Bolt In Shear And Tension Connected To A Bracket
n where P = load, kips, on the bracket n = total number of fasteners
In addition, the moment is resisted by the upper fasteners in tension and the pressure of the lower part of the bracket against the support. The neutral axis is usually located above the bottom of the connection by about V6 of the connection length, but its exact location requires a trialanderror approach. However, an alternative is to use a conservative plastic distribution, which is valid for both ASD and LRFD design methods. For this distribution, each bolt
above the neutral axis is assumed to carry an axial tensile force, T, and each bolt below the neutral axis an axial compressive force T. Thus, the neutral axis falls at the centroid of the bolt group. There is no axial force on the bolts located at the neutral axis.
In bearingtype connections, allowable stresses or design strengths are determined from interaction equations for tension and shear. However, in slipcritical connections, since the shear load is carried by friction at the faying surface, the reduction in friction resistance above the neutral axis of the bolt group (due to the tensile force from bending) is compensated for by an increase in friction resistance below the neutral axis (due to the compressive force from bending). Thus an interaction equation is not required in this case, but both the shear and tensile stresses must be less than those allowable. Also, since slip is a serviceability limit state, the strengthlimit state of bearing also must be checked. In addition, the tension forces on the fasteners and the bending of the flanges must be checked for prying (Sec. 5.25.3).
Example—Bracket with Bolts in Tension and Shear—AISC LRFD. Investigate the slipcritical connection in Fig. 5.48. The A36 steel bracket is to be connected with 7/8indiameter A325 bolts to a flange of a building column. The bracket carries a 115kip factored load 14 in from the flange.
First consider the connections as slipcritical with A325SCAN 7/8in diameter bolts in standard 15/16 in holes. The bolt notation indicates slipcritical (SC), surface class (A), with threads not excluded from the shear planes (N). The design strength in shear in this case is farv = fa1.13^T„ = 1.0 X 1.13 X 0.33 X 39 = 14.5 kips
The design strength for tension is fart = faF,Ab = 0.75 X 90 X 0.6013 = 40.6 kips
The required design strength per bolt in shear is simply V = 115/14 = 8.21 kips < 14.5 kips, OK. For the required design strength in tension, take moments about the neutral axis with a force T in each bolt: 2T(3 + 6 + 9) = 115 X 14. Solve for T = 22.4 kips < 40.6 kips, OK. The bolts are satisfactory for a slipcritical connection.
Next consider as a bearing type connection with A325N 7/8in diameter bolts in standard 15/i6 in holes. The design strength in shear in this case is farv = faFv Ab = 0.75 X 48 X 0.6013 = 21.6 kips
V = 8.21 kips < 21.6 kips, OK. The design strength in pure tension is the same as for the slipcritical condition, 40.6 kips. The design tensile strength in the presence of shear is calculated from the following interaction equation:
where fa = resistance factor, 0.75 Ab = area of bolt, in2 V = shear force per bolt, kips
For this case, faB = 0.75 X 0.6013[117  2.5 (8.21/0.6013)] = 37.3 kips, and faAb(90) = 0.75 X 0.6013 X 90 = 40.6 kips. Therefore, faB = 37.3 kips > 22.4 kips required, OK. The bolts are satisfactory for a bearing type connection. This type of connection would be used unless there was a specific requirement for a slipcritical connection.
Next, check bolts and bracket flange for bending and prying action using the notation from Art. 5.25.3:
b = (4  0.480)/2 = 1.76 in a = (11.090  4)/2 = 3.545 in, but a < 1.25b = 1.25 X 1.76 = 2.20 in; a = 2.20 in b' = b  d/2 = 1.76  0.875/2 = 1.32 in a' = a + d/2 = 2.20 + 0.875/2 = 2.64 in
A check shows that the W18 X 36 bracket would be unsatisfactory if of A36 steel. Try A57250 steel.
4.44fBb' 4.44 X 40.6 X 1.32 i ^  i  = 1.260 in pFy V 3 X 50
Renewable Energy 101
Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of nonrenewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a nonrenewable supply, the nonrenewable energy sources release emissions into the air, which has an adverse effect on the environment.
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