Design Principles for Roof Steel Truss

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 THE LAYOUT AND OTHER DESIGN PRINCIPLES.

Steel roof trusses are used for mainly for the Industrial buildings where free space requirement are essential for more working areas. The span of truss varies from 10’-0” to 300’-0” depending on the type of requirement and the available spaces.

The following steps should be considered when designing a truss:

1. Select the general layout of truss members and truss spacing.
2. Estimate external loads to be applied including self weight of truss, purlins and roof covering together with wind loads.
3. Determine critical (worst combination) loading. It is usual to consider Dead loads alone and then Dead and Imposed loads combined.
4. Analyze the frame work to find forces in all members.
5. Select material and section to produce in each member a stress value which does not exceed the permissible value. Particular care must be taken with compression members (struts) or members normally in tension but subject to stress reversal due to wind uplift.

For span upto about 20.00 m, the spacing of steel trusses is likely to be about 4.00m i.e. 1/5 of span.

A slope of 22Ø(degree) is common for corrugated steel and asbestos roofing sheets.

For economic spacing of roof trusses, the cost of truss should be equal to twice the cost of purlins +the cost of roof covering. As a guide the spacing of the roof trusses can be kept :

1. ¼ of span upto 15.0m.
2. 1/5 of span upto 15m to 30m.

Trusses with parallel chords are often referred to as LATTICE GIRDERS.

DIFFERENT SHAPES OF TRUSSES FOR DIFFERENT SPANS.

7.0M TO 11.0m

Belgium truss

CONFIGURATIONS:

The pitch of roof truss depends on the roofing materials.

a)Min. recommended for GI sheet—1in 6.i.e h/l=1/6 h=l/6

b)For A.C sheet -1 in 12i.e h=l/12.

Parallel chord trusses: The economical span to depth ratio =12 to 24.

Trapezoidal trusses:

The configuration shown below reduces the axial forces in the chord members adjacent to supports.

Economical span to depth ratio is around 10. The slope is 1/5. Spacing of trusses should be in the region of 1/4 to 1/5 of span.

Fan trusses are used when the Rafter members of the roof trusses have to be subdivided into ODD number of panels.

Pitch =L/h=4 to 10

h=L/4 to L/10

The mass per sq.m of :

a)Fink trusses is lowest for spans from 15m upwards.

b)Pratt trusses from 10 m to 20m.

c)And of Portal frames from 10m to 20m.

The roof slope is normally chosen to 1:16 or 1:10 depending on type of roofing. A slope less than 1:16 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 accumulation(Ponding). The smallest possible slope depends on the size of the snow load.

A rough estimate of section height for a gabled truss is that for roof slope 1:16, H=L/25 to L/30.

For slope 1:10, H=L/35 to L/40 where H is the depth at support.

For parallel trusses the relation is approximately H=L/20.

The most advantageous angle between the diagonals and the bottom chord is 45°-50° in a triangular lattice and 35° -45°in a diagonal one.

In the practice of designing industrial and residential buildings, the most frequent case is use of support diagonals upwards.

Triangular trusses are employed only in roofs with steep pitches.

Loadings:

False ceiling------200N/sq.m

Duct ------40N/sq.m

G.I.Sheet-0.63mm thick to 1,6 mm thick------55 to 140 N/sq.m

Asbestos sheet ------171 N/sq.m.

Roofing tiles ------350 to 850 N/sq.m

Bracings ------12-15 N/sq.m

Purlins ------200 to 400 N/sq.m

Mangalore tiles with battens ------650N/sq.m.

Self weight of truss:

Various Handbooks and text book furnish different formulae for the self weight of steel truss. One has to make use of it judiciouslyand with engineering judement.

Welded sheeted roof trusses is given approximately as:

1. W =1/100(5.37+0.0534A)Kn/sq.m where A is the plan area in sq.m.

From the HB for Building Engineers in Metric system,

a)Fink type roof truss(From Ketchum’s structural engineers HB)

W=0.0222P.A.L(1+0.3622L/√A)in Kg where

P= capacity of truss in Kg/sq.m in horizontal projection of

roof(150- 400Kg/sq.m)

A= spacing c/c of truss in m.

L= span of truss in m.

b)for steel truss in general

W= o.4(4.42VL+L) Kg/sq.m of horizontal covered area.

L= span in m.

1. DL of truss=(Span/3+5)*10 N/sq.m

Refering to page 273 of Design of Metal Structures by k.Mukhanov-MIR publication.

The Minimum weight of truss is approximately obtained when the weight of the chords equal to that of the lattice(including the gusset plate) which will be the case with comparatively large truss depth to span ratio.(h/L≈1/5).

The weight of standard trusses g in kg/sq.m area covered depending up on the design load q(in Kg/sq.m) is:

Spang(Kg/sq.m)

L =18.0mg=2.2+q/125

L =24.0mg=2.78+q/54.2

L =30.0mg=4.44+q/34.7

L =36.0mg=5.27+q/21

Ref:P391Design of Metal structures by K.Mukhanov.

Approximate weights of elements of steel Industrial building framework in Kg/sq.m of building area:

Sl.# / Element of steel frame work / Group of shops
Light / Medium / Heavy
1. / Roof:
Roof trusses / 16-25 / 18-30 / 20-40
Secondary trusses / 0-6 / 4-7 / 8-20
Purlins / 10-12 / 12-18 / 12-16
Skylights / 0-10 / 8-12 / 8-12
Ties / 3-4 / 3-5 / 8-15
Total / 30-40 / 45-70 / 50-80
2. / Columns with tie & platforms / 10-18 / 18-40 / 70-120
Crane girder with bracing beams / 0-14 / 14-40 / 50-150
Wall frame work / 0-3 / 5-14 / 12-20
Miscellaneous / - / 0-10 / 3-12
Grand total / 35-80 / 75-170 / 200-400

Ref: Table 2A-Reynold’s handbook on RC Design:

Roof Trusses:

Span of trusses / Weights(apprx) of steel roof trusses. Lbs/sft or Kg/sq.m
Spacing of truss
10’ / 15’ / 3m / 4.5m
Weights(apprx) of steel roof trusses. Lbs/sft or Kg/sq.m
25’0” / 7.5m / 2 / 1.5 / 10 / 7.5
30’0” / 9.0m / 2.5 / 1.5 / 11.5 / 7.5
40’0” / 12.0m / 2.75 / 1.75 / 14.0 / 9.0
50’0” / 15.0m / 3.0 / 2.25 / 15.0 / 11.0
60’0” / 18.0m / 4.25 / 3.0 / 21.0 / 15.0
80’0” / 25.0 / 5.0 / 3.5 / 25.0 / 17.5

GRAVITY LOADS:

Gravity loading about 1kpa(including LL but excluding the self weight of purlins and roof principals) and basic wind speed 46m/s.

Where the maximum gravity loading(DL+LL) exceeds the net uplift loading(DL+WL) as usual in roofs of buildings, the web compression members under gravity loading attract higher forces because of their slope.

LIVE LOADS:

Roof slope Access load

≤10° provided 1500N/sq.m of plan area

≤10° not provided 750N/sq.m of plan area.

≥10° 750N/s.m reduced by 10N/sq.m for every

degree increase upto & including 20°.

Reduced by 20N/sq.m for each one

degree increase above 20°.

But not less than 400N/sq.m.

The loads on truss can be taken 2/3 as per IS code 875. This reduction is not for the design of Purlins.

WIND LOADS:

On roof trusses, unless the roof slope is too high, would be usually uplift force perpendicular to the roof , 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 loads, causing reversal of forces in truss members.(Ref:Teaching resources on structural steel design-chapter-27).

For buildings up to 10.0m in height, the intensity of wind pressure may be reduced by 25% for stability calculations and for the design of frame work.

EARTHQUAKE LOADS:

Since Earthquake load on a building depends on the mass of the building, earthquake loads usually does not govern the design of LIGHT INDUSTRIAL STEEL BUILDINGS. Wind loads usually govern.(Ref: Teaching resource on structural Design-Chapter 27).

DESIGN PRINCIPLES:

The spacing of purlins adjacent to the eaves and the ridge of a roof may be reduced to give a more uniform moment distribution in the roof sheets.

For 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 spans(i.e. at the end bays of the building)smaller than the interior.

If the purlins are placed at intermediate points i.e. between the joints of the top chord, the chord will be subjected to moments.

RECOMMENDED THICKNESS OF ROOF TRUSS GUSSETS
Max.design forces in support /diagonals(tons) / Upto 20 / 20-45 / 45-75 / 75-115 / 115-165 / 165-225 / 225-300
Thickness of gussets-mm / 8 / 10 / 12 / 14 / 16 / 18 / 20

MEMBER SIZES:

Common practice is to specify a minimum angle size 50x50x6mm in the case of trusses.

Single angle tension member having twisting tendency and produce eccentric forces in the joints. 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. When the load is light and the span is short, 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

SUBDIVISION OF THE MAIN PANELS:

SECONDARY STRESSES:

Normally the secondary stresses in roof trusses may be disregarded if

1. the slenderness ratio of the chord member is greater than 50.(l/r>50)
2. that of the web member is greater than 100.(l/r>100).

All the members of the roof truss usually do not reach their limit state of collapse simultaneously.

The design code suggest an effective length factor between 0.7 and 1.0 for the in-plane buckling of member depending upon this restraint and 1.0 for the out of plane buckling. Zin the case of roof trusses, a member normally UNDER TENSION due to gravity loads(DL+LL) may experience stress reversal into compression due to DL+WL combination.

SLENDERNESS RATIO:

The design standard (IS800) imposes restrictions on the max.slenderness ratio as given below:

Sl.no / Member type / Max l/r limit
1. / Member under COMPRESSION under loads other than Wind/EQload / 180
2. / TENSION members undergoing reversal due to loads other than WL / 180
3. / Members normally under TENSION but may have to resist COMPRESSION under Wind load / 250
4. / Members designed only for TENSION even though they may experience stress reversal / 350
5. / Members always under TENSION / 400

For smaller or where there is net uplift loading a WARREN truss will be lighter than PRATT-truss.

Ref: Design of Metal Structures by K.Mukhanov.

Selection of sections and type of sections:

Thetop chord if unequal angle section is chosen then the short leg should project downwards as shown to have more rxx. (outstanding leg is smller from the plane of the truss)

If each joint of the top chord is fixed in someway by ties or roof slab(Ly=Lx) equal stability of the chord is ensured by section formed of unequal 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 differences(Lx=0.8L,Ly=L) are most frequently designed of equal leg angles.

For 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 requirements for design. Thus for example, chord made from channels are employed when they are subjected not only to an axial 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 tqo equal leg angles.

EFFECTIVE LENGTH OF COMPRESSION ELEMENTS:

The effective length of a compression top chord in the plane of truss is equal to its geometrical length(between panel point centres) Le=L.

For diagonals(except for the support one which is considered as a continuation of chord) and verticals the effective length in the plane of truss is taken equal to Le=0.8L.

When selecting angle sections for compression elements, the tendency should be to use angles of the smallest possible thickness since their radii of gyration have the relatively greatest value.

Limiting slenderness ratio λ for compression and tension elements

NAME OF ELEMENT / COMPRESSION ELEMENTS / TENSION ELEMENTS
UNDER DIRECT ACTION OF DYNAMIC LOADS / STATIC LOAD / IN BUILDING WITH HEAVY SERVICE CONDITIONS
Chords, support diagonals & verticals of trusses, transmitting support reactions / 120 / 250 / 400 / 250
Other truss elements / 150 / 350 / 400 / 300
Roofing ties(except brace rods) / 200 / 400 / 400 / 300

Lecture notes by Dr.L.S.Jeyagopal, a leading structural consultant is given below for further guidence:

1. A 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.

H= rise of the truss which is 1/8 for AC sheet.

1. As suggested earlier the top main chord(rafter) 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 G98 means bolt is having a strength of 9 Mpa 8 is % of strength used for calculation.
2. The structural design procedure consists of six principal steps.
3. Selection of type and layout of structure.
4. Determination of loads on the structure.
5. Determination of internal forces and moments in the structural components.
6. Selection of material and proportioning of members and connections for safety and economy.
7. Checking the performance of the structure under service conditions, and
8. Finial review.
9. Fabrication: Ease of fabrication and erection has an important influence on

the economy of the design.

In general, small and medium trusses of symmetrical design are lifted at the ridge during erection. In order to prevent buckling of the bottom chord, it is necessary to proportion it to carry the compressive stressesdeveloped during hoisting. An empirical relation is given by b/L =1/125. where b is the width of the bottom chord at its centre and L the span length.

For example a 50 m span truss shall have the top chord and bottom chord width =span/125.i.e. 50x1000/125=400mm. (≈8times span- in mm).

This is to avoid bending of truss on either side during erection.

The shape of a truss :

TRUSSED BEAMS:

FORMULAE FOR TRUSSED BEAMS-REF: Building engineers hand book

Used 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.

Es=2.1x10^6Kg/sq.cm(steel)

Design formulae.

Sl.no / Description / Single strut / Double strut
Uniformly distributed load –in Kg
1. / Tension in rod / 0.312Wh/r / Wh/3r
2. / Compression in strut / 0.625W / W/3
3. / Compression in beam / 0.312WL/2r / WL/9r
Concentrated load over strut,Kg
1. / Tension in rod / Ph/2r / Ph/r
2. / Compression in strut / P / P
3. / Compression in beam / PL/4r / PL/3r

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