• ## Example of Strength Design of a Single Anchor Loaded in Shear

Using strength design, compute the design shear capacity of a 1/2-in. diameter, A307 bent-bar anchor with a 1-in. hook, embedded horizontally in a grouted cell of a nominal 8-in. wall with a specified compressive strength, f â˛ m, of 1500 lb/in.2. Assume that the bottom of the anchor hook is embedded a distance of 4.5 in., and that the anchor is located far from free edges in the direction of applied shear. This might represent an anchor used to attach a ledger to a masonry wall. Because free edges are not a factor, shear breakout does not apply. First, compute the effective embedment, lb. In accordance with Sec. 1.16.5 of the 2008 MSJC Code, this is equal to the total embedment of 4.5 in., minus the diameter of the anchor (to get to the inside of the hook), and minus an additional anchor diameter, or 3.5 in. The projected tensile breakout area has a radius of 3.5 in. (diameter of 7 in.).

Now obtain the design capacity by multiplying the nominal capacity by the corresponding strength-reduction factor from Sec. 3.1.4.4 of the 2008 MSJC Code:

Now obtain the design capacity by multiplying the nominal capacity by the corresponding strength-reduction factor from Sec. 3.1.4.4 of the 2008 MSJC Code:

ĎBvns = 0.9 â 5400 lb 2008 MSJC Code, Sec. 3.1.4.4
ĎBÂ vns Â = 4860lb
The governing design shear capacity is the lowest of that governedÂ by masonry crushing (2033 lb), pryout (5962 lb), and yield of the anchorÂ shank (4860 lb). Because the anchor is not close to a free edge, shearÂ breakout does not apply. Masonry crushing governs, and the designÂ shear capacity is 2033 lb.
If this problem had involved an anchor loaded toward a free edge,Â then shear breakout would have had to be checked.

• ## Behavior and Design of Anchor Bolts Loaded in Shear

Anchor bolts loaded in shear, and located without a nearby free edge in the direction of load, can fail by local crushing of the masonry under bearing stresses from the anchor bolt; by pryout of the head of the anchor in a direction opposite to the direction of applied load, or by yield and fracture of the anchor bolt steel. Anchor bolts loaded in shear, and located near a free edge in the direction of load, can also fail by breakout of a roughly semi-conical volume of masonry in the direction of the applied shear. Pryout and shear breakout are shown in parts (a) and (b), respectively, of Fig. 5.30.

• ## Example of Strength Design of a Single Anchor Loaded in Tension

Using strength design, compute the design tensile capacity of a 1/2-in. diameter, A307 bent-bar anchor with a 1-in. hook, embedded vertically in a grouted cell of a nominal 8-in. wall with a specified compressiveÂ strength, fâ˛m , of 1500 lb/in.2. Assume that the bottom of the anchor hook is embedded at a distance of 4.5 in. This example might represent a tensile anchor used to attach a roof diaphragm to a wall.

First, compute the effective embedment, lb. In accordance with Sec. 1.16.5 of the 2008 MSJC Code, this is equal to the total embedment of 4.5 in., minus the diameter of the anchor (to get to the inside of the hook), and minus an additional anchor diameter, or 3.5 in. As shown in Fig. 5.29, the projected tensile breakout area has a radius of 3.5 in. (diameter of 7 in.). Because the masonry wall has a specified thickness of 7.63 in., the projected tensile breakout area is not affected by adjacent ungrouted cells or regions outside of the wall.

Now compute the nominal tensile capacity as governed by steel yield. In this computation, Ab is the effective tensile stress area of the anchor bolt, including the effect of threads. According to ANSI/ ASME B1.1,

Now obtain the design capacity by multiplying the nominal capacityÂ by the corresponding strength-reduction factor from Sec. 3.1.4.4 of theÂ 2008 MSJC Code:

ĎB C anp = 0.65 Ă 3481 lb 2008 MSJC ode, Sec. 3.1.4.4

ĎB = 2263 lb

The governing design tensile capacity is the lowest of that governed by masonry breakout (2981 lb), yield of the anchor shank (8100 lb), and pullout (2263 lb). Pullout governs, and the design tensile capacity is 2263 lb.

If this problem had involved an anchor with deeper embedment (so that the projected tensile breakout area would have been affected by adjacent ungrouted cells or regions outside of the wall), only the anchor capacity as governed by tensile breakout would have been affected, due to a reduced projected tensile breakout area.

Similarly, if this problem had involved adjacent anchors with overlapping tensile breakout areas, only the anchor capacity as governed by tensile breakout would have been affected, again due to a reduced projected tensile breakout area.

• ## Behavior and Design of Anchor Bolts Loaded in Tension

Anchor bolts loaded in tension can fail by breakout of a roughly conical body of masonry, or by yield and fracture of the anchor bolt steel. Bentbar anchor bolts (such as J-bolts or L-bolts) can also fail by straightening of the bent portion of the anchor bolt, followed by pullout of the anchor bolt from the masonry. Nominal tensile capacity as governed by masonry breakout is evaluated using a design model based on a uniform tensile stress of 4 square(f mâ˛) Â acting perpendicular to the inclined surface of an idealized breakout body consisting of a right circular cone (Fig. 5.27). The capacity associated with that stress state is identical with the capacity corresponding to a uniform tensile stress of 4Â quare(f mâ˛) acting perpendicular to the projected area of the right circular cone. This design approach, while less sophisticated than that of ACI 318-08 App. D, has been shown to be userfriendly and safe for typical masonry applications.

Nominal tensile capacities for anchors as governed by masonry breakout are identical for headed and bent-bar anchors, and are given by Eqs. (3-1) and (3-3) of the 2008 MSJC Code. B A f Code anb pt m = 4 â˛ 2008 MSJC , Eqs. (3-1) and (3-3) In Eqs. (3-1) and (3-3), the projected area Apt is evaluated in accordance with Eq. (1-2) of the 2008 MSJC Code: A l Code pt b = Ď 2 2008 MSJC , Eq. (1-2)

As required by Sec. 1.16.4 of the 2008 MSJC Code, the effective embedment length, lb , for headed anchors is the length of the embedment measured perpendicular from the masonry surface to the compression bearing surface of the anchor head. As required by Sec. 1.16.5 of the 2008 MSJC Code, the effective embedment for a bent-bar anchor bolt, lb , is the length of embedment measured perpendicular from the masonry surface to thecompression bearing surface of the bent end, minus one anchor bolt diameter. These are shown in Fig. 5.27. As shown in Fig. 5.28, the projected area must be reduced for the effect of overlapping projected circular areas, and for the effect of any portion of the project area falling in an open cell or core.

Nominal tensile capacities for anchors as governed by steel yield and fracture are also identical for headed and bent-bar anchors, and are given by Eqs. (3-2) and (3-5) of the 2008 MSJC Code. In those equations, Ab is the effective tensile stress area of the anchor bolt, including the effect of threads.

In that equation, the first term represents capacity due to the hook, and the second term represents capacity due to adhesion along the anchor shank. Article 3.2A of the 2008 MSJC Specification requires that anchor shanks be cleaned of material that could interfere with that adhesion. The failure mode with the lowest design capacity governs.

• ## Strength Design of Anchor Bolts

In masonry construction, anchor bolts are most commonly used to anchor roof or floor diaphragms to masonry walls. As shown in Fig. 5.26, vertically oriented anchor bolts can be placed along the top of a masonry wall to anchor a roof diaphragm resting on the top of the wall. Alternatively, horizontally oriented anchor bolts can be placed along the face of a masonry wall to anchor a diaphragm through a horizontal ledger. In these applications, anchor bolts are subjected to combinations of tension and shear. In this section, the behavior of anchors under those loadings is discussed, and 2008 MSJC strength design provisions are reviewed.