A Beginner's Guide to the Steel Construction Manual, 13th ed. (old) Chapter 4 - Bolted Connections |
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Section 4.9 Example Problem 4.3 The example problems presented in this section refer to a spreadsheet solution. Click on the link below to get the file: Chapter 4: Excel Spreadsheet Solutions Given: A WT is bolted to a W section as part of a beam/brace connection as shown in Figure 4.9.3.1. The connection is subjected to axial tension, P. Assume that the load transferred consists only of Wind Load (100%). The W and WT are made from ASTM A992 steel. The HSS is made from ASTM A500 Gr B steel. The bolts are fully pretensioned 3/4" diameter ASTM A325-N in standard holes. The faying surfaces are class A. Figure 4.9.3.1 Wanted: Determine the capacity of the connection based on bolt strength as specified below. Consider both LRFD and ASD. Express your results in terms of comparable service level loads.
Solution: Note that the line of force passes through the center of the bolt group so that there is no eccentricity. This makes the bolt force computations much easier. The six bolts are subjected to both tension and shear. The first thing that we want to do is break P into its horizontal (shear, Pv) and vertical (tension, Pt) components: Pv = (4/5)Pbrace Pt = (3/5)Pbrace From the problem statement we can deduce: Ps,eq = W (the wind load). Considering load cases, for LRFD the critical cases have Pu = 1.6 W = 1.6 Ps,eq. For ASD the critical case is Pa = W = 1.0 Ps,eq. To find the controlling capacity in each of the given situations, the two applicable limit states (shear and tensile rupture) must be considered. a) Slip-Critical As an aside, this connection is very likely to be designed as slip critical because wind loads reverse direction making slip an issue. Tension Rupture Limit State - (See specification section J3.6) Rn = FntAb = 39.8 k/bolt Where Fnt = 90 ksi (from Table J3.2) and Ab = .4418 in2 (area of a 3/4" diameter circle). There are six bolts in the connection so: Rn = FntAb = 239 k/connection For LRFD: Pvu = 1.6Pvs,eq = 1.6 (0.60Pbrace) < fRn = .75(239 k/connection) = 179 kips Pbrace < 186 kips (LRFD) For ASD: Pva = Pvs,eq = 0.60 Pbrace < Rn/W = (239 k/connection)/2.00 = 199 kips/connection Pbrace < 199 kips (ASD) Slip Limit State - (See specification section J3.8 and J3.9) rn = mDuhscTbNs = 11.1 kips/per bolt where: m = 0.35, Du = 1.13, hsc = 1.00, Tb = 28 k (from Table J3.1), and Ns = 1 (each bolt has only 1 shear plane). The connection has 6 bolts, so, for the connection: Rn = (11.1 k/bolt)(6 bolts) = 66.4 kips/connection This value needs to be reduced for the presence of tension using the factor ks found in section J3.9. The equation varies for LRFD and ASD. For LRFD: Tu = Ptu = 1.6 (0.60 Pbrace)
= 1.28 Pbrace and The limit state inequality becomes
Pbrace < 41.1 kips (LRFD) For ASD: Ta = Pts,eq = 0.60 Pbrace and Va = Pvs,eq = 0.80 Pbrace The limit state inequality becomes
Pbrace < 43.9 kips (ASD) b) Bearing For the bearing-type connection, we check the shear capacity first, then the tension capacity reduced for the presence of shear. Shear Rupture Limit State - (See specification section J3.6) With Fnv = 48 ksi and Ab = 0.4418 in2: rn = 21.2 k/shear plane Rn = 127 k/connection for LRFD: Pvu = 1.6(.8Pbrace) < fRn = 0.75(127 k/connection) = 95.4 k/connection Pbrace < 74.6 k/connection (LRFD) for ASD: Pva = 0.8Pbrace < Rn/W = (127 k/connection)/2 = 63.6 k/connection Pbrace < 79.5 k/connection (ASD) Tension Rupture Limit State - (See specification sections J3.6 and J3.7) The SCM equations are set up for analysis (i.e. where you know what the applied load is). Since we don't know what the applied force is (we are solving for that), we will need to do a bit of algebra. First, we will compute the capacity without the reduction. This is the upper limit on capacity. If, after applying the reduction formulas, the value turns out to be larger than the capacity without the reduction, we will use the lower value. This approach is consistent with the limits given in J3.7. With Fnt = 90 ksi and Ab = 0.4418 in2: rn = 39.8 k/bolt Rn = 239 k/connection for LRFD: Ptu = 1.6(.6Pbrace) < fRn = 0.75(239 k/connection) = 179 k/connection Pbrace < 186 k/connection (LRFD) for ASD: Pta = 0.6Pbrace < Rn/W = (239 k/connection)/2 = 119 k/connection Pbrace < 199 k/connection (ASD) Applying the reduction equations for F'nt in J3.7: For LRFD:
Pbrace < 69.2 k/connection (LRFD) for ASD:
Pbrace < 73.8 k/connection (ASD) Since the reduced values are less than the unreduced values, those are the ones that control. Solution Summary:
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