Tension Member Design
Gross area
A_{g} = Gross area of cross section.
Net Area
Net area A_{n} 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: s^{2}.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:
A_{e} = A_{n} . 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:
A_{e} = A_{g} . U
U - reduction coefficient = 1 - x/L <= 0.9
A_{g} - gross area of member
(b) When the tension load is transmitted only by transverse welds:
A_{e} = 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)
fT_{n} =
f.F_{y}.A_{g}= 0.90 F_{y}.A_{g}
Rupture in the net section: (appendix B, C2.2)
fT_{n} =
f. F_{u}.(L_{c}. t) = 0.75 F_{u}.(L_{c}.
t)
1). for failure normal to force due to direct tension
L_{c} = L_{t},
not involving stagger
L_{c} = 0.9 L_{s},
involving stagger
2). for failure parallel to force due to shear
L_{c} = 0.6 L_{nv}
3). for failure due to block tear-out at end of member
L_{c} = L_{t} + 0.6 L_{v},
not involving stagger
L_{c} = 0.9 (L_{t} + L_{s}) +
0.6 L_{v}, involving stagger
4). for failure of coped beams
L_{c} = 0.5 L_{t} + 0.6 L_{v},
not involving stagger
L_{c} = 0.45 (L_{t} + L_{s}) +
0.6 L_{v}, involving stagger
L_{v} - the lesser of (F_{y}/F_{u}).L_{gv}
and L_{nv}
L_{t} - net failure path length normal to force
due to direct tension
L_{s} - net failure path length inclined to
force
L_{gv} - gross failure path length parallel to
force
L_{nv} - net failure path length parallel to
force
Design Rupture Strength:
Tension Rupture Strength for Welded Connection: (Eq. E2.7-1)
fR_{n} =
f.F_{u}.A_{e}= 0.5 F_{u}.A_{e}
Tension Rupture Strength for Bolted Connection: (Eq. E3.2-1)
fR_{n} =
f.F_{u}.A_{e}= 0.55 F_{u}.A_{e}
Reference: AISI S100-2016
Combined Bending and Tension C5.1.2
1). M_{fx}
/ (f_{b} .M_{nxt})+ M_{fy} /
(f_{b} .M_{nyt}) + T_{f} / (f_{t}.
T_{n}) < = 1.0
2). M_{fx}
/ (f_{b} .M_{nx})+ M_{fy} /
(f_{b} .M_{ny}) - T_{f} / (f_{t}.
T_{n}) < = 1.0
M_{fx} - factored moment about axis
X
M_{fy} - factored moment about axis
Y
T_{f} - factored shear force
M_{nxt} = S_{ftx} . F_{y}
- Nominal flexural strength about axis X
M_{nyt} = S_{fty} . F_{y}
- Nominal flexural strength about axis Y
S_{ftx} - Section modulus of full
unreduced section relative to extreme tension fibre about axis X
S_{fty} - Section modulus of full
unreduced section relative to extreme tension fibre about axis Y
M_{nx} - Nominal flexural strength
about axis X
M_{ny} - Nominal flexural strength
about axis Y
T_{n} - Nominal tensile strength
f_{b} =
0.9 - resistance factor for bending
f_{t} =
0.9 - resistance factor for shear