Design of Tens Memb Slides
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Transcript of Design of Tens Memb Slides
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Design of Tension Members in Steel
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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
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T
C
T
TC
Tension members in a truss
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Which are the tension members?
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Tension members in a bridge truss
Mississippi River Bridge, St. Louis
Can you identify the tension members ?
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Compression and tension
members in a space truss
SkyDome,Toronto
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Tension member design
Tr Tr
Tr = φ A Ft
For steel Ft = Fy (yield stress)or slm*Fu (ultimate str.)
A = cross-sectional area
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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
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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
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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)]
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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
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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