Конструкция моментного соединения заподлицо с концевой пластиной

Flush end plate moment connection design to AISC 360 и Руководство по проектированию AISC 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 in A490-N bolts, carrying a 200 kip-ft moment, а 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. Каждое уравнение записано с его номерами, in the same order as the AISC calc sheet the SkyCiv Connection Design module produces for it.

ПОПРОБУЙТЕ НАШ БЕСПЛАТНЫЙ ИНСТРУМЕНТ СЕЙЧАС КУПИТЬ МОДУЛЬ КОНСТРУКЦИИ ПОДКЛЮЧЕНИЯ

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 момент связи: 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. В момент соединения page compares it with the flange plate moment connection and other details.

высота. 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.

Section A-A. Four rows of two bolts at a 7 1/2 в норме, 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: шаги с первого взгляда

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. Check bolt bearing and tear-out on the column flange.
12. Check column flange bending at the tension bolts.
13. Check the column under the compression flange force.

Проектирование входных данных для этого примера

Код дизайна: AISC. 360-16 LRFD, with the end plate procedure from AISC Design Guide 39. Свойства раздела взяты из руководства AISC..

 

 

шаг 1: Detailing limits (Aisc 360-16 J2.2b, J3.3, J3.4, J3.5)

Before any strength check, the connection has to be buildable and match the assumptions behind the Design Guide 39 уравнения. 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, и 3/16 in for the 0.5 в сети. The minimum bolt spacing is [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, so Table J3.5 adds 1/8 in to its horizontal edge distance, дающий 1.375 в. The maximum gage on the end plate is the beam flange width, 12.3 в, so the bolts stay inside the flange.

Для минимального предела соотношение превышает фактическое значение., а для максимума это актуально сверх лимита. The governing row is the plate height:

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

Прочность на единицу размера сварного шва 0.979 < 1.0, Прочность на единицу размера сварного шва

The minimum plate height is 1.125 in more than the 21.4 in beam depth, или 0.5625 in past each flange: room for the 7/16 in flange weld plus 1/8 в. В 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.

шаг 2: Required bolt diameter (Руководство по проектированию AISC 39, уравнение. 3-30 and 5-3a)

The bolts near the tension flange carry the moment as tension. Руководство по проектированию 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 (шаг 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, и [mathin] h_{2} = 15.2\,in [mathin] is the distance to the next row, 3 in further in. Есть [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

куда [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]

Прочность на единицу размера сварного шва 0.942 < 1.0, Прочность на единицу размера сварного шва

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

шаг 3: Required end plate thickness (Руководство по проектированию AISC 39, Стол 5-3 Оценка емкости сваи. 5-5а )

The end plate bends around the tension bolts. Руководство по проектированию 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, Стол 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]

С [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] и [mathin] s_{r} = 3\,in [mathin]:

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

Required plate thickness

куда [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]

Прочность на единицу размера сварного шва 0.988 < 1.0, Прочность на единицу размера сварного шва

В 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.

шаг 4: Fillet weld at the beam flange (Руководство по проектированию AISC 39 уравнение. 3-38а , Aisc 360-16 Дж2.4)

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.

Эффективная длина сварного шва

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. Руководство по проектированию 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 кип , Итак 60% floor of 295.2 kip governs.

Прочность сварного шва

куда [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]

Прочность на единицу размера сварного шва 0.930 < 1.0, Прочность на единицу размера сварного шва

шаг 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.

С [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]

Прочность на единицу размера сварного шва 0.755 < 1.0, Прочность на единицу размера сварного шва

шаг 6: Fillet weld at the beam web in tension (Руководство по проектированию AISC 39 инжир. 3-17, уравнение. 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 в, but no further than mid-depth. С [mathin] k_{det} = 2.0625\,in [mathin] и [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

Все [mathin] n_{t} = 4 [mathin] tension bolts are next to the web, так [mathin] n_{trib} = 4 [mathin] and the web takes the full tension flange force. Again there is a floor, Вот 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]

Прочность сварного шва

[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]

Прочность на единицу размера сварного шва 0.885 < 1.0, Прочность на единицу размера сварного шва

шаг 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]

Прочность на единицу размера сварного шва 0.985 < 1.0, Прочность на единицу размера сварного шва

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

шаг 8: Fillet weld at the beam web in shear (Aisc 360-16 Дж2.4, Ручное уравнение AISC. 9-2)

The beam shear goes into the end plate through the web welds. Руководство по проектированию 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. Manual Eq. 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.

Прочность сварного шва

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]

Прочность на единицу размера сварного шва 0.988 < 1.0, Прочность на единицу размера сварного шва

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.

шаг 9: Срез болта (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].

куда [mathin] \phi = 0.75 [mathin], [mathin] N_{s} = 1 [mathin] shear plane, и [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]

Прочность на единицу размера сварного шва 125 кип / 480.66 кип = 0.260 < 1.0, Прочность на единицу размера сварного шва

Руководство по проектированию 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.

шаг 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 (несущий) or tears a strip out toward the next hole (tear-out). 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]

С [mathin] t_{p} = 1\,in [mathin], [mathin] F_{up} = 65\,ksi [mathin], [mathin] n_{v} = 12 [mathin] и [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]

Прочность на единицу размера сварного шва 125 кип / 1316.3 кип = 0.095 < 1.0, Прочность на единицу размера сварного шва

шаг 11: Bolt bearing and tear-out on the column flange (Aisc 360-16 J3.10)

The same check applies to the column flange, which has standard holes and is 1.56 Вы можете заметить, что основное отличие заключается в соединении полок балки с опорной колонной.:

[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]

Прочность на единицу размера сварного шва 125 кип / 2053.3 кип = 0.061 < 1.0, Прочность на единицу размера сварного шва

шаг 12: Column flange bending at the tension bolts (Руководство по проектированию AISC 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, с участием [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]

Прочность на единицу размера сварного шва 0.346 < 1.0, Прочность на единицу размера сварного шва

The W14x211 flange is 1.56 Вы можете заметить, что основное отличие заключается в соединении полок балки с опорной колонной., and strength goes up with the square of the thickness, so no stiffeners are needed.

шаг 13: Column under the compression flange force (Aisc 360-16 J10, Руководство по проектированию AISC 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 (уравнение. 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 (уравнение. 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 (Руководство по проектированию 39 уравнение. 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]: в 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]

Локальное веб-калечество (уравнение. 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]

Локальный веб-выход (Руководство по проектированию 39 уравнение. 3-46)

куда [mathin] C_{t} = 1 [mathin] because the connection is far from the end of the column, и [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 (уравнение. 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]

Прочность на единицу размера сварного шва 191.5 кип / 415.42 кип = 0.461 < 1.0, Прочность на единицу размера сварного шва

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

Summary of design checks

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. Срез болта, 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.

Что изменить, если проверка не удалась

• Required bolt diameter: используйте болт большего размера, 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: используй более толстую тарелку, 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. В 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, does.
• 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.

Часто задаваемые вопросы

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?

Руководство по проектированию 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 (шаг 2) and the plate thickness second, с 1.10 factor on the moment (шаг 3).

What is the 0.8 reduction factor for flush end plates?

Flush end plates are more flexible than extended ones. Руководство по проектированию 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.

Does this example follow the AISC 15th edition or the AISC 16th edition Manual?

It follows AISC 360-16 и Руководство AISC, 15-е издание., which is written around that Specification, with the end plate procedure from Design Guide 39. The AISC 16th Edition Manual pairs with the later 360-22 Спецификация. Clause and equation numbers changed in the newer edition, so check the references against the edition your project uses.

Как это изменится для AISC ASD вместо LRFD??

The limit states and nominal strengths are the same. With AISC ASD you compare service-level forces against the nominal strength divided by a safety factor instead of multiplying by a resistance factor. Коэффициент сопротивления 0.75 становится фактором безопасности 2.00, 0.90 становится 1.67, и 1.00 становится 1.50. Сочетания нагрузок тоже меняются., so the moment, shear and axial load are lower.

Design a flush end plate moment connection for free

Каждое число на этой странице получено из одного решения. Pick the end plate moment configuration, войти в свой луч, колонка, болты, сварные швы, момент, сдвиговая и осевая нагрузка, и просмотрите каждую из этих проверок в своем браузере. Нечего устанавливать.

РАЗРАБОТАЙТЕ СОЕДИНЕНИЕ БЕСПЛАТНО

Модуль SkyCiv Connection Design — это программное обеспечение для проектирования соединений, лежащее в основе этого примера.. Он дает вам полный отчет о расчетах с каждым уравнением и вашими числами в нем., как шаги выше, плюс каждая емкость и DCR, для AISC 360-16 (ЛРФД и АСД) и, как 4100:2020. В калькулятор болтов и сварочный калькулятор cover bolt groups and weld groups on their own.

КУПИТЬ МОДУЛЬ КОНСТРУКЦИИ ПОДКЛЮЧЕНИЯ

Ссылки

• Aisc 360-16, Спецификация для зданий из конструкционной стали: J2.2b (Таблица J2.4), Дж2.4 (уравнение. J2-4), J3.2, J3.3, J3.4 (Таблица J3.4), J3.5 (Таблица J3.5), J3.6 (уравнение. J3-1), J3.10 (уравнение. J3-6а, J3-6c), J4.1 (уравнение. J4-1, J4-2), J4.2, J10.1 (уравнение. J10-1), J10.3 (уравнение. J10-4), J10.5 (уравнение. J10-8), J10.6 (уравнение. J10-9).
• Руководство по проектированию AISC 39, End-Plate Moment Connections: уравнение. 3-30, 3-38а , 3-39 to 3-41a, 3-43, 3-46, 3-47, 5-1, 5-3а , 5-5а ; инжир. 3-17; Стол 5-3, Table A-2.
• Руководство по стальным конструкциям AISC, 15й выпуск: Часть 1 свойства раздела; Часть 9 уравнение. 9-2.
• Проектирование стальных соединений с использованием AISC 360-16
• Болты и сварные швы в дизайне соединений SkyCiv