Design of Tension Members in Steel

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

T

C

T

TC

Tension members in a truss

Which are the tension members?

Tension members in a bridge truss

Mississippi River Bridge, St. Louis

Can you identify the tension members ?

Compression and tension

members in a space truss

SkyDome,Toronto

Tension member design

Tr Tr

Tr = φ A Ft

For steel Ft = Fy (yield stress)or slm*Fu (ultimate str.)

A = cross-sectional area

Steel tension members

Tension stress distribution

This part of the steel angle is not properly connected and will thus carry less stress-SHEAR LAG –Reduce effective area Tension

stresses

Shear stresses

Combination of shear and tension stresses

Tension and shear strength of steel

From the von Mises yield criterion:

Tension strength of steel = σy

Shear strength τy = σy / √3= 0.58 σy≈ 0.6 σy

Steel tension members

t

t

To calculate tension capacity, convert all failure plains to equivalent tension areas, i.e multiply shear areas by 0.6 and for inclined areas use the projected tension area, increased by an additional (s2/4g)t

Ls

Lt

Li wn

s

g

Ane = t [Lt + 0.6 Ls + (wn + s2/4g)]

COMPUTATIONS FOR BOLTED CONNECTION

Preliminary Design Selectionestimate to prevent elongation Aelong = Tf/(phi*Fy)*1000 = 1481 mm2

estimate to prevent fracture Afract = Tf/(0.85*phi*Fu)*1000 = 1162 mm2

select cross section greater than Areq = MAX(Aelong,Afract) = 1481 mm2

Slenderness Ratios in Tension Membersabout x-axis slx = kx*l/rx = 65 $10.4.2.2about y-axis sly = ky*l/ry = 65about z-axis slz = IF(rz=0,0,kz*l/rz) = 101check maximum for limit IF(MAX(slx,sly,slz)<=300,"o.k","too

slender")= o.k

Failure in Tension MemberYielding / Excessive Elongationtensile resistance of entire cross section Tri = phi*Atot*Fy/1000 = 424 kN $13.2(a)(i)

Block Shear, Entire Block Tearoutgross shear area of connected element Agv = bl*(en+(n/bl-1)*pitch)*t = 2280 mm2

net tension area Ant = (gauge-h)*t = 720 mm2

end tearout entire block Trii = (phiu*(Ut*Ant*Fu+0.6*Agv*(Fy+Fu)/2))/1000

= 628 kN $13.2(a)(ii)$13.11

Fracture through Net Cross Section, bolted endsnet cross section, regular Anp = w*t-bl*h*t = 1560 mm2 $12.3.1(a)net cross section, staggeredneeds to be modified to include all inclined sections of fracture path

Ans = Anp+ni*pitch^2*t/(4*gauge) = 2160 mm2 $12.3.1(b)

net cross section An = IF(pattern="yes",Anp,Ans) = 2160 mm2

Ane = slm*An = 2160 mm2

tensile resistance of plate Triii = phiu*Ane*Fu/1000 = 729 kN $13.2(a)(iii)

Fracture through Net Cross Section, pinned endsnet area pinned Anep = 1.33*w*t = 3990 mm2 $12.4.1

tensile resistance of connecting element Trp = 0.75*phiu*Anep*Fu/1000 = 1010 kN $13.2(b)

resistance to factored load per interconnected element

Tr_c = IF(bolted="yes",MIN(Trii,Triii),Trp) = 628 kN

Summarytotal resistance to factored load Tr_tot = MIN(nc*Tr_c,Tri) = 424 kN

FIXED OR TABLE PARAMETERS

specified hole size h = IF(punch="yes",dia+4,dia+2) = 24 mm $22.3.5.1performance factor block tear phiu = 0.75 $13.1(a)performance factor phi = 0.90 $13.1(a)

TABLES

Bolt Type Ultimate Strength Fuin Mpa

A325M 830A490M 1040A325<=1" 825A325 or F1852 >1" 735

Connected EfficiencyFactorElement Ut

plates, flanges 1angles, one legor stem of T 0.6coped beams,one bolt line 0.9

Effective Net Area Modifier due to Shear Lag  slm

(a) WWF, W, M, S‐shape flange 0.90(b)(i) angles, one leg, four lines of fasteneres 0.80(b)(ii) angles, less than four lines of fasteners 0.60(c)(i) other, three or more lines of fasteners 0.85(c)(ii) other, two lines of fasteners 0.75

no shear lag effects 1.00