30 November 1998
PG = 0.75φ t cLFcu
For tc ≤ tw < 2tc (single shear)
PG = 1.5φ t cLFcu
For tw ≥ 2tc (double shear)
φ = the resistance factor for flare grove welds, equal to 0.55.
tc = the thickness of the column material.
L = the length of the flare bevel grove weld.
Fcu = the ultimate strength of the column steel.
C18. ANCHOR BOLT CONE FAILURE. Embedded anchors shall be used for all anchor bolts described
here. The anchor bolt cone failure design strength, Pc shall exceed the applied tensile force per bolt,
PtAB (Equation 3-37). Either one or two anchor bolts may be installed on both sides of the columns (i.e.,
nAB equal to 2 or 4). If only one bolt is installed, the cone failure surface will be that of a simple cone. If
two bolts are installed, the critical failure surface will be the minimum failure surface defined by two
independent cones or a surface that accounts for the overlap of two cones. If the two bolts on the same
side of the column are close enough relative to the bolt embedment length, then the combined surface
will control. The column anchor bolts at the outside of the shear panel will always be more highly
stressed than those at the inside. These bolts will be more critically loaded by uplift forces due to the
direction of diagonal strap forces and moment in the column. A cone failure surface including bolts on
both sides of the columns will never be more critical than the cone for bolts only at the outside of the
shear panel. Therefore, only the cone with bolts on the outside are considered. The anchor bolt cone
failure design strength, Pc (in pounds) is determined by :
Pc = 4φc f' c A c
φ = the cone strength reduction factor - a value of 0.85 for uncracked concrete.
f' = the specified concrete compressive strength in psi
Ac = the minimum of the area of a single anchor bolt stress cone (Ac1) or the summation of the
combined failure surface for two overlapping stress cones divided by two (Ac2), in inches .
The area of individual stress cones is dependent on the angle of cone failure. In the case of
expansion anchors this angle varies from about 60 degrees (measure from the axis of the
anchor) for short embedments (lAB ≤ 2 inches) to 45 degrees for lAB ≥ 6 inches. In this
guidance this angle will conservatively be set equal to 45 degrees. Then the radius of the
cone at the concrete surface, rc is equal to anchor embedment length, lAB. The area of an
individual stress cone failure surface, Ac1 shall be calculated as follows:
A c1 = πrc rc2 + l2 B = 2πl2 B
The area of the combined failure surface for two overlapping stress cones, divided by two for an
individual anchor bolt, Ac2 shall be calculated as follows:
πrc + 2dcc
l AB (πl AB + 2d cc )
A c2 =
rc2 + l2 B =
ACI 355.1R-91, Equation 3.2.