design_of_tension_members

CAN/CSA-S16-01 S.F.Stiemer

design_of_tension_members.docx 1/2/2010 page 1 of 13

Design of Tension Members

Summary applications as principal structural members in trusses, bridges, transmission

towers, bracing systems applications as secondary members such as sag rods, bracing of OWSJs most efficient because limit of usefulness not reduced by stability problems single shape most economical in applications, when doubling up use

advantages of symmetry limiting slenderness ratio exists because of potential of vibrations design member in two steps:

select tentative cross section using approximate formulae check design according to code requirements

failure modes: 1. excessive elongation (Fy governs) 2. rupture in net area (Fu governs) 3. rupture in effective net area (considers shear lag effects)

use “s2/4g - rule” for staggered bolt patterns composite members need to be evaluated for minimum ratio of gyration of

individual elements, stitch fasteners may help bolt hole size:

punched bolt hole diameter need to be increase by 2 mm for analysis purposes, because of material damage at the hole edge by punching process

hole should be 2 mm lager than bolt shafts therefore take bolt diameter + 4 mm for analysis purposes of net

sections Welded connections of tensile member require an investigation of the size,

length and orientation of the individual weldlines pin-ended tension members = eye-bars need to be treated differently tension rods are not covered by this section, use specifications and fasteners according to fabricator’s catalog

Figure T-1: Use of Tension Members in Structures

roof truss

ties

bracing system

ties

buildings

ties

tie

hanger

bridge truss

ties

cable stay bridge

main cables deck hangers

suspension bridge



General Tension members can be found in most steel structures where they are used as principal structural members in trusses, bridges, transmission towers, bracing systems in single and multistory buildings. Other applications are secondary members in roof and wall systems e.g. sag rods for purlins or girts. The tension member is the most efficient structural member as it can be stressed up to and beyond the yield limit in most cases without being susceptible to stability problems or other limiting states. It may consist of a single structural shape or be built up from several shapes. The use of a single member is usually preferred because of economical reasons. Built-up members are used when a single member would not be sufficient or when the slenderness ratio is too high and resulting in excessive vibrations or when a built-up member would reduce the complexity of the connection. Figure T-2: typical Cross Sections of Tension Members

Load Deflection Behaviour

rolled shapes

composite shapes

welded shapes

rods, bars

cables



General Design Steps (ref. Clause 13.2) design member in two steps:

select tentative cross section using approximate formulae and check slenderness ratio limit

o Tr = Φ Ag Fy

check design according to code requirements (least of the following): o Tr = Φ Ag Fy or o Tr = 0.85Φ An Fu or o Tr = 0.85Φ Ane Fu

failure modes: excessive elongation (Fy governs) rupture in net area (Fu governs) rupture in effective net area (considers shear lag effects)

use “s2/4g - rule” for staggered bolt patterns

bn = b - ∑D + ∑s2/(4g) where

d = bolt diameter D = d + 2mm for drilled holes D = d + 4mm for punched holes

Note: if shear block failure is involved, reduce shear path by a factor of 0.6

Effective Net Area, Ane (ref. Clause 12.3.3) applicable when critical net area includes the net area of unconnected elements For bolted connections:

Ane = 0.60 to 0.90 An (refer to S16.1)

For welded connections: Ane = An1 + An2 + An3 where

An1 for elements connected by transverse welds An2 for elements connected by longitudinal welds along two parallel edges An3 for elements connected by a single longitudinal weld

Slenderness Ratio Limit (ref. Clause 10.4.2.2) The value of slenderness ratio (KL/r) limit of 300 stems from experience and parallels values from foreign steel standards (i.e. German, Russian, American).



Design Selection Now the designer can select an appropriate trial cross section following the guidance given by the tentative cross section; or one can find the shape designation by the required mass per length and the required radius of gyration.

Required Mass for Tension Member

required mass / lengthreqMass = gSteel * MAX( An1, An2 )0.037 kg/mm

density of steel7.85e-6 kg/mm^3

required gross area, failure mode: elongation

An1 = Tf

phi * Fy4762 mm^2

factored tensile load1500 kN

performance factorphi = 0.9

yield strength350 MPa

required net area, failure mode: fracture in net area

An2 = Tf

0.85 * phi * Fu4085 mm^2

factored tensile loadTf = 1500 * kN


ultimate strength480 MPa

Inputs:Fu 480 MPaFy 350 MPaTf 1500 kNgSteel 7.85e-6 kg/mm^3phi 0.9

Outputs:reqMass 0.037 kg/mm



Slenderness Ratio Once a particular shape has been chosen, one should perform all checks of code compliance. Before going through the somewhat lengthy process of checking for connection and cross sectional resistance, it is advisable to examine the slenderness of the member first. The standard provides the reasoning for this check. The value of slenderness limit of 300 stems from experience and parallels values from foreign steel standards (i.e. German, Russian, American). If one has to deal with non-(point)-symmetrical members, the highest slenderness ratio corresponds to the smallest radius of gyration. Thus we have to evaluate the three principal radii for a double angle arrangement.

Design Check of Slenderness Ratio

checked slenderness ratiochecked_sl = IF( MAX( slx, sly, slz )max_slr, "all o.k.", "too slender" )all o.k.

slenderness about x-axis

slx = Kx * Lx

rx75

effective length factorKx = 1.0

unbraced member lengthLx = 1.5 * m

radius of gyration about x-axisrx = 20 * mm

slenderness about y-axis

sly = Ky * Ly

ry60

effective length factorKy = 1.0

unbraced member lengthLy = 1.5 * m

radius of gyration about y-axisry = 25 * mm

slenderness about z-axis

slz = Kz * Lz

rz15

effective length factorKz = 1.0

unbraced member lengthLz = .75 * m

radius of gyration about z-axisrz = 50 * mm

maximum slenderness ratio, $10.2.2 max_slr = 300

Inputs:Kx 1Ky 1Kz 1Lx 1500 mmLy 1500 mmLz 750 mmrx 20 mmry 25 mmrz 50 mm



Failure Modes Although the design of a tension member is considered to be one of the simplest and most straightforward problems in structural engineering, we still have to deal with a few peculiarities. Before considering the failure modes one must understand the basic assumption of the standard for the load carrying mechanism. When one designs a tension member without perforations, one can assume a uniform stress distribution over the full cross section. For members with holes, as required by bolted connections, one can experience stress concentrations in the vicinity of the hole of up to three times the average stress. The standard assumes a deformation of those overstressed fibres beyond yield until the average stress is evenly distributed over the complete cross section at a magnitude of the yield stress Fy. Stability is only of secondary concern and vibrational problems have been dealt with above by taking care by the comparative value of slenderness ratio. Basically one must provide sufficient cross-sectional area to resist the applied loads with an adequate margin of safety. However, we must accommodate three different types of failure (limit states) as shown in the following:

Excessive Elongation Rupture in Net Area Rupture in Effective Net Area

tensile resistanceTr = MIN( Tri, Trii, Triii )715 kN

yielding in gross cross sectionTri = phi * Ag * Fy2700 kN


gross cross section10000 mm^2

yield strength300 MPa

rupture in net cross sectionTrii = 0.85 * phi * Ane * Fu715.5 kN


net cross sectionAne = Ana + Anb + Anc2078 mm^2


shear lag effects consideredTriii = 0.85 * phi * A'ne * Fu3443 kN

Inputs:Ag 10000 mm^2Ane 2078 mm^2Fu 450 MPaFy 300 MPaLn 484 mmLoad_Transfer_Type 1c_Type 1dh 24 mme 30 mmg1 80 mmg2 80 mms1 80 mmt 6 mmtwelds Truew 50 mmwL 100 mmx 0 mm

Outputs:Tr 715 kN



Bolted Connections of Tension Members, Effective Net Area In bolted connections, the net area Ane considered is equal to the anticipated fracture path. If the path is extending diagonally from a bolt hole of one gauge line to a hole of another gauge line, you could gain by having a longer path. On the downside, more holes are intercepted. Furthermore, an inclined path has less resistance to tensile failure than one which is transverse to the loading direction. A few researchers have dealt with this problem and the “s2/4g - rule” has evolved.

Although it is not applicable for the full range of parameter variations of pitch, s, and gauge, g, it is quite accurate within the limits as stated by the standard. The effective area is computed by adding all critical areas of all segments. Hereby one has to check all possible fracture paths in order to find the lowest resistance. In order to conveniently place the bolts for a connection in a structural member it is necessary to have holes slightly bigger than the bolt diameter. The greater the holes are, the easier is the erection of a building. However, in order to achieve a behaviour of the connection, which can be predicted and modeled by simple mathematical expressions one has to keep the bolt to hole tolerance in a certain limit.

The “specified hole diameter” is 2 mm greater than the bolt diameter. This is the diameter to be specified on the shop drawings. The bolt holes are punched into the steel members. During the punching process the edge of the hole is slightly deformed or damaged and cannot be expected to carry the same load as the unaffected metal. From experience the standard allows for this local damage due to fabrication. Therefore, one must add a total of 4 mm to the bolt diameter to arrive at the “nominal hole diameter”, which is the value to be used for the analysis.

nominal hole diameter = spec. dia+4 [mm] For a detailed treatment of fasteners and their behaviour please see the appropriate sections on bolted connections. The previous considerations are based on connections, where the individual bolts carry equal loads and are arranged symmetrically with respect to the centroidal axial of the tension member and thus, axis of load application. Furthermore one needs to consider shear lag effects, which can lead to a further decrease of effective net area. However, it is recommended to check if it is better to replace requirements of this clause by another engineering approach: One can

leave out the unconnected elements and consider the resistance of the connected elements only, which can result in more efficient designs without reduction in the safety margin.

PPd

h

e s1s2

g1

g2



The effective net area must be calculated as follows: Bolted Connection at Ends of Tension Member

net cross sectionAne = Ana + Anb + Anc2078 mm^2

Ana = wn2 * t336 mm^2

net widthwn2 = g2 - dh

gauge 280 mm

nominal hole diameter24 mm

plate thickness6 mm

Anb = 0.6 * Ln * t1742 mm^2

net length

Ln = 2 * e - dh2

+ 8 * s1 - 8 * dh

end distance30 mm


pitch 180 mmplate thickness

6 mm

Anc = Ans, 0 * mm2 : pattern0 mm^2

Ans = wn1 * t + s12 * t4 * g1

456 mm^2

wn1 = g1 - dh56 mm

gauge 1g1 = 80mm


plate thickness6 mm

pitch 180 mm

gauge 1g1 = 80mm

stagger=1, parallel=2pattern = 2



Shear Lag Effect Consideration due to Bolted Connection

shear lag effects consideredTriii = 0.85 * phi * A'ne * Fu3443 kN


reduced effective net areaA'ne = [ A0, A1, A2, A3, A4, A5, Aw ] : c_Type10000 mm^2

no connection consideredA0 = Ag10000 mm^2

gross cross section10000 mm^2

bolted WWF, W, M, or S-shapesA1 = 0.9 * Ane1871 mm^2

bolted angles, one leg, four lines and moreA2 = 0.8 * Ane1663 mm^2

bolted angles, one leg, less than four linesA3 = 0.6 * Ane1247 mm^2

bolted other shapes, three lines and moreA4 = 0.85 * Ane1767 mm^2

bolted other shapes, less than three linesA5 = 0.75 * Ane1559 mm^2

welded connectionAw = Ane1 + Ane2 + Ane3900 mm^2

selected member and connection casec_Type = 1




Welded Connection of Tension Members Welded connections of tensile member require an investigation of the size, length and orientation of the individual weldlines. Any set (transverse, parallel and longitudinal) weldlines will be considered as follows:

welded connectionAw = Ane1 + Ane2 + Ane3900 mm^2

transverse weldsAne1 = IF( twelds, w * t, 0 )300 mm^2

transverse weldstwelds = TRUE

plate width50 mm

plate thickness6 mm

two parallel longitudinal weldsAne2 = [ Ane2i, Ane2ii, Ane3iii ] : Load_Transfer_Type300 mm^2

when wL>= 2*wAne2i = w * t300 mm^2

plate width50 mm

plate thickness6 mm

when 2*w > wL >= 1.5*wAne2ii = 0.87 * w * t261 mm^2

plate width50 mm

plate thickness6 mm

when 1.5*w > wL >= wAne3iii = 0.75 * w * t225 mm^2

plate width50 mm

plate thickness6 mm

method of load transfer (i=1, ii=2, iii=3)Load_Transfer_Type = 1

one longitudinal weld

Ane3 = 1 - x

wL * w * t

300 mm^2

weld eccentricityx = 0 * mm

weld length100 mm

plate width50 mm

plate thickness6 mm



Pin-Connected Tension Members In pin-connected tension members, the non-uniform distribution of stress makes it desirable that the net area across the pin hole be at least one third greater than the area of the body of the member. In order to avoid end splitting, the area beyond the pin hole within a 45 degree arc each side of longitudinal axis of the member must be at least 90% of the area of the body of the member.

Tension Rods Previous considerations are not applicable to tension rods, which are quite common members in buildings, but usually used as secondary members. The design stress is often rather small i.e. in sag rods for purlins or wall girts. Special care must be taken in case the tension rods are used as primary hangers for balconies or ties of structural arches. The tie rods are connected by nuts on their threaded ends. When prestress is applied to the rods, the vibration can be reduced to manageable amounts and requirements of slenderness ratios need not be complied with.

Figure T-3: Use of Tension Rods in Buildings

TierodsGirt

Col. GirtCol.

A

A

(b) Wall system

Tierods

Girts

Section A-A

Tie rod

Balcony

(c)

Roof trussSag rodSag rod

Pur

lin

Pur

lin

Rid

ge

Roof truss

Top viewElevation view

Sag rods

Purlins

(a) Roof truss



Examples of tension members in Structures



Gimme Five Tension members fail in:

strength mode [_] stability mode [_]

serviceability mode [_] A tentative cross section is useful to:

determine the tensile capacity [_] check a suitable shape [_] select a suitable shape [_]

Shear lag effects:

improve the member resistance [_] reduce the member resistance [_]

have no influence on the member resistance [_] In order to check a connection capacity, one needs to consider:

the fracture image [_] the fracture path [_]

the edge distance of the load [_] The eccentricity of resultant force of the tension member is determined by:

the distance of shape edge from bolt [_] the distance of centroid of bolt group from centre of member [_]

the distance of centroid of bolt group from centroid of cross section [_]

design_of_tension_members

Documents