齐平端板力矩连接设计

Flush end plate moment connection design to AISC 360 和 AISC 设计指南 39 comes down to three things: bolts big enough to carry the flange tension without prying, an end plate thick enough to stay stiff around those bolts, and welds and a column flange that can deliver the force on both sides. The beam moment and axial load are turned into an equivalent moment, and the bolt diameter and plate thickness are sized from a yield line pattern around the tension bolts.

This page works through one real flush end plate moment connection from start to finish: a W21x101 beam bolted to the flange of a W14x211 column through a 1 in end plate with eight 1 在 A490-N 螺栓中, carrying a 200 急转瞬间, 一个 125 kip shear and 150 kip of axial tension or compression. It is designed to AISC 360-16 LRFD, the AISC Manual 15th Edition and Design Guide 39. 每个方程都用它的数字写出来, 按照与 AISC 计算表相同的顺序 SkyCiv连接设计 模块为其生成.

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What is a flush end plate moment connection?

An end plate moment connection is a plate welded to the end of a beam in the shop and bolted to the column on site. In a flush end plate, the plate stops at the beam flanges, so every bolt sits between the flanges. In an extended end plate, the plate projects past the tension flange and carries a bolt row outside it. The flush version is easier to fit into a floor and has nothing sticking up past the beam, but its bolts have a shorter lever arm, so it suits moderate moments.

It is a 矩连接: the welds and bolts are designed so the joint transfers the full beam moment into the column, rather than letting the beam end rotate. The same plate made shallower and welded to the web only is an end plate shear connection, and both are covered by the end plate connection calculator. 的 瞬间连接 page compares it with the flange plate moment connection and other details.

海拔. The end plate is welded to the end of the W21x101 and bolted to the W14x211 column flange with two bolt rows near each beam flange.

A-A部分. Four rows of two bolts at a 7 1/2 在规格中, 2 in from the inside face of each flange and 3 in apart. The plate extends 1 1/2 in past each flange so the flange welds fit.

Flush end plate moment connection design: 步骤一目了然

The design follows AISC Design Guide 39: size the bolts and the plate for the moment first, then check the welds, the bolts in shear and the column.

1. Check the detailing limits for the welds, bolts and plate.
2. Find the equivalent moment and the required bolt diameter.
3. Find the yield line parameter and the required end plate thickness.
4. Check the fillet welds at the beam flange.
5. Check the beam flange base metal at the weld.
6. Check the fillet welds at the beam web for tension.
7. Check the beam web base metal at the weld.
8. Check the fillet welds at the beam web for shear.
9. Check the bolts in shear.
10. Check bolt bearing and tear-out on the end plate.
11. 检查柱法兰上的螺栓轴承和撕裂情况.
12. Check column flange bending at the tension bolts.
13. Check the column under the compression flange force.

本示例的设计输入

设计代码为AISC 360-16 LRFD, with the end plate procedure from AISC Design Guide 39. 截面属性来自 AISC 手册.

 

 

步 1: 详细限制 (AISC 360-16 J2.2b, J3.3, J3.4, J3.5)

在进行任何力量检查之前, the connection has to be buildable and match the assumptions behind the Design Guide 39 方程式. The welds must be at least the minimum size for the parts they join, the bolts must be far enough apart and far enough from the edges, and the plate must be deep enough to take the flange welds.

The minimum fillet weld sizes come from Table J2.4: 5/16 in for the flanges, where the thinner part joined is the 0.8 in flange, 和 3/16 in for the 0.5 in web. 最小螺栓间距为 [mathin] 2\tfrac{2}{3} d_{b} [mathin] from J3.3, and the edge distances come from Table J3.4. The end plate has horizontal short slots, 因此表 J3.5 添加了 1/8 in to its horizontal edge distance, 给予 1.375 在. The maximum gage on the end plate is the beam flange width, 12.3 在, so the bolts stay inside the flange.

For a minimum limit the ratio is limit over actual, and for a maximum it is actual over limit. The governing row is the plate height:

[math] DCR = \frac{d}{c} = \frac{(22.525)}{(23)} = 0.97935 [math]

DCR = 0.979 < 1.0, 行

The minimum plate height is 1.125 in more than the 21.4 in beam depth, 要么 0.5625 in past each flange: room for the 7/16 in flange weld plus 1/8 在. 的 23 in plate gives 0.8 in each side, so it passes with little to spare. That is normal for a flush plate, which is meant to stop just past the flanges.

步 2: Required bolt diameter (AISC 设计指南 39, 情商. 3-30 and 5-3a)

The bolts near the tension flange carry the moment as tension. 设计指南 39 sizes them so they reach their tensile strength without any prying force, which is only possible if the end plate is then made thick enough to stay stiff (步 3).

Equivalent moment with axial tension

Axial tension pulls on the tension bolts as well. The guide adds it to the moment as half the tension acting over the distance between the flange centroids:

[math] M_{u,eq} = M_{ux} + \frac{T_{u}}{2} \left( d_{bm} – t_{fb} \right) [math]

[math] M_{u,eq} = (200\,kip\text{-}ft) + \frac{(150\,kip)}{2} \times \left( (21.4\,in) – (0.8\,in) \right) = 328.75\,kip\text{-}ft [math]

Bolt lever arms

The tension bolts rotate about the centre of the compression flange. [mathin] h_{1} = 18.2\,in [mathin] is the distance from there to the farther tension bolt row, the one 2 in inside the tension flange, 和 [mathin] h_{2} = 15.2\,in [mathin] is the distance to the next row, 3 in further in. 有 [mathin] n_{c} = 2 [mathin] bolts in each row:

[math] \sum_{i} n_{i} h_{i} = n_{c} \left( h_{1} + h_{2} \right) = 66.8\,in [math]

Required bolt diameter

在哪里 [mathin] \phi = 0.75 [mathin] is the resistance factor for bolt tension and [mathin] F_{nt} = 113\,ksi [mathin] is the nominal tensile stress of an A490 bolt:

[math] d_{b,reqd} = \sqrt{\frac{4\, M_{u,eq}}{\pi\, \phi\, F_{nt} \sum_{i} n_{i} h_{i}}} [math]

[math] d_{b,reqd} = \sqrt{\frac{4 \times (328.75\,kip\text{-}ft)}{\pi \times (0.75) \times (113\,ksi) \times (66.8\,in)}} [math]

[math] d_{b,reqd} = 0.94193\,in [math]

[math] DCR = \frac{d_{b,reqd}}{d_{b}} = \frac{(0.94193\,in)}{(1\,in)} = 0.94193 [math]

DCR = 0.942 < 1.0, 行

The axial tension adds 128.75 kip-ft to the 200 急转瞬间, so it drives a large share of the bolt size.

步 3: Required end plate thickness (AISC 设计指南 39, 桌子 5-3 和情商. 5-5一个)

The end plate bends around the tension bolts. 设计指南 39 finds its strength from a yield line pattern: the set of hinge lines that form in the plate when it fails. The plate is then made thick enough that it stays elastic, so the bolts see no prying.

Yield line parameter

The yield line pitch s locates the hinge lines below the bolts:

[math] s = \frac{\sqrt{b_{p}\, g}}{2} = \frac{\sqrt{(12.5\,in)(7.5\,in)}}{2} = 4.8412\,in [math]

For a four-bolt flush unstiffened end plate, 桌子 5-3 gives:

[math] Y_{p} = \frac{b_{p}}{2} \left( \frac{h_{1}}{p_{f}} + \frac{h_{2}}{s} \right) + \frac{2}{g} \left( h_{1} \left( p_{f} + \frac{3 s_{r}}{4} \right) + h_{2} \left( s + \frac{s_{r}}{4} \right) \right) + \frac{g}{2} [math]

和 [mathin] b_{p} = 12.5\,in [mathin], [mathin] g = 7.5\,in [mathin], [mathin] h_{1} = 18.2\,in [mathin], [mathin] h_{2} = 15.2\,in [mathin], [mathin] p_{f} = 2\,in [mathin], [mathin] s = 4.8412\,in [mathin] 和 [mathin] s_{r} = 3\,in [mathin]:

[math] Y_{p} = 123.54\,in [math]

Required plate thickness

在哪里 [mathin] \gamma_{r} = 0.8 [mathin] is the Design Guide 39 reduction factor for flush end plates, which keeps the connection fully restrained, [mathin] \phi = 0.9 [mathin] is the resistance factor for flexure and [mathin] F_{yp} = 50\,ksi [mathin]:

[math] t_{p,reqd} = \sqrt{\frac{1.10\, M_{u,eq}}{\gamma_{r}\, \phi\, F_{yp}\, Y_{p}}} [math]

[math] t_{p,reqd} = \sqrt{\frac{1.10 \times (328.75\,kip\text{-}ft)}{(0.8) \times (0.9) \times (50\,ksi) \times (123.54\,in)}} [math]

[math] t_{p,reqd} = 0.9878\,in [math]

[math] DCR = \frac{t_{p,reqd}}{t_{p}} = \frac{(0.9878\,in)}{(1\,in)} = 0.9878 [math]

DCR = 0.988 < 1.0, 行

的 1.10 factor keeps the plate’s yield line strength 10% above the demand, so the plate stays stiff and the no-prying assumption in Step 2 holds.

步 4: Fillet weld at the beam flange (AISC 设计指南 39 情商. 3-38一个, AISC 360-16 J2.4)

The flange welds carry the flange force from the beam into the end plate. They are fillet welds on both faces of the flange, loaded perpendicular to their length.

Effective weld length

The outside weld runs the full width of the flange. The inside weld stops short of the web on each side, by the distance [mathin] k_{1} = 1.4375\,in [mathin] from the web centreline to the toe of the flange fillet:

[math] L_{w} = 2 \left( \min\left( b_{fb},\, b_{p} \right) \right) – 2 k_{1} [math]

[math] L_{w} = 2 \left( \min\left( (12.3\,in),\, (12.5\,in) \right) \right) – 2 (1.4375\,in) = 21.725\,in [math]

Flange force

The flange force is the moment divided by the distance between flange centroids, plus half the larger axial load. 设计指南 39 also sets a floor of 60% of the flange’s yield strength, so the welds are never the weak link even when the moment is small:

[math] P_{fl} = \max\left( \frac{M_{ux}}{d_{bm} – t_{fb}} + \frac{\max\left( T_{u},\, C_{u} \right)}{2},\, 0.6\, F_{yb}\, b_{fb}\, t_{fb} \right) [math]

[math] P_{fl} = \max\left( \frac{(200\,kip\text{-}ft)}{(21.4\,in) – (0.8\,in)} + \frac{\max\left( (150\,kip),\, (150\,kip) \right)}{2},\, 0.6\,(50\,ksi)\,(12.3\,in)\,(0.8\,in) \right) [math]

[math] P_{fl} = 295.2\,kip [math]

The moment and axial load give 191.5 基普, 所以 60% floor of 295.2 kip governs.

焊接强度

在哪里 [mathin] F_{EXX} = 70\,ksi [mathin], [mathin] W_{1} = 0.4375\,in [mathin], [mathin] \phi = 0.75 [mathin], and the factor 1.5 is the J2.4 directional strength increase for a weld loaded perpendicular to its axis:

[math] \phi R_{n} = \phi\, 0.6\, F_{EXX} \left( \frac{\sqrt{2}}{2} W_{1} \right) L_{w}\, 1.5 [math]

[math] \phi R_{n} = (0.75)\, 0.6\, (70\,ksi) \left( \frac{\sqrt{2}}{2} (0.4375\,in) \right) (21.725\,in)\, 1.5 [math]

[math] \phi R_{n} = 317.56\,kip [math]

[math] DCR = \frac{P_{fl}}{\phi R_{n}} = \frac{(295.2\,kip)}{(317.56\,kip)} = 0.9296 [math]

DCR = 0.930 < 1.0, 行

步 5: Beam flange base metal at the weld (AISC 360-16 J4.1)

The flange metal next to the weld has to carry the same force. It is checked as a tension element, yielding and rupture, over the length of one weld line, because the welds on both faces of the flange load the same piece of flange.

和 [mathin] 0.5 L_{w} = 10.863\,in [mathin] for one weld line:

[math] \phi R_{n,ty} = \phi\, F_{yb}\, t_{fb}\, 0.5 L_{w} = (0.9) \times (50\,ksi) \times (0.8\,in) \times (10.863\,in) = 391.05\,kip [math]

[math] \phi R_{n,tr} = \phi\, F_{ub}\, t_{fb}\, 0.5 L_{w} = (0.75) \times (65\,ksi) \times (0.8\,in) \times (10.863\,in) = 423.64\,kip [math]

[math] \phi R_{n} = \min\left( \phi R_{n,ty},\, \phi R_{n,tr} \right) = \min\left( (391.05\,kip),\, (423.64\,kip) \right) = 391.05\,kip [math]

[math] DCR = \frac{P_{fl}}{\phi R_{n}} = \frac{(295.2\,kip)}{(391.05\,kip)} = 0.75489 [math]

DCR = 0.755 < 1.0, 行

步 6: Fillet weld at the beam web in tension (AISC 设计指南 39 图. 3-17, 情商. 3-39 to 3-41a)

The tension bolts sit right next to the beam web, so part of their force goes into the web rather than the flange. The web welds near the tension bolts have to carry that force into the end plate.

Effective weld length in tension

Only the web weld near the tension bolts counts: from the end of the flange fillet down past the last tension bolt row plus 6 在, but no further than mid-depth. 和 [mathin] k_{det} = 2.0625\,in [mathin] 和 [mathin] n_{rt} = 2 [mathin] bolt rows in tension:

[math] L_{wt} = 2 \left( \min\left( p_{f} – \left( k_{det} – t_{fb} \right) + s_{r} \left( n_{rt} – 1 \right) + 6\,in,\, 0.5\, d_{bm} – k_{det} \right) \right) [math]

[math] L_{wt} = 2 \left( \min\left( (2\,in) – \left( (2.0625\,in) – (0.8\,in) \right) + (3\,in)\left( (2) – 1 \right) + 6\,(1\,in),\, 0.5\,(21.4\,in) – (2.0625\,in) \right) \right) [math]

[math] L_{wt} = 17.275\,in [math]

The mid-depth limit governs here.

Force on the web weld

全部 [mathin] n_{t} = 4 [mathin] tension bolts are next to the web, 所以 [mathin] n_{trib} = 4 [mathin] and the web takes the full tension flange force. Again there is a floor, 这里 60% of the yield strength of the web over the weld length:

[math] P_{w} = \max\left( \frac{n_{trib}}{n_{t}} \left( \frac{M_{ux}}{d_{bm} – t_{fb}} + \frac{T_{u}}{2} \right),\, 0.6\, F_{yb} \left( 0.5 L_{wt} \right) t_{wb} \right) [math]

[math] P_{w} = \max\left( \frac{(4)}{(4)} \left( \frac{(200\,kip\text{-}ft)}{(21.4\,in) – (0.8\,in)} + \frac{(150\,kip)}{2} \right),\, 0.6\,(50\,ksi)\,(0.5\,(17.275\,in))\,(0.5\,in) \right) [math]

[math] P_{w} = 191.5\,kip [math]

焊接强度

[math] \phi R_{n} = \phi\, 0.6\, F_{EXX} \left( \frac{\sqrt{2}}{2} W_{2} \right) L_{wt}\, 1.5 [math]

[math] \phi R_{n} = (0.75)\, 0.6\, (70\,ksi) \left( \frac{\sqrt{2}}{2} (0.375\,in) \right) (17.275\,in)\, 1.5 = 216.44\,kip [math]

[math] DCR = \frac{P_{w}}{\phi R_{n}} = \frac{(191.5\,kip)}{(216.44\,kip)} = 0.8848 [math]

DCR = 0.885 < 1.0, 行

步 7: Beam web base metal at the weld (AISC 360-16 J4.1)

The web next to the tension weld has to carry the same 191.5 kip without yielding or rupturing. As with the flange, the length is one weld line, [mathin] 0.5 L_{w} = 8.6375\,in [mathin].

[math] \phi R_{n,ty} = \phi\, F_{yb}\, t_{wb}\, 0.5 L_{w} = (0.9) \times (50\,ksi) \times (0.5\,in) \times (8.6375\,in) = 194.34\,kip [math]

[math] \phi R_{n,tr} = \phi\, F_{ub}\, t_{wb}\, 0.5 L_{w} = (0.75) \times (65\,ksi) \times (0.5\,in) \times (8.6375\,in) = 210.54\,kip [math]

[math] \phi R_{n} = \min\left( (194.34\,kip),\, (210.54\,kip) \right) = 194.34\,kip [math]

[math] DCR = \frac{P_{w}}{\phi R_{n}} = \frac{(191.5\,kip)}{(194.34\,kip)} = 0.98539 [math]

DCR = 0.985 < 1.0, 行

的 1/2 in web is what limits this check. A bigger web weld would not help, because the web itself yields first.

步 8: Fillet weld at the beam web in shear (AISC 360-16 J2.4, AISC Manual Eq. 9-2)

The beam shear goes into the end plate through the web welds. 设计指南 39 assigns it to the web weld outside the tension zone of Step 6.

Effective weld length in shear

[math] L_{wv} = 2 \left( \min\left( d_{bm} – 2 k_{det} – 0.5 L_{wt},\, 0.5\, d_{bm} – k_{det} \right) \right) [math]

[math] L_{wv} = 2 \left( \min\left( (21.4\,in) – 2\,(2.0625\,in) – 0.5\,(17.275\,in),\, 0.5\,(21.4\,in) – (2.0625\,in) \right) \right) = 17.275\,in [math]

Base metal limit on the weld size

A fillet weld can be no stronger than the metal it is welded to. 手动均衡器. 9-2 gives the largest weld size, in sixteenths of an inch, that the base metal can support. The web has welds on both faces, so each weld gets half the web thickness:

[math] D_{max} = \frac{t_{p}\, F_{up} \le \frac{t_{wb}}{2}\, F_{ub}}{3.09\,kip/in \times F_{EXX}/F_{E70XX}} [math]

[math] D_{max} = \frac{(1\,in) \times (65\,ksi) \le (0.25\,in) \times (65\,ksi)}{(3.09\,kip/in) \times (1)} = 5.2589 [math]

The effective weld size is therefore [mathin] 5.2589/16 = 0.3287\,in [mathin], less than the 3/8 in specified.

焊接强度

The shear runs along the weld, so there is no directional increase:

[math] \phi R_{n} = \phi\, 0.6\, F_{EXX} \frac{\sqrt{2}}{2} \left( W_{2} \le \frac{D_{max}}{16} \right) L_{wv} [math]

[math] \phi R_{n} = (0.75) \times 0.6 \times (70\,ksi) \times \frac{\sqrt{2}}{2} \times \left( (0.375\,in) \le \frac{(5.2589)}{(16)} \right) \times (17.275\,in) [math]

[math] \phi R_{n} = 126.47\,kip [math]

[math] DCR = \frac{V_{u}}{\phi R_{n}} = \frac{(125\,kip)}{(126.47\,kip)} = 0.98837 [math]

DCR = 0.988 < 1.0, 行

This is the governing check of the connection, just ahead of the end plate thickness. The capacity is set by the beam web, so a larger weld adds nothing.

步 9: 螺栓剪 (AISC 360-16 J3.6)

The bolts also carry the beam shear across the joint between the end plate and the column flange. They are bearing-type A490-N bolts, with threads included in the shear plane, so each has a nominal shear stress of [mathin] F_{nv} = 68\,ksi [mathin].

在哪里 [mathin] \phi = 0.75 [mathin], [mathin] N_{s} = 1 [mathin] shear plane, 和 [mathin] n_{v} = 12 [mathin] is the number of bolts the report counts as resisting shear:

[math] \phi R_{n} = \phi\, F_{nv} \frac{\pi}{4} \left( d_{b} \right)^{2} N_{s}\, h_{f}\, n_{v} [math]

[math] \phi R_{n} = (0.75) \times (68\,ksi) \times \frac{\pi}{4} \times \left( (1\,in) \right)^{2} \times (1) \times (1) \times (12) [math]

[math] \phi R_{n} = 480.66\,kip [math]

DCR = 125 基普 / 480.66 基普= 0.260 < 1.0, 行

设计指南 39 normally assigns the shear to the compression side bolts, because the tension bolts are already working in tension. Bolt shear has a lot of reserve here either way.

步 10: Bolt bearing and tear-out on the end plate (AISC 360-16 J3.10)

Each bolt pushes on the edge of its hole in the end plate. The plate either deforms at the hole (轴承) or tears a strip out toward the next hole (撕掉). The beam shear pushes the end plate down, so each bolt bears on the top edge of its hole.

The slots run horizontally, so the vertical load meets the 1.125 in slot width:

[math] l_{c2} = s_{r} – d_{h} = (3\,in) – (1.125\,in) = 1.875\,in [math]

和 [mathin] t_{p} = 1\,in [mathin], [mathin] F_{up} = 65\,ksi [mathin], [mathin] n_{v} = 12 [mathin] 和 [mathin] \phi = 0.75 [mathin]:

[math] \phi R_{n,tearout} = \phi\, \min\left( 1.2\, l_{c2},\, 2.4\, d_{b} \right) t_{p}\, F_{up}\, n_{v} [math]

[math] \phi R_{n,tearout} = (0.75) \times \min\left( 1.2 \times (1.875\,in),\, 2.4 \times (1\,in) \right) \times (1\,in) \times (65\,ksi) \times (12) [math]

[math] \phi R_{n,tearout} = 1316.3\,kip [math]

DCR = 125 基普 / 1316.3 基普= 0.095 < 1.0, 行

步 11: 柱法兰上的螺栓轴承和撕裂 (AISC 360-16 J3.10)

The same check applies to the column flange, which has standard holes and is 1.56 在厚:

[math] \phi R_{n,tearout} = \phi\, \min\left( 1.2\, l_{c2},\, 2.4\, d_{b} \right) t_{fs}\, F_{us}\, n_{v} [math]

[math] \phi R_{n,tearout} = (0.75) \times \min\left( 1.2 \times (1.875\,in),\, 2.4 \times (1\,in) \right) \times (1.56\,in) \times (65\,ksi) \times (12) [math]

[math] \phi R_{n,tearout} = 2053.3\,kip [math]

DCR = 125 基普 / 2053.3 基普= 0.061 < 1.0, 行

步 12: Column flange bending at the tension bolts (AISC 设计指南 39, Table A-2 and Eq. 3-43)

The tension bolts pull on the column flange as well as on the end plate, so the column flange can bend into the same kind of yield line pattern. If it is too thin, the column needs stiffeners or backing plates at the tension bolts.

The yield line pitch for the column flange uses its width:

[math] s = \frac{\sqrt{b_{fs}\, g}}{2} = \frac{\sqrt{(15.8\,in)(7.5\,in)}}{2} = 5.4429\,in [math]

For a four-bolt pattern on an unstiffened column that continues above and below the connection, Table A-2 gives, 与 [mathin] c = 3\,in [mathin] (the bolt row spacing, for a flush plate):

[math] Y_{c} = \frac{b_{fs}}{2} \left( \frac{h_{1}}{s} + \frac{h_{2}}{s} \right) + \frac{2}{g} \left( h_{1} \left( s + \frac{3c}{4} \right) + h_{2} \left( s + \frac{c}{4} \right) \right) + \frac{g}{2} = 114.67\,in [math]

The flexural strength of the column flange is:

[math] M_{cf} = \phi\, F_{ys}\, t_{fs}^{2}\, Y_{c} = (0.9)\,(50\,ksi)\,(1.56\,in)^{2}\,(114.67\,in) = 1046.4\,kip\text{-}ft [math]

It is compared with the same 1.10 times the equivalent moment used for the end plate:

[math] DCR = \frac{1.1\, M_{u,eq}}{M_{cf}} = \frac{(361.62\,kip\text{-}ft)}{(1046.4\,kip\text{-}ft)} = 0.34558 [math]

DCR = 0.346 < 1.0, 行

The W14x211 flange is 1.56 在厚, and strength goes up with the square of the thickness, so no stiffeners are needed.

步 13: Column under the compression flange force (AISC 360-16 J10, AISC 设计指南 39)

The compression flange of the beam pushes the end plate into the column flange. That concentrated force has to be carried by the column flange and web without local failure, and the column web panel has to carry it as shear.

Compression flange force

[math] P_{fc} = \frac{M_{ux}}{d_{bm} – t_{fb}} + \frac{C_{u}}{2} = \frac{(200\,kip\text{-}ft)}{(21.4\,in) – (0.8\,in)} + \frac{(150\,kip)}{2} = 191.5\,kip [math]

Flange local bending (情商. J10-1)

[math] \phi R_{n,flb} = \phi\, 6.25\, F_{ys} \left( t_{fs} \right)^{2} = (0.9) \times 6.25 \times (50\,ksi) \times \left( (1.56\,in) \right)^{2} = 684.45\,kip [math]

Web compression buckling (情商. J10-8)

With the column T dimension, [mathin] T_{sup} = 10\,in [mathin], as the web depth and [mathin] Q_{f} = 1 [mathin]:

[math] \phi R_{n,wcb} = \phi \left( \frac{24\, t_{ws}^{3} \sqrt{E\, F_{ys}}}{T_{sup}} \right) Q_{f} = (0.9) \times \left( \frac{24 \times (0.98\,in)^{3} \times \sqrt{(29000\,ksi) \times (50\,ksi)}}{(10\,in)} \right) \times (1) = 2448\,kip [math]

Bearing length (设计指南 39 情商. 3-47)

The flange force spreads through the flange welds and the end plate before it reaches the column. Below the flange, the spread stops at the edge of the plate. That distance is [mathin] d_{pe} = 0.3625\,in [mathin]: 的 0.8 in the plate extends past the flange, less the 7/16 in weld.

[math] l_{b} = t_{fb} + 2 W_{1} + t_{p} + \min\left( d_{pe},\, t_{p} \right) [math]

[math] l_{b} = (0.8\,in) + 2\,(0.4375\,in) + (1\,in) + \min\left( (0.3625\,in),\, (1\,in) \right) = 3.0375\,in [math]

Web local crippling (情商. J10-4)

[math] \phi R_{n,wlc} = \phi\, 0.8 \left( t_{ws} \right)^{2} \left[ 1 + 3 \left( \frac{l_{b}}{d_{sup}} \right) \left( \frac{t_{ws}}{t_{fs}} \right)^{1.5} \right] \sqrt{\frac{E\, F_{ys}\, t_{fs}}{t_{ws}}}\, Q_{f} [math]

[math] \phi R_{n,wlc} = (0.75) \times 0.8 \times \left( (0.98\,in) \right)^{2} \times \left[ 1 + 3 \times \left( \frac{(3.0375\,in)}{(15.7\,in)} \right) \times \left( \frac{(0.98\,in)}{(1.56\,in)} \right)^{1.5} \right] \times \sqrt{\frac{(29000\,ksi) \times (50\,ksi) \times (1.56\,in)}{(0.98\,in)}} \times (1) = 1128.5\,kip [math]

Web local yielding (设计指南 39 情商. 3-46)

在哪里 [mathin] C_{t} = 1 [mathin] because the connection is far from the end of the column, 和 [mathin] k_{des} = 2.16\,in [mathin]:

[math] \phi R_{n,wly} = \phi \left( 6\, C_{t}\, k_{des} + l_{b} \right) F_{ys}\, t_{ws} = (1)\,(6\,(1)\,(2.16\,in) + (3.0375\,in))\,(50\,ksi)\,(0.98\,in) = 783.88\,kip [math]

Web panel zone shear (情商. J10-9)

[math] \phi R_{n,wpz} = \phi\, 0.6\, F_{ys}\, d_{sup}\, t_{ws} = (0.9) \times 0.6 \times (50\,ksi) \times (15.7\,in) \times (0.98\,in) = 415.42\,kip [math]

Governing column strength

[math] \phi R_{n} = \min\left( (684.45\,kip),\, (2448\,kip),\, (1128.5\,kip),\, (783.88\,kip),\, (415.42\,kip) \right) = 415.42\,kip [math]

DCR = 191.5 基普 / 415.42 基普= 0.461 < 1.0, 行

Panel zone shear governs the column. The heavy W14x211, 与一个 0.98 in web and a 1.56 in flange, needs no stiffeners or doubler plate for this load.

设计检查总结

The flush end plate passes every check, with four of them within 3% of capacity. The web weld in shear governs at 0.98837, with the end plate thickness at 0.9878 right behind it, then the beam web base metal at 0.985 and the plate height at 0.979. 螺栓剪, bearing and the column checks all have a lot of reserve, so any change to make this connection carry more load starts with the beam web and the end plate.

如果检查失败要更改什么

• Required bolt diameter: use a larger bolt, or add bolt columns so more bolts share the tension. If the flush plate cannot work, an extended end plate puts a bolt row outside the tension flange, where its lever arm is longer.
• Required end plate thickness: 使用较厚的板, or reduce the gage or the bolt flange offset to increase the yield line parameter. An extended or stiffened end plate gives a much larger yield line parameter.
• Flange weld: increase the weld size, or use a complete joint penetration weld. 的 0.6 Fy floor means the flange weld is sized for the flange, not the moment.
• Web weld or web base metal: the beam web is usually the limit, so a bigger weld does not help. A beam with a thicker web, or a deeper beam with more web weld length, 做.
• Bolt shear or bearing: use a larger bolt or a higher grade, or add bolt rows.
• Column flange bending: add stiffeners at the level of the tension bolts, or use a heavier column with a thicker flange.
• Column in compression: add stiffeners opposite the compression flange for local flange and web checks, or a doubler plate for panel zone shear.

经常问的问题

What is the difference between a flush and an extended end plate moment connection?

A flush end plate stops at the beam flanges, so all the bolts are between the flanges. An extended end plate projects past the tension flange with a bolt row outside it. The outside row has a longer lever arm and the extension adds yield lines, so an extended plate carries a much larger moment. A flush plate is used where the connection must stay within the beam depth, for example under a floor slab.

Why are the bolts designed for no prying?

设计指南 39 uses a thick plate approach for end plates: it sizes the bolts for their tensile strength without prying, then makes the end plate thick enough to stay stiff, so prying forces never develop. That is why the bolt diameter is checked first (步 2) and the plate thickness second, 与一个 1.10 factor on the moment (步 3).

What is the 0.8 reduction factor for flush end plates?

Flush end plates are more flexible than extended ones. 设计指南 39 multiplies their yield line strength by a reduction factor of 0.8, so that the connection is stiff enough to be treated as fully restrained. The factor sits in the denominator of the plate thickness equation in Step 3, so it makes the required plate thicker.

How does axial load change the end plate design?

Axial tension adds to the tension in the tension bolts. The guide converts it to an equivalent moment, half the tension times the distance between the flange centroids, and adds it to the beam moment: 200 kip-ft becomes 328.75 kip-ft here. Axial compression adds half its value to the compression flange force that the column has to resist in Step 13.

Why are short-slotted holes allowed with bearing-type bolts?

AISC 360-16 J3.2 allows short-slotted holes in bearing-type connections when the slot is perpendicular to the direction of the load. The slots in this end plate are horizontal and the shear is vertical, so the bolts can be A490-N rather than slip-critical. The slots give the erector some horizontal fit-up tolerance.

此示例是否遵循 AISC 第 15 版或 AISC 第 16 版手册?

它遵循 AISC 360-16 和 AISC 手册第 15 版, 这是围绕该规范编写的, with the end plate procedure from Design Guide 39. AISC 第 16 版手册与后续版本配对 360-22 规范. Clause and equation numbers changed in the newer edition, 因此，请根据您的项目使用的版本检查参考文献.

对于 AISC ASD 而不是 LRFD 来说，这会如何变化?

极限状态和标称强度相同. 使用 AISC ASD，您可以将服务水平力与标称强度除以安全系数进行比较，而不是乘以阻力系数. 阻力系数为 0.75 成为安全系数 2.00, 0.90 变成 1.67, 和 1.00 变成 1.50. 荷载组合也发生变化, so the moment, shear and axial load are lower.

Design a flush end plate moment connection for free

此页上的每个数字都来自一个解决方案. Pick the end plate moment configuration, 输入你的光束, 柱子, 螺栓, 焊缝, 片刻, 剪切和轴向载荷, 并在浏览器中查看每项检查. 没有什么可安装的.

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参考资料

• AISC 360-16, 钢结构建筑规范: J2.2b (Table J2.4), J2.4 (情商. J2-4), J3.2, J3.3, J3.4 (表J3.4), J3.5 (表 J3.5), J3.6 (情商. J3-1), J3.10 (情商. J3-6a, J3-6c), J4.1 (情商. J4-1, J4-2), J4.2, J10.1 (情商. J10-1), J10.3 (情商. J10-4), J10.5 (情商. J10-8), J10.6 (情商. J10-9).
• AISC 设计指南 39, End-Plate Moment Connections: 情商. 3-30, 3-38一个, 3-39 to 3-41a, 3-43, 3-46, 3-47, 5-1, 5-3一个, 5-5一个; 图. 3-17; 桌子 5-3, Table A-2.
• AISC 钢结构手册, 15第版: 部分 1 截面属性; 部分 9 情商. 9-2.
• 使用 AISC 进行钢连接设计 360-16
• 螺栓 和 焊缝 SkyCiv 连接设计