truss elements ,:- 1:- 8-- 1--
&oofing ties6e4cept brace rods7 3-- 8-- 8-- 1--
12
!ecture notes by %r.!.S.Teyagopal5 a leading structural consultant is given
below for further guidence2
,. " truss is a beam which is bent to the shape of the bending moment
diagram in opposite direction.
The shape shown is better to take care of the Bending moment.
HB rise of the truss which is ,=D for "* sheet.
3. "s suggested earlier the top main chord 6rafter7 is divided into main
divisions which in turn subdivided to suite the roof covering sheets.
1. Nowadays it became obsolete to use the rivets but customary to make use
of welding as well as high tension bolts. There are four types of bolts
available. Bolt (KD means bolt is having a strength of K Mpa D is O of
strength used for calculation.
1
8. The structural design procedure consists of si8 principal steps.
a. Selection of type and layout of structure.
b. %etermination of loads on the structure.
c. %etermination of internal forces and moments in the structural
components.
d. Selection of material and proportioning of members and
connections for safety and economy.
e. *hecking the performance of the structure under service
conditions5 and
f. <inial review.
:. <abrication2 ase of fabrication and erection has an important influence on
the economy of the design.
'n general5 small and medium trusses of symmetrical design are lifted at the
ridge during erection. 'n order to prevent buckling of the bottom chord5 it is
necessary to proportion it to carry the compressive stresses developed during
hoisting. "n empirical relation is given by b=! B,=,3:. where b is the width of
the bottom chord at its centre and ! the span length.
<or e4ample a :- m span truss shall have the top chord and bottom chord
width Bspan=,3:.i.e. :-4,---=,3:B8--mm. 6Dtimes span/ in mm7.

This is to avoid bending of truss on either side during erection.
The shape of a truss 2
1$
TRUSSED 6EA5S:
<O&M$!" <O& T&$SS% B"MS/&<2 Building engineers hand book
$sed for long spans and are built up of wooden beams and struts of steel
rods. But the wooden beams may be replaced by steel sections.
1%
sB3.,4,-UAGg=s+.cm6steel7
Dsign !or<ula9
Sl.n
o
%escription
Single strut %ouble strut
$niformly distributed load Vin Gg
,. Tension in rod -.1,3Fh=r Fh=1r
3. *ompression in strut -.A3:F F=1
1. *ompression in beam -.1,3F!=3r F!=Kr
*oncentrated load over strut5Gg
,. Tension in rod )h=3r )h=r
3. *ompression in strut ) )
1. *ompression in beam )!=8r )!=1r
1&