Tension Member Design
Gross area
Ag = Gross area of cross section.
Net Area
Net area An of a member is the sum of the products of
the thickness and the net width of each element.
For a part in any diagonal or zigzag line, the
additional quantity is: s2.t / (4g)
s = longitudinal center-to-center spacing (pitch) of any two
consecutive holes.
g = transverse center-to-center spacing (gage) between fastner gage
lines.
Effective Net Area, Reduction-Shear Lag Coefficient (U)
Bolts:
Ae = An . U
For angle members having two and more bolts in the line of force:
U = 1 - 1.2 x/L < 0.9, but >= 0.4
For channel members having two and more bolts in the line of force:
U = 1 - 0.36 x/L < 0.9, but >= 0.5
x - distance from shear plane to centroid of the cross section
L - length of the connection in the direction of loading
Welds:
(a) When the tension load is transmitted only by longitudinal welds
or by longitudinal welds in combination with transverse welds:
Ae = Ag . U
U - reduction coefficient = 1 - x/L <= 0.9
Ag - gross area of member
(b) When the tension load is transmitted only by transverse welds:
Ae = A . U
U = 1.0
A - area of directly connected elements
(c) Otherwise:
for angle members: U = 1 - 1.2 X/L < 0.9 but U
>= 0.4
for channel members: U = 1 - 0.36 X/L < 0.9 but U
>= 0.5
x - distance from shear plane to centroid of cross section
L - length of longitudinal weld
Design Strength for Tension Members:
Yielding in the gross section: (Eq. C2.1-1)
fTn =
f.Fy.Ag= 0.90 Fy.Ag
Rupture in the net section: (appendix B, C2.2)
fTn =
f. Fu.(Lc. t) = 0.75 Fu.(Lc.
t)
1). for failure normal to force due to direct tension
Lc = Lt,
not involving stagger
Lc = 0.9 Ls,
involving stagger
2). for failure parallel to force due to shear
Lc = 0.6 Lnv
3). for failure due to block tear-out at end of member
Lc = Lt + 0.6 Lv,
not involving stagger
Lc = 0.9 (Lt + Ls) +
0.6 Lv, involving stagger
4). for failure of coped beams
Lc = 0.5 Lt + 0.6 Lv,
not involving stagger
Lc = 0.45 (Lt + Ls) +
0.6 Lv, involving stagger
Lv - the lesser of (Fy/Fu).Lgv
and Lnv
Lt - net failure path length normal to force
due to direct tension
Ls - net failure path length inclined to
force
Lgv - gross failure path length parallel to
force
Lnv - net failure path length parallel to
force
Design Rupture Strength:
Tension Rupture Strength for Welded Connection: (Eq. E2.7-1)
fRn =
f.Fu.Ae= 0.5 Fu.Ae
Tension Rupture Strength for Bolted Connection: (Eq. E3.2-1)
fRn =
f.Fu.Ae= 0.55 Fu.Ae
Reference: AISI S100-2016
Combined Bending and Tension C5.1.2
1). Mfx
/ (fb .Mnxt)+ Mfy /
(fb .Mnyt) + Tf / (ft.
Tn) < = 1.0
2). Mfx
/ (fb .Mnx)+ Mfy /
(fb .Mny) - Tf / (ft.
Tn) < = 1.0
Mfx - factored moment about axis
X
Mfy - factored moment about axis
Y
Tf - factored shear force
Mnxt = Sftx . Fy
- Nominal flexural strength about axis X
Mnyt = Sfty . Fy
- Nominal flexural strength about axis Y
Sftx - Section modulus of full
unreduced section relative to extreme tension fibre about axis X
Sfty - Section modulus of full
unreduced section relative to extreme tension fibre about axis Y
Mnx - Nominal flexural strength
about axis X
Mny - Nominal flexural strength
about axis Y
Tn - Nominal tensile strength
fb =
0.9 - resistance factor for bending
ft =
0.9 - resistance factor for shear