Как спроектировать сдвиговое соединение одной пластины

To design a single plate shear connection (a shear tab) в AISC 360, you check the bolts, the plate and the weld against the beam end reaction. That means bolt shear, подшипник болта и вырыв, сдвиг блока, plate shear yielding and rupture, plate flexure, and weld strength, plus the detailing and ductility limits that keep the connection flexible enough to act as a simple support.

This page works through one real example from start to finish: a W18x35 beam framing into the flange of a W14x90 column, с 50 kip LRFD reaction, три 1 in A490-N bolts and a 1/2 в тарелке, предназначен для AISC 360-16 и Руководство AISC, 15-е издание.. 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 single plate shear connection?

A single plate shear connection is a steel plate shop-welded to the supporting member and field-bolted to the web of the supported beam. It transfers the beam’s end shear, and it is classified as a simple connection under AISC 360-16 Б3.4, so it is detailed to rotate rather than resist moment. It is also called a shear tab or shear plate.

It is the most common сдвиговое соединение in US steel buildings because it needs one plate, one weld and one line of bolts, and the beam can be swung into place from the side during erection. The alternatives for the same job are the double angle connection, в single angle connection and the shear end plate connection. You can check this one directly in the single plate connection calculator.

Высота примера соединения. The plate is welded to the column flange and bolted to the beam web, with the bolt line 2 in from the weld.

Section A-A. The plate has horizontal short-slotted holes and a 5/16 in fillet weld on both sides.

How do you design a single plate shear connection? The steps at a glance

1. Check the detailing limits at the beam: расстояние между болтами, краевые расстояния, plate depth.
2. Find the bolt group shear strength with the instantaneous center of rotation.
3. Check plate ductility: the plate must not be stronger than the bolts.
4. Check bolt bearing and tear-out on the plate.
5. Check bolt bearing and tear-out on the beam web.
6. Combine shear, bearing and tear-out per bolt for the effective group strength.
7. Check block shear of the plate.
8. Check shear yielding and shear rupture of the plate.
9. Check plate flexure using the double coped beam procedure.
10. Check shear and flexure interaction, for yielding and for rupture.
11. Check the detailing limit at the support.
12. Size the weld to develop the plate.
13. Check the weld strength to the column flange.

Проектирование входных данных для этого примера

Код дизайна: AISC. 360-16 LRFD. Свойства раздела взяты из руководства AISC..

 

 

шаг 1: Detailing limits at the beam side (Aisc 360-16 J3.3, J3.4)

Before any strength check, the bolt layout has to be buildable and match the assumptions behind the strength equations. Болты, затянутые слишком близко, рвутся между отверстиями., края, которые расположены слишком близко, вырываются, and a plate that is too short or too deep changes how the connection rotates.

The minimum bolt spacing is [mathin] 2\tfrac{2}{3} d_{b} [mathin] from J3.3. The minimum edge distance for a 1 in bolt is 1 1/4 in from Table J3.4. On the plate, the horizontal edge is measured across the short slot, so the Table J3.5 increment raises it to 1.375 в. The plate depth has to be at least half the beam’s T dimension, so the connection is stiff enough to brace the beam end, and it must also fit inside the beam web.

[math] s_{min} = 2\tfrac{2}{3}\, d_{b} = 2.667 \times (1\,in) = 2.667\,in [math]

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

[math] DCR = \frac{1.375\,in}{1.5\,in} = 0.917 [math]

Прочность на единицу размера сварного шва 0.917 < 1.0, Прочность на единицу размера сварного шва

шаг 2: Bolt group shear strength by the instantaneous center of rotation (Aisc 360-16 J3.6)

The beam reaction acts away from the bolt line, so the bolts carry a small moment as well as the shear. The instantaneous center of rotation (ИКОР) method finds the point the bolt group rotates about and turns that into a coefficient C, which is how many bolts’ worth of shear strength the group actually delivers.

Design eccentricity

The bolt line is 2 in from the weld, but the bolt group is designed for an eccentricity of 1 в, because AISC Manual Table 10-9 sets the design eccentricity for a conventional single plate connection, and for this bolt count and hole type it is half the weld-to-bolt distance:

[math] e = \frac{a}{2} = \frac{2\,in}{2} = 1\,in [math]

Strength of one bolt

[math] \phi r_{v} = \phi\, F_{nv}\, \frac{\pi}{4} d_{b}^{2}\, N_{s}\, h_{f} [math]

[math] \phi r_{v} = (0.75) \times (68\,ksi) \times \frac{\pi}{4} (1\,in)^{2} \times (1) \times (1) = 40.055\,kip [math]

Вот [mathin] h_{f} = 1 [mathin] потому что нет наполнителей (Aisc 360-16 J5.2(а )):

[math] h_{f} = 1 – 0.4 \left( t – 0.25\,in \right) = 1 – 0.4 \left( 0\,in – 0.25\,in \right) \le 1 \;\Rightarrow\; h_{f} = 1 [math]

Locating the instantaneous center

Болт 1 is at the bottom of the line, with the coordinates below. The IC is found by iteration, using the load-deformation curve of AISC Manual Equation (7-1) на страницах 7-6 в 7-8. В bolt group calculation using ICOR walks through that iteration in full.

The iteration converges with the IC at:

[math] x_{ic} = -5.7728\,in, \qquad y_{ic} = 3\,in [math]

The bolt reactions at that location are:

That gives the two coefficients used in the rest of the design:

[math] C = 2.71 \qquad C’ = 5.889\,in [math]

C = 2.71 for three bolts means the 1 in eccentricity costs the group about 10% of its concentric strength. С’ is the coefficient for moment alone, which the ductility check in Step 3 использует.

Bolt group strength

[math] \phi R_{n} = \phi\, F_{nv}\, \frac{\pi}{4} d_{b}^{2}\, N_{s}\, C\, h_{f} [math]

[math] \phi R_{n} = (0.75) \times (68\,ksi) \times \frac{\pi}{4} (1\,in)^{2} \times (1) \times (2.71) \times (1) [math]

[math] \phi R_{n} = 108.55\,kip [math]

Прочность на единицу размера сварного шва 50 кип / 108.55 кип = 0.461 < 1.0, Прочность на единицу размера сварного шва

шаг 3: Plate ductility, maximum plate thickness (Ручное уравнение AISC. 10-3, 10-4)

A shear tab has to rotate as the beam deflects. If the plate is stronger in bending than the bolts are in shear, the bolts fracture before the plate yields, which is a sudden, brittle failure. Capping the plate thickness makes sure the plate yields first.

Первый, the moment strength of the bolt group, using C’ from Step 2:

[math] M_{max} = \frac{F_{nv}}{0.90}\, \frac{\pi}{4} d_{b}^{2}\, C’ [math]

[math] M_{max} = \frac{68\,ksi}{0.90} \times \frac{\pi}{4} (1\,in)^{2} \times (5.889\,in) = 29.122\,kip\text{-}ft [math]

Then the thickest plate whose plastic moment does not exceed it:

[math] t_{max} = \frac{6\, M_{max}}{F_{yp}\, d_{p}^{2}} [math]

[math] t_{max} = \frac{6 \times (29.122\,kip\text{-}ft)}{(50\,ksi) \times (9\,in)^{2}} = 0.51772\,in [math]

Прочность на единицу размера сварного шва 0.5 в / 0.51772 в = 0.966 < 1.0, Прочность на единицу размера сварного шва

В 0.966 this is the tightest strength check in the connection. А 5/8 in plate would fail it, even though a thicker plate looks “сильнее”.

шаг 4: Bolt bearing and tear-out on the single plate (Aisc 360-16 J3.10)

Each bolt pushes down on the edge of its hole in the plate. The plate either deforms at the hole (несущий, capped at 2.4 Поскольку расстояние до края меньше, чем соседнее расстояние до следующего отверстия под болт) or tears a strip out to the next hole or to the bottom edge (tear-out, 1.2 Поскольку расстояние до края меньше, чем соседнее расстояние до следующего отверстия под болт). The bottom bolt has the shortest clear distance, so it is the weak one.

Clear distance for the edge bolt, с участием [mathin] d_{h} = 1.125\,in [mathin], the hole dimension across the member length:

[math] l_{c1} = L_{ev,pl} – \frac{d_{h}}{2} = 1.5\,in – \frac{1.125\,in}{2} = 0.9375\,in [math]

Clear distance between the inner bolts:

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

The bearing and tear-out strength of the group, scaled by C / n for the eccentricity:

[math] \phi R_{n} = \phi \left[ \min\left(1.2\, l_{c1},\, 2.4\, d_{b}\right) t_{p} F_{up} + \min\left(1.2\, l_{c2},\, 2.4\, d_{b}\right) t_{p} F_{up} \left( n_{r} – 1 \right) \right] \frac{C}{n_{r}} [math]

[math] \phi R_{n} = (0.75) \left[ \min\left(1.125,\, 2.4\right)(0.5)(65) + \min\left(2.25,\, 2.4\right)(0.5)(65)(3 – 1) \right] \times \frac{2.71}{3} [math]

[math] \phi R_{n} = 123.86\,kip [math]

Прочность на единицу размера сварного шва 50 кип / 123.86 кип = 0.404 < 1.0, Прочность на единицу размера сварного шва

шаг 5: Bolt bearing and tear-out on the beam web (Aisc 360-16 J3.10)

The same check applies to the beam web. The beam is not coped and its bottom flange is far below the bolts, so there is no edge to tear out to, and every bolt bears like an inner bolt.

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

[math] \phi R_{n} = \phi\, \min\left(1.2\, l_{c2},\, 2.4\, d_{b}\right) t_{wb} F_{ub}\, C [math]

[math] \phi R_{n} = (0.75) \times \min\left(1.2 \times 1.875\,in,\, 2.4 \times 1\,in\right) \times (0.3\,in) \times (65\,ksi) \times (2.71) [math]

[math] \phi R_{n} = 89.176\,kip [math]

Прочность на единицу размера сварного шва 50 кип / 89.176 кип = 0.561 < 1.0, Прочность на единицу размера сварного шва

The beam web and the plate have the same tensile strength (65 KSI), но 0.3 in web is thinner than the 1/2 в тарелке, so the web has the lower capacity of the two.

шаг 6: Effective strength of the bolt group (Aisc 360-16 J3.6 Commentary)

Срез болта, bearing and tear-out are not really separate checks. Each bolt delivers the least of its shear strength and its bearing or tear-out strength in each ply it passes through, and the group strength is the sum of those per-bolt values.

The per-bolt bearing and tear-out strengths, for the plate edge bolt, a plate inner bolt and the beam web:

[math] \phi r_{n1e} = \phi\, \min\left(1.2\, l_{c1},\, 2.4\, d_{b}\right) t_{p} F_{up} = (0.75) \times \min\left(1.125\,in,\, 2.4\,in\right) \times (0.5\,in) \times (65\,ksi) = 27.422\,kip [math]

[math] \phi r_{n1i} = \phi\, \min\left(1.2\, l_{c2},\, 2.4\, d_{b}\right) t_{p} F_{up} = (0.75) \times \min\left(2.25\,in,\, 2.4\,in\right) \times (0.5\,in) \times (65\,ksi) = 54.844\,kip [math]

[math] \phi r_{n2} = \phi\, \min\left(1.2\, l_{c2},\, 2.4\, d_{b}\right) t_{wb} F_{ub} = (0.75) \times \min\left(2.25\,in,\, 2.4\,in\right) \times (0.3\,in) \times (65\,ksi) = 32.906\,kip [math]

Bolts are numbered from the top of the line here, so bolt 3 is the edge bolt on the plate:

[math] \sum \phi r_{eff} = n_{1}\, \phi r_{eff,1} + n_{2}\, \phi r_{eff,2} = (2) \times (32.906\,kip) + (1) \times (27.422\,kip) = 93.234\,kip [math]

[math] \phi R_{n,eff} = \frac{C}{n_{r}} \sum \phi r_{eff} = \frac{2.71}{3} \times (93.234\,kip) = 84.222\,kip [math]

Прочность на единицу размера сварного шва 50 кип / 84.222 кип = 0.594 < 1.0, Прочность на единицу размера сварного шва

None of the three bolts is limited by AISC bolt shear. Bearing in the beam web and tear-out at the bottom of the plate govern, which is typical when the bolts are high-strength and the plies are thin. You can run the same connection in the free connection design calculator and change the bolt grade or the plate edge distance to see which bolt moves.

шаг 7: Block shear of the single plate (Aisc 360-16 J4.3)

A block of the plate can tear out along the bolt line: shear down the line of holes plus tension across the short leg to the plate’s free edge. With one bolt column this is an L-shaped block.

The net tension area uses the hole dimension along the member length, [mathin] d_{h} = 1.3125\,in [mathin], because the slots run horizontally. Каждое отверстие добавляет 1/16 за повреждение во время удара кулаком (Б4.3):

[math] A_{nt} = t_{p} \left[ (n_{c}-1)\, s_{c} + L_{eh,pl} – (n_{c} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] [math]

[math] A_{nt} = (0.5\,in) \times \left[ (0)(0\,in) + 1.5\,in – (0.5)(1.3125\,in + 0.0625\,in) \right] = 0.40625\,in^{2} [math]

Gross and net shear areas, с участием [mathin] d_{h} = 1.125\,in [mathin] across the member length:

[math] A_{gv} = t_{p} \left[ L_{ev,pl} + (n_{r}-1)\, s_{r} \right] = (0.5\,in) \times \left[ 1.5\,in + (2)(3\,in) \right] = 3.75\,in^{2} [math]

[math] A_{nv} = t_{p} \left[ d_{p} – L_{ev,pl} – (n_{r} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] = (0.5\,in) \times \left[ 9\,in – 1.5\,in – (2.5)(1.1875\,in) \right] = 2.2656\,in^{2} [math]

Блок прочности на сдвиг, с участием [mathin] U_{bs} = 1 [mathin] for uniform tension:

[math] \phi R_{n} = \phi \left( 0.6\, F_{up} A_{nv} + U_{bs} F_{up} A_{nt} \right) \le \phi \left( 0.6\, F_{yp} A_{gv} + U_{bs} F_{up} A_{nt} \right) [math]

[math] \phi R_{n} = (0.75) \left( 0.6 \times 65 \times 2.2656 + 1 \times 65 \times 0.40625 \right) \le (0.75) \left( 0.6 \times 50 \times 3.75 + 1 \times 65 \times 0.40625 \right) [math]

[math] \phi R_{n} = 86.074\,kip [math]

Прочность на единицу размера сварного шва 50 кип / 86.074 кип = 0.581 < 1.0, Прочность на единицу размера сварного шва

шаг 8: Shear yielding and shear rupture of the single plate (Aisc 360-16 J4.2)

The full reaction passes through the plate as vertical shear. The gross section must not yield, and the net section through the bolt holes must not rupture.

Shear yielding (уравнение. J4-3)

[math] A_{gv} = d_{p}\, t_{p} = (9\,in) \times (0.5\,in) = 4.5\,in^{2} [math]

[math] \phi R_{n,sy} = \phi\, 0.6\, F_{yp} A_{gv} = (1.00) \times 0.6 \times (50\,ksi) \times (4.5\,in^{2}) = 135\,kip [math]

Shear rupture (уравнение. J4-4)

[math] A_{nv} = t_{p} \left[ d_{p} – n_{r}\left( d_{h} + 0.0625\,in \right) \right] = (0.5\,in) \times \left[ 9\,in – 3 \times (1.1875\,in) \right] = 2.7188\,in^{2} [math]

[math] \phi R_{n,sr} = \phi\, 0.6\, F_{up} A_{nv} = (0.75) \times 0.6 \times (65\,ksi) \times (2.7188\,in^{2}) = 79.523\,kip [math]

[math] \phi R_{n} = \min\left( 135\,kip,\, 79.523\,kip \right) = 79.523\,kip [math]

Прочность на единицу размера сварного шва 50 кип / 79.523 кип = 0.629 < 1.0, Прочность на единицу размера сварного шва

шаг 9: Plate flexure using the double coped beam procedure (Aisc 360-16 F11.2)

The reaction acts 2 in from the weld, so the plate is a short cantilever in bending. Глубина, thin plate can buckle sideways before it yields. The AISC Manual handles this with the procedure for a coped beam coped at both flanges, treating the plate like a beam web with the flanges cut away. The unbraced length is the weld-to-bolt distance, [mathin] L_{b} = 2\,in [mathin].

Flexural yielding and lateral-torsional buckling

Первый, confirm the plate is in the range where Eq. F11-2 applies:

[math] \frac{L_{b} d}{t^{2}} = \frac{(2\,in)(9\,in)}{(0.5\,in)^{2}} = 72 [math]

[math] \frac{0.08 E}{F_{y}} = \frac{0.08 \times 29000\,ksi}{50\,ksi} = 46.4 \lt 72 \le \frac{1.9 E}{F_{y}} = \frac{1.9 \times 29000\,ksi}{50\,ksi} = 1102 [math]

Section moduli of the plate:

[math] Z = \frac{t_{p} d_{p}^{2}}{4} = \frac{(0.5\,in)(9\,in)^{2}}{4} = 10.125\,in^{3} \qquad S = \frac{t_{p} d_{p}^{2}}{6} = \frac{(0.5\,in)(9\,in)^{2}}{6} = 6.75\,in^{3} [math]

Lateral-torsional buckling modification factor, Ручное уравнение AISC. (9-15), with no cope ([mathin] d_{ct} = 0 [mathin]):

[math] C_{b} = \left[ 3 + \ln\left( \frac{L_{b}}{d_{p}} \right) \right] \left( 1 – \frac{d_{ct}}{d_{p}} \right) \ge 1.84 [math]

[math] C_{b} = \left[ 3 + \ln\left( \frac{2\,in}{9\,in} \right) \right] \times \left( 1 – \frac{0\,in}{9\,in} \right) \ge 1.84 \;\Rightarrow\; C_{b} = 1.84 [math]

[math] \phi M_{n} = \phi\, C_{b} \left[ 1.52 – 0.274 \left( \frac{L_{b} d}{t^{2}} \right) \left( \frac{F_{yp}}{E} \right) \right] F_{yp} S \le \phi\, F_{yp} Z [math]

[math] \phi M_{n} = (0.9)(1.84) \left[ 1.52 – 0.274 \times (72) \times \frac{50\,ksi}{29000\,ksi} \right] (50\,ksi)(6.75\,in^{3}) \le (0.9)(50\,ksi)(10.125\,in^{3}) [math]

[math] \phi M_{n} = 37.969\,kip\text{-}ft \;(455.6\,kip\text{-}in) [math]

The plastic moment cap governs, so the plate is not prone to buckling at this depth and thickness. As an equivalent shear at the bolt line:

[math] \phi V_{n,y} = \frac{\phi M_{n}}{L_{b}} = \frac{455.6\,kip\text{-}in}{2\,in} = 227.81\,kip [math]

Flexural rupture on the net section

The net plastic section modulus through the holes, from AISC Manual Part 15 Стол 15-3:

[math] Z_{net} = \frac{t_{p} d_{p}^{2}}{4} – t_{p}\left( d_{h} + 0.0625\,in \right) s_{r} \left\lfloor \frac{n_{r}^{2}}{4} \right\rfloor – \left[ n_{r}\ \text{odd} \right] \frac{t_{p}\left( d_{h} + 0.0625\,in \right)^{2}}{4} [math]

[math] Z_{net} = \frac{(0.5)(9)^{2}}{4} – (0.5)(1.1875)(3) \left\lfloor \frac{9}{4} \right\rfloor – (1) \frac{(0.5)(1.1875)^{2}}{4} = 6.3862\,in^{3} [math]

[math] \phi M_{n} = \phi\, F_{up} Z_{net} = (0.75) \times (65\,ksi) \times (6.3862\,in^{3}) = 25.944\,kip\text{-}ft \;(311.3\,kip\text{-}in) [math]

[math] \phi V_{n,r} = \frac{\phi M_{n}}{L_{b}} = \frac{311.3\,kip\text{-}in}{2\,in} = 155.66\,kip [math]

[math] \phi V_{n} = \min\left( 227.81\,kip,\, 155.66\,kip \right) = 155.66\,kip [math]

Прочность на единицу размера сварного шва 50 кип / 155.66 кип = 0.321 < 1.0, Прочность на единицу размера сварного шва

шаг 10: Shear and flexure interaction of the single plate (Часть руководства AISC 10)

The plate carries shear and bending at the same section at the same time, so the two have to be checked together. The Manual uses a circular interaction, done once with the yielding strengths and once with the rupture strengths.

Уступая

[math] \left( \frac{V_{u}}{\phi V_{n,y}} \right)^{2} + \left( \frac{V_{u}}{\phi R_{n,sy}} \right)^{2} = \left( \frac{50\,kip}{227.81\,kip} \right)^{2} + \left( \frac{50\,kip}{135\,kip} \right)^{2} = 0.185 [math]

Прочность на единицу размера сварного шва 0.185 < 1.0, Прочность на единицу размера сварного шва

Rupture

[math] \left( \frac{V_{u}}{\phi V_{n,r}} \right)^{2} + \left( \frac{V_{u}}{\phi R_{n,sr}} \right)^{2} = \left( \frac{50\,kip}{155.66\,kip} \right)^{2} + \left( \frac{50\,kip}{79.523\,kip} \right)^{2} = 0.498 [math]

Прочность на единицу размера сварного шва 0.498 < 1.0, Прочность на единицу размера сварного шва

шаг 11: Detailing limit at the support side

The fillet weld sits in the gap between the column flange and the end of the beam, so the weld cannot be larger than the beam clearance or the beam will not fit.

[math] DCR = \frac{W}{clr} = \frac{0.3125\,in}{0.5\,in} = 0.626 [math]

Прочность на единицу размера сварного шва 0.626 < 1.0, Прочность на единицу размера сварного шва

шаг 12: Weld required to develop the single plate (Часть руководства AISC 10)

The ductility check in Step 3 makes the plate yield first. That only works if the weld does not fail before the plate does. Two fillet welds, each at least 5/8 of the plate thickness, develop the plate’s strength.

[math] W_{min} = \frac{5}{8}\, t_{p} = \frac{5}{8} \times (0.5\,in) = 0.3125\,in [math]

Прочность на единицу размера сварного шва 0.3125 в / 0.3125 в = 1.000, Прочность на единицу размера сварного шва

Соотношение ровно 1.000 is normal here. В 5/16 in weld was picked from this rule, not from the load.

шаг 13: Fillet weld capacity to the column flange (Aisc 360-16 Дж2.4)

Последний, the welds have to carry the reaction itself. Their strength depends on size, length and load direction. The base metal on either side of the weld, here the plate and the column flange, can also limit how much of the weld size counts.

Предел основного металла по размеру сварного шва (Ручное уравнение AISC. 9-2)

The largest weld size, in sixteenths of an inch, that the thinner connected part can support. The plate is welded both sides, so half its thickness is available to each weld:

[math] D_{max} = \frac{ \min\left( \frac{t_{p}}{2} F_{up},\; t_{fs} F_{us} \right) }{3.09\,kip/in \times \left( F_{EXX} / 70\,ksi \right)} = \frac{ \min\left( (0.25\,in)(65\,ksi),\; (0.71\,in)(65\,ksi) \right) }{(3.09\,kip/in)(1)} = 5.2589 [math]

So up to 5.26/16 in of weld size counts. В 5/16 in weld is below that, so the full size is used.

Effective length

Two lines of weld, each reduced by 2W at the ends:

[math] L_{w} = 2 \left( d_{p} – 2W \right) = 2 \times \left[ 9\,in – 2 \times (0.3125\,in) \right] = 16.75\,in [math]

Прочность сварного шва

The load runs parallel to the welds, так [mathin] \theta = 0 [mathin] и нет направленного увеличения:

[math] \phi R_{n} = \phi\, 0.6\, F_{EXX} \frac{\sqrt{2}}{2} \min\left( W,\, \frac{D_{max}}{16} \right) \left[ 1 + 0.5 \sin^{1.5}\theta \right] L_{w} [math]

[math] \phi R_{n} = (0.75) \times 0.6 \times (70\,ksi) \times \frac{\sqrt{2}}{2} \times (0.3125\,in) \times \left[ 1 + 0.5 \sin^{1.5}(0) \right] \times (16.75\,in) [math]

[math] \phi R_{n} = 116.59\,kip [math]

Прочность на единицу размера сварного шва 50 кип / 116.59 кип = 0.429 < 1.0, Прочность на единицу размера сварного шва

Summary of design checks

The connection passes every check. Two ratios sit near 1.0, and neither one measures load against capacity. The weld-to-develop check is exactly 1.000 because the weld was sized from the 5/8 t rule, and the ductility check is 0.966 because a 1/2 in plate is just under the thickest plate that still yields before the bolts break. Of the checks that compare load with capacity, shear rupture of the plate (0.629) is the highest, closely followed by the effective bolt group strength (0.594), which is set by bearing in the 0.3 in beam web and tear-out at the bottom of the plate.

Что изменить, если проверка не удалась

• Bolt group shear or effective strength: добавить ряд болтов, which raises C, or use a larger bolt. Moving the bolt line closer to the weld reduces e and raises C.
• тягучесть (t_max): use a thinner plate, or a lower-strength plate grade. A thicker plate makes this check worse.
• Tear-out on the plate: increase the vertical edge distance below the bottom bolt.
• Bearing on the beam web: this depends on the web thickness and grade, so add a bolt row or pick a heavier beam.
• Блок сдвиг, shear rupture or flexural rupture: make the plate deeper with another bolt row, or make it thicker if the ductility check has room.
• Weld to develop the plate: increase the weld to 5/8 of the plate thickness, provided it still fits within the beam clearance.

Часто задаваемые вопросы

Why is the bolt group designed for a 1 in eccentricity when the bolts are 2 in from the weld?

AISC Manual Table 10-9 sets the design eccentricity for a conventional single plate connection based on the number of bolts and the hole type. For this three-bolt connection it is half the distance from the weld line to the bolt line, так 2 in becomes 1 в. The weld is then designed for the reaction alone. This calibration comes from tests on real shear tabs, which rotate and shed most of the end moment.

What is the difference between the conventional and extended single plate configurations?

The conventional configuration covers a single vertical row of 2 в 12 bolts with the bolt line no more than 3 1/2 in from the weld, plus the edge distance and thickness limits in Part 10 Руководства AISC. Within those limits, the simplified Table 10-9 approach in this example applies. Anything outside them, such as a longer plate reaching past a column flange to a deeper bolt line, is the extended configuration and needs a fuller analysis including plate buckling.

Why does the plate use short-slotted holes?

Horizontal short slots in the plate let the beam end rotate and give the erector some fit-up tolerance, both of which suit a simple connection. Because the slots run perpendicular to the vertical load, the bearing and tear-out checks use the hole dimension across the slot. The horizontal edge distance on the plate picks up a small increment from Table J3.5, which is why its limit is 1.375 in rather than 1.25 в.

Why is the fillet weld sized at 5/8 of the plate thickness?

The design relies on the plate yielding before anything brittle happens. Two fillet welds, каждый 5/8 of the plate thickness, are strong enough to develop the plate, so the weld cannot become the weak link even if the plate yields. Для 1/2 in plate that gives a 5/16 in weld, which is why that check lands at exactly 1.0.

Which check usually governs a shear tab?

For a typical shear tab with high-strength bolts, bearing or tear-out on the thinner ply and the ductility limit on plate thickness tend to govern rather than bolt shear. In this example the highest load ratio is plate shear rupture at 0.629, with the effective bolt group strength next at 0.594, controlled by bearing in the beam web. The ductility check sits at 0.966.

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. The AISC 16th Edition Manual pairs with the later 360-22 Спецификация. The limit states for a single plate shear connection are the same in both, but clause and page references move, so check them against the edition your project uses.

Как это изменится для AISC ASD вместо LRFD??

Предельные состояния и номинальная прочность идентичны.. With AISC ASD you compare the service-level reaction 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, and shear yielding’s 1.00 становится 1.50. Сочетания нагрузок тоже меняются., поэтому спрос ниже.

Is the column checked in this design?

The column flange enters through the weld base metal check in Step 13, where its thickness and tensile strength limit the usable weld size. In this example the plate, not the 0.71 in column flange, controls that limit. Column web and flange local limit states are not part of this single plate check.

Design a single plate shear connection for free

Каждое число на этой странице получено из одного решения. Pick the single plate configuration, войти в свой луч, служба поддержки, bolts and reaction, 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 прикрыть затворную группу и приварить чеки самостоятельно.

КУПИТЬ МОДУЛЬ КОНСТРУКЦИИ ПОДКЛЮЧЕНИЯ

Ссылки

• Aisc 360-16, Спецификация для зданий из конструкционной стали: Б3.4, Б4.3, F11.2 (уравнение. F11-2), Дж2.4 (уравнение. J2-4), J3.3, J3.4 (Таблица J3.4), J3.5 (Таблица J3.5), J3.6 (уравнение. J3-1) and Commentary, J3.10 (уравнение. J3-6а, J3-6c), J4.2 (уравнение. J4-3, J4-4), J4.3 (уравнение. Дж4-5), J5.2(а ).
• Руководство по стальным конструкциям AISC, 15й выпуск: Часть 7, страницы 7-6 в 7-8 (уравнение. 7-1); Часть 9, уравнение. 9-2, 9-4 и 9-15; Часть 10, уравнение. 10-3 и 10-4, Стол 10-9 and page 10-87; Часть 15, Стол 15-3.
• Расчет группы болтов с использованием ICOR
• Проектирование стальных соединений с использованием AISC 360-16
• Болты и сварные швы в дизайне соединений SkyCiv