加长端板力矩连接设计

Extended end plate moment connection design to AISC 360 和 AISC 设计指南 39 comes down to the same three things as any end plate: 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 that can deliver the force on both sides. The extended plate adds a bolt row outside the tension flange, which gives the bolts a longer lever arm and the plate more yield lines, so it carries much larger moments than a flush plate.

This page works through one real extended end plate moment connection from start to finish: a W21x166 beam bolted to the flange of a W14x193 column through a 7/8 in end plate with 3/4 在 A325-N 螺栓中, carrying a 300 急转瞬间, 一个 120 kip shear and 200 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 an extended 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 an extended end plate, the plate projects past the beam flanges and carries a row of bolts outside them. In a flush end plate, the plate stops at the flanges and every bolt sits between them. The outside row is the furthest bolt from the compression flange, so it does the most work, and the extension adds yield lines that make the plate stronger in bending.

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. Both the flush and extended versions are covered by the end plate connection calculator, 和 瞬间连接 page compares them with the flange plate moment connection and other details.

The plate in this example extends past both flanges, so the connection works the same way if the moment reverses. Its bolt pattern is the Design Guide 39 multiple-row extended 1/3 four-wide/two-wide configuration: one row outside each flange and three inside, with four bolts across the outside row and the first inside row, and two across the rest.

海拔. The end plate extends past both flanges of the W21x166 and is bolted to the W14x193 column flange with eight bolt rows.

A-A部分. One bolt row outside each flange and three inside, 2 in from the flange faces and 3 in apart. Each row is four bolts wide: 一个 7 1/2 in gage with a 2 in column spacing outside it.

Extended 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 extension, 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 extended portion of the end plate in shear.
5. Check the fillet welds at the beam flange.
6. Check the beam flange base metal at the weld.
7. Check the fillet welds at the beam web for tension.
8. Check the beam web base metal at the weld.
9. Check the fillet welds at the beam web for shear.
10. Check the bolts in shear.
11. Check bolt bearing and tear-out on the end plate.
12. 检查柱法兰上的螺栓轴承和撕裂情况.
13. Check column flange bending at the tension bolts.
14. 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, and the bolts must be far enough apart and far enough from the edges.

The minimum fillet weld sizes come from Table J2.4: 5/16 in for the flanges, where the thinner part joined is the 7/8 在盘子里, 和 1/4 in for the 3/4 in web. 最小螺栓间距为 [mathin] 2\tfrac{2}{3} d_{b} [mathin] from J3.3, 这是 2 in for a 3/4 in bolt, and it applies both between rows and between columns. 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 1.125 在. The maximum gage on the end plate is the beam flange width, 12.4 在.

For a minimum limit the ratio is limit over actual, and for a maximum it is actual over limit. The governing row is the bolt column spacing:

[math] DCR = \frac{d}{c} = \frac{(2)}{(2)} = 1 [math]

DCR = 1.000 ≤ 1.0, 行

的 2 in column spacing sits exactly on the J3.3 minimum. That passes, but J3.3 prefers a spacing of 3d, so there is no room left for a larger bolt in this pattern without widening it. 的 2.1 in support edge distance is what is left of the 15.7 in column flange outside the outer bolts.

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} = (300\,kip\text{-}ft) + \frac{(200\,kip)}{2} \times \left( (22.5\,in) – (1.36\,in) \right) = 476.17\,kip\text{-}ft [math]

Bolt lever arms

The tension bolts rotate about the centre of the compression flange. The four tension rows sit at these distances from it:

• [mathin] h_{1} = 23.82\,in [mathin]: the row outside the tension flange, 2 in past its outside face
• [mathin] h_{2} = 18.46\,in [mathin]: the first row inside, 2 in from the inside face of the flange
• [mathin] h_{3} = 15.46\,in [mathin] 和 [mathin] h_{4} = 12.46\,in [mathin]: the next two rows, 3 in apart

In the four-wide/two-wide pattern, the two rows nearest the tension flange count four bolts each and the other two count only the two bolts at the 7.5 在规格中, 这是 12 tension bolts in all. The outer bolts of rows 3 和 4 are too far from both the flange and the web to pick up much tension, so Design Guide 39 leaves them out:

[math] \sum_{i} n_{i} h_{i} = 4 \left( h_{1} + h_{2} \right) + 2 \left( h_{3} + h_{4} \right) = 224.96\,in [math]

Required bolt diameter

在哪里 [mathin] \phi = 0.75 [mathin] is the resistance factor for bolt tension and [mathin] F_{nt} = 90\,ksi [mathin] is the nominal tensile stress of an A325 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 (476.17\,kip\text{-}ft)}{\pi \times (0.75) \times (90\,ksi) \times (224.96\,in)}} [math]

[math] d_{b,reqd} = 0.69218\,in [math]

[math] DCR = \frac{d_{b,reqd}}{d_{b}} = \frac{(0.69218\,in)}{(0.75\,in)} = 0.92291 [math]

DCR = 0.923 < 1.0, 行

The axial tension adds 176.17 kip-ft to the 300 急转瞬间, so the axial load drives a large share of the bolt size.

步 3: Required end plate thickness (AISC 设计指南 39, 桌子 5-17 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.

Effective plate width and yield line pitch

Plate wider than the beam flange does little to resist the yield lines, so the guide limits the width it counts to the flange width plus the larger of 1 in and the plate thickness:

[math] b_{pe} = \min\left( b_{p},\, b_{fb} + \max\left( 1\,in,\, t_{p} \right) \right) = \min\left( (14.5\,in),\, (12.4\,in) + \max\left( (1\,in),\, (0.875\,in) \right) \right) = 13.4\,in [math]

The yield line pitch s locates the hinge lines below the inside bolts. The report calculates it from the full plate width:

[math] s = \frac{\sqrt{b_{p}\, g}}{2} = \frac{\sqrt{(14.5\,in)(7.5\,in)}}{2} = 5.2142\,in [math]

Yield line parameter

For the 12-bolt multiple-row extended 1/3 four-wide/two-wide unstiffened end plate, 桌子 5-17 gives:

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

和 [mathin] b_{pe} = 13.4\,in [mathin], [mathin] g = 7.5\,in [mathin], [mathin] h_{1} = 23.82\,in [mathin], [mathin] h_{2} = 18.46\,in [mathin], [mathin] h_{4} = 12.46\,in [mathin], [mathin] p_{fi} = p_{fo} = 2\,in [mathin], [mathin] s = 5.2142\,in [mathin] 和 [mathin] s_{r} = 3\,in [mathin]:

[math] Y_{p} = 212.35\,in [math]

A flush plate’s yield line pattern only has the tension rows between the flanges. Here the extension adds the outside row and its yield lines, and that is where the extra strength of an extended plate comes from.

Required plate thickness

在哪里 [mathin] \gamma_{r} = 1 [mathin] is the Design Guide 39 情商. 5-1 factor for full restraint (an extended plate needs no reduction, unlike the 0.8 used for flush plates), [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 (476.17\,kip\text{-}ft)}{(1) \times (0.9) \times (50\,ksi) \times (212.35\,in)}} [math]

[math] t_{p,reqd} = 0.81102\,in [math]

[math] DCR = \frac{t_{p,reqd}}{t_{p}} = \frac{(0.81102\,in)}{(0.875\,in)} = 0.92687 [math]

DCR = 0.927 < 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: Shear yielding and rupture of the extended portion of the end plate (AISC 360-16 J4.2)

The bolts outside the tension flange pull on the part of the plate that sticks out past the flange. That force has to cross into the flange as shear through the plate, along a horizontal line at the face of the flange.

Shear on the extension

The outside bolts take their share of the flange force: [mathin] n_{to} = 4 [mathin] 的 [mathin] n_{t} = 12 [mathin] tension bolts.

[math] V_{ep} = \frac{n_{to}}{n_{t}} \left( \frac{M_{ux}}{d_{bm} – t_{fb}} + \frac{T_{u}}{2} \right) [math]

[math] V_{ep} = \frac{(4)}{(12)} \left( \frac{(300\,kip\text{-}ft)}{(22.5\,in) – (1.36\,in)} + \frac{(200\,kip)}{2} \right) = 90.098\,kip [math]

剪切屈服 (情商. J4-3)

The gross shear area is the full plate width times its thickness, 和 [mathin] \phi = 1.00 [mathin] for shear yielding:

[math] A_{gv} = b_{p}\, t_{p} = (14.5\,in) \times (0.875\,in) = 12.688\,in^{2} [math]

[math] \phi R_{n,sy} = \phi\, 0.6\, F_{yp}\, A_{gv} = (1) \times 0.6 \times (50\,ksi) \times (12.688\,in^{2}) = 380.62\,kip [math]

剪切断裂 (情商. J4-4)

The net area takes out the four bolt holes in the outside row. The shear line runs horizontally, so it cuts each slot along its 1 in length, plus the 1/16 in AISC adds for hole damage (B4.3b):

[math] A_{nv} = t_{p} \left[ b_{p} – n_{co} \left( d_{h} + 0.0625\,in \right) \right] = (0.875\,in) \times \left[ (14.5\,in) – (4) \times \left( (1\,in) + (0.0625\,in) \right) \right] = 8.9687\,in^{2} [math]

[math] \phi R_{n,sr} = \phi\, 0.6\, F_{up}\, A_{nv} = (0.75) \times 0.6 \times (65\,ksi) \times (8.9687\,in^{2}) = 262.34\,kip [math]

Governing strength

[math] \phi R_{n} = \min\left( \phi R_{n,sy},\, \phi R_{n,sr} \right) = \min\left( (380.62\,kip),\, (262.34\,kip) \right) = 262.34\,kip [math]

[math] DCR = \frac{V_{ep}}{\phi R_{n}} = \frac{(90.098\,kip)}{(262.34\,kip)} = 0.34344 [math]

DCR = 0.343 < 1.0, 行

Rupture governs because four slots come out of a single line across the plate. The extension still has plenty of reserve.

步 5: 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} = 1.5625\,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( (12.4\,in),\, (14.5\,in) \right) \right) – 2 (1.5625\,in) = 21.675\,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{(300\,kip\text{-}ft)}{(22.5\,in) – (1.36\,in)} + \frac{\max\left( (200\,kip),\, (200\,kip) \right)}{2},\, 0.6\,(50\,ksi)\,(12.4\,in)\,(1.36\,in) \right) [math]

[math] P_{fl} = 505.92\,kip [math]

The moment and axial load give 270.29 基普 (the same force Step 14 uses for the column), 所以 60% floor governs. With a flange as heavy as the W21x166’s, the welds end up sized for the flange, not the load.

焊接强度

在哪里 [mathin] F_{EXX} = 70\,ksi [mathin], [mathin] W_{1} = 0.75\,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} (0.75\,in) \right) (21.675\,in)\, 1.5 [math]

[math] \phi R_{n} = 543.13\,kip [math]

[math] DCR = \frac{P_{fl}}{\phi R_{n}} = \frac{(505.92\,kip)}{(543.13\,kip)} = 0.93148 [math]

DCR = 0.931 < 1.0, 行

This is the highest strength ratio in the connection. It is driven by the 60% 地面, not the applied load.

步 6: 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} = 10.837\,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 (1.36\,in) \times (10.837\,in) = 663.25\,kip [math]

[math] \phi R_{n,tr} = \phi\, F_{ub}\, t_{fb}\, 0.5 L_{w} = (0.75) \times (65\,ksi) \times (1.36\,in) \times (10.837\,in) = 718.53\,kip [math]

[math] \phi R_{n} = \min\left( \phi R_{n,ty},\, \phi R_{n,tr} \right) = \min\left( (663.25\,kip),\, (718.53\,kip) \right) = 663.25\,kip [math]

[math] DCR = \frac{P_{fl}}{\phi R_{n}} = \frac{(505.92\,kip)}{(663.25\,kip)} = 0.76278 [math]

DCR = 0.763 < 1.0, 行

步 7: 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 inside tension bolts sit close to the beam web, so part of their force goes into the web rather than the flange. The web welds near those 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 inside tension row plus 6 在, but no further than mid-depth. 和 [mathin] k_{det} = 2.625\,in [mathin] 和 [mathin] n_{ti} = 3 [mathin] inside bolt rows in tension:

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

[math] L_{wt} = 2 \left( \min\left( (2\,in) – \left( (2.625\,in) – (1.36\,in) \right) + (3\,in)\left( (4) – 1 \right) + 6\,(1\,in),\, 0.5\,(22.5\,in) – (2.625\,in) \right) \right) [math]

[math] L_{wt} = 17.25\,in [math]

The substituted line prints 4 rows where the inputs list 3. The result is set by the mid-depth limit, the second term, which does not depend on the row count.

Force on the web weld

的 [mathin] n_{t} = 12 [mathin] tension bolts, [mathin] n_{trib} = 6 [mathin] sit next to the web: the inner pair in each of the three inside rows. The outside row is beyond the flange, so it loads the flange rather than the web. There is again 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{(6)}{(12)} \left( \frac{(300\,kip\text{-}ft)}{(22.5\,in) – (1.36\,in)} + \frac{(200\,kip)}{2} \right),\, 0.6\,(50\,ksi)\,(0.5\,(17.25\,in))\,(0.75\,in) \right) [math]

[math] P_{w} = 194.06\,kip [math]

Half of the 270.29 kip flange force is less than 194.06 基普, so the floor governs here too.

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) (17.25\,in)\, 1.5 = 216.13\,kip [math]

[math] DCR = \frac{P_{w}}{\phi R_{n}} = \frac{(194.06\,kip)}{(216.13\,kip)} = 0.89791 [math]

DCR = 0.898 < 1.0, 行

步 8: Beam web base metal at the weld (AISC 360-16 J4.1)

The web next to the tension weld has to carry the same 194.06 kip without yielding or rupturing. As with the flange, the length is one weld line, [mathin] 0.5 L_{w} = 8.625\,in [mathin].

[math] \phi R_{n,ty} = \phi\, F_{yb}\, t_{wb}\, 0.5 L_{w} = (0.9) \times (50\,ksi) \times (0.75\,in) \times (8.625\,in) = 291.09\,kip [math]

[math] \phi R_{n,tr} = \phi\, F_{ub}\, t_{wb}\, 0.5 L_{w} = (0.75) \times (65\,ksi) \times (0.75\,in) \times (8.625\,in) = 315.35\,kip [math]

[math] \phi R_{n} = \min\left( (291.09\,kip),\, (315.35\,kip) \right) = 291.09\,kip [math]

[math] DCR = \frac{P_{w}}{\phi R_{n}} = \frac{(194.06\,kip)}{(291.09\,kip)} = 0.66667 [math]

DCR = 0.667 < 1.0, 行

The ratio is exactly 0.6 / 0.9: the demand is the 60% floor and the capacity is 90% of the same yield strength over the same length.

步 9: 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 7.

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( (22.5\,in) – 2\,(2.625\,in) – 0.5\,(17.25\,in),\, 0.5\,(22.5\,in) – (2.625\,in) \right) \right) = 17.25\,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{(0.875\,in) \times (65\,ksi) \le (0.375\,in) \times (65\,ksi)}{(3.09\,kip/in) \times (1)} = 7.8883 [math]

That is more than the 6 sixteenths of the 3/8 in weld, so the base metal does not limit the weld and its full size counts.

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{(7.8883)}{(16)} \right) \times (17.25\,in) [math]

[math] \phi R_{n} = 144.08\,kip [math]

[math] DCR = \frac{V_{u}}{\phi R_{n}} = \frac{(120\,kip)}{(144.08\,kip)} = 0.83285 [math]

DCR = 0.833 < 1.0, 行

步 10: 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. 设计指南 39 leaves the 12 tension bolts to carry tension and gives the shear to the rest: 的 16 bolts on the compression side and the 4 outer bolts of rows 3 和 4, which were not counted in tension. 那是 [mathin] n_{v} = 20 [mathin] 的 32 螺栓.

They are bearing-type A325-N bolts, with threads included in the shear plane, 所以 [mathin] F_{nv} = 54\,ksi [mathin]. 和 [mathin] \phi = 0.75 [mathin] 和 [mathin] N_{s} = 1 [mathin] shear plane:

[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 (54\,ksi) \times \frac{\pi}{4} \times \left( (0.75\,in) \right)^{2} \times (1) \times (1) \times (20) [math]

[math] \phi R_{n} = 357.85\,kip [math]

[math] DCR = \frac{V_{u}}{\phi R_{n}} = \frac{(120\,kip)}{(357.85\,kip)} = 0.33534 [math]

DCR = 0.335 < 1.0, 行

步 11: 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 13/16 in slot width:

[math] l_{c2} = s_{r} – d_{h} = (3\,in) – (0.8125\,in) = 2.1875\,in [math]

和 [mathin] t_{p} = 0.875\,in [mathin], [mathin] F_{up} = 65\,ksi [mathin], [mathin] n_{v} = 20 [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 (2.1875\,in),\, 2.4 \times (0.75\,in) \right) \times (0.875\,in) \times (65\,ksi) \times (20) [math]

[math] \phi R_{n,tearout} = 1535.6\,kip [math]

[math] DCR = \frac{V_{u}}{\phi R_{n,tearout}} = \frac{(120\,kip)}{(1535.6\,kip)} = 0.078144 [math]

DCR = 0.078 < 1.0, 行

步 12: 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 1.44 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 (2.1875\,in),\, 2.4 \times (0.75\,in) \right) \times (1.44\,in) \times (65\,ksi) \times (20) [math]

[math] \phi R_{n,tearout} = 2527.2\,kip [math]

[math] DCR = \frac{V_{u}}{\phi R_{n,tearout}} = \frac{(120\,kip)}{(2527.2\,kip)} = 0.047483 [math]

DCR = 0.047 < 1.0, 行

步 13: Column flange bending at the tension bolts (AISC 设计指南 39, Table A-7 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{(15.7\,in)(7.5\,in)}}{2} = 5.4256\,in [math]

For a 12-bolt four-wide/two-wide pattern on an unstiffened column that continues above and below the connection, Table A-7 gives:

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

和 [mathin] b_{fs} = 15.7\,in [mathin], [mathin] g = 7.5\,in [mathin], [mathin] h_{1} = 23.82\,in [mathin], [mathin] h_{4} = 12.46\,in [mathin], [mathin] s = 5.4256\,in [mathin], [mathin] s_{r} = 3\,in [mathin], 和 [mathin] c = 5.44\,in [mathin] for the bolt distance across the beam flange:

[math] Y_{c} = 172.74\,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)\,(1.44\,in)^{2}\,(172.74\,in) = 1343.2\,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{(523.78\,kip\text{-}ft)}{(1343.2\,kip\text{-}ft)} = 0.38995 [math]

DCR = 0.390 < 1.0, 行

The W14x193 flange is 1.44 在厚, much thicker than the 7/8 in end plate, and bending strength goes up with the square of the thickness. No stiffeners are needed at the tension bolts.

步 14: 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{(300\,kip\text{-}ft)}{(22.5\,in) – (1.36\,in)} + \frac{(200\,kip)}{2} = 270.29\,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( (1.44\,in) \right)^{2} = 583.2\,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 (0.89\,in)^{3} \times \sqrt{(29000\,ksi) \times (50\,ksi)}}{(10\,in)} \right) \times (1) = 1833.6\,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. On an extended plate, the plate continues past the compression flange, so the force spreads through the full plate thickness on both sides:

[math] l_{b} = t_{fb} + 2 W_{1} + 2 t_{p} [math]

[math] l_{b} = (1.36\,in) + 2\,(0.75\,in) + 2\,(0.875\,in) = 4.61\,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( (0.89\,in) \right)^{2} \times \left[ 1 + 3 \times \left( \frac{(4.61\,in)}{(15.5\,in)} \right) \times \left( \frac{(0.89\,in)}{(1.44\,in)} \right)^{1.5} \right] \times \sqrt{\frac{(29000\,ksi) \times (50\,ksi) \times (1.44\,in)}{(0.89\,in)}} \times (1) = 1043.5\,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} = 2.04\,in [mathin]. 设计指南 39 uses 6k rather than the 5k in J10.2, because the end plate spreads the load further:

[math] \phi R_{n,wly} = \phi \left( 6\, C_{t}\, k_{des} + l_{b} \right) F_{ys}\, t_{ws} = (1)\,(6\,(1)\,(2.04\,in) + (4.61\,in))\,(50\,ksi)\,(0.89\,in) = 749.83\,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 (15.5\,in) \times (0.89\,in) = 372.46\,kip [math]

Governing column strength

[math] \phi R_{n} = \min\left( (583.2\,kip),\, (1833.6\,kip),\, (1043.5\,kip),\, (749.83\,kip),\, (372.46\,kip) \right) = 372.46\,kip [math]

[math] DCR = \frac{P_{fc}}{\phi R_{n}} = \frac{(270.29\,kip)}{(372.46\,kip)} = 0.72569 [math]

DCR = 0.726 < 1.0, 行

Panel zone shear governs the column, and no stiffeners or doubler plate are needed for this load. Of the column checks, it is the one closest to its limit.

设计检查总结

The extended end plate passes every check. The detailing ratio of 1.000 comes from the bolt column spacing sitting exactly on the AISC minimum, which is allowed. 强度检查, the flange weld governs at 0.93148, followed by the end plate thickness at 0.92687 and the bolt diameter at 0.92291. 螺栓剪, bearing and the extension have a lot of reserve. To carry more moment, the bolts and plate need to grow together, and the column panel zone at 0.726 is the next limit after that.

如果检查失败要更改什么

• 详细限制: widen the bolt column spacing or the gage, or use a wider plate if the edge distances run short. The column flange width limits how far the bolts can spread.
• Required bolt diameter: use a larger or higher grade bolt, or a pattern with more bolts in tension. A deeper beam gives every row a longer lever arm.
• Required end plate thickness: 使用较厚的板, or reduce the gage or the bolt flange offsets to increase the yield line parameter. A stiffened extended end plate gives a much larger yield line parameter.
• Extended portion in shear: 使用较厚的板, or fewer or smaller holes across the outside row.
• 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: increase the web weld size up to what the web can support. A beam with a thicker web also helps.
• Bolt shear or bearing: use a larger bolt or a higher grade, or add bolts on the compression side.
• 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

When should you use an extended end plate instead of a flush end plate?

Use an extended end plate when a flush plate cannot carry the moment. The row outside the tension flange has the longest lever arm of any bolt, and the extension adds yield lines, so the same bolts and plate thickness carry far more moment. The trade-off is the projection past the beam, which can clash with a floor slab or a roof deck. A flush plate stays within the beam depth.

What does four-wide/two-wide mean in an end plate connection?

It describes how many bolts across each row Design Guide 39 counts in tension. In this example the outside row and the first inside row each count four bolts, and the next two inside rows count only the two bolts near the web. The outer bolts in those lower rows are too far from both the flange and the web to pick up much tension, so they are left out of the tension calculation and used for shear instead.

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).

Why is the flange weld sized for more than the flange force?

设计指南 39 sets a minimum flange force of 60% of the yield strength of the beam flange, so the weld is never the weak link in the connection. For a heavy flange like the W21x166’s, that minimum is far above the force from the moment and axial load, and it is what sets the 3/4 in weld size here.

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 A325-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.

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参考资料

• AISC 360-16, 钢结构建筑规范: B4.3b, 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 (情商. J4-3, J4-4), 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 5-17, Table A-7.
• 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