梁拼接连接设计

Beam splice connection design to AISC 360 comes down to splitting the moment, shear and axial load between the flange plates and the web plates, then checking every bolt group, plate and beam section that load passes through, on both sides of the joint. The flange plates carry the moment as a tension and compression couple plus their share of the axial load. The web plates carry the shear and the rest of the axial load.

This page works through one real bolted beam splice from start to finish: a W27x84 spliced to a W27x94, 与一个 400 急转瞬间, 一个 250 kip shear and 300 kip of axial tension or compression, 设计符合 AISC 360-16 LRFD 和 AISC 手册第 15 版. 每个法兰都有一个 3/4 in flange plate with 1 in A490 slip-critical bolts, and the web has a pair of 1/2 in web plates with ten 1 in A490 slip-critical bolts on each side of the splice. 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.

立即尝试我们的免费工具 购买连接设计模块

What is a beam splice connection?

A beam splice joins two beam segments end to end so the member behaves as if it were continuous. In a bolted beam splice, splice plates lap across the joint on the flanges and the web and are bolted to both beams. It is used when a beam is too long to ship or erect in one piece, or when the section changes along the span, as it does here from a W27x84 to a W27x94.

The splice in this example is a full moment splice: 一个 矩连接 between two beams rather than between a beam and a column. The flange plates work exactly like the plates of a flange plate moment connection, except that they are bolted to a beam flange at both ends instead of being welded to a column. The web plates sit on both faces of the web, so the web bolts are in double shear. You can check this configuration directly in the beam splice connection calculator. 的 螺栓接头连接计算器 和 瞬间连接 page cover the related types.

Plan of the flange splice. 的 3/4 in flange plate has two bolt lines at a 5 1/2 在规格中, six bolt columns on the W27x84 side and five on the W27x94 side, all at 3 在间距. The beam ends are 1 in apart.

A-A部分. The web plates are 14 1/2 in deep, with five rows of two bolts on each side of the joint at 3 在间距. The loads are shown at the splice.

Beam splice connection design: 步骤一目了然

The loads are split between the flanges and the web first. Then the flange plate splice is checked on both sides of the joint, and then the web plate splice.

1. 检查法兰板螺栓的详细限制.
2. Find the flange force and check slip of the slip-critical flange bolts.
3. 检查法兰板上的螺栓轴承和撕裂情况.
4. Check bolt bearing and tear-out on the beam flange.
5. 检查法兰板的块剪切是否存在三种撕裂模式.
6. Check block shear of the beam flange.
7. 检查法兰板的拉伸屈服和破裂情况.
8. Check tension rupture of the beam, 有剪切滞后.
9. Check flexural rupture of the beam at the flange bolt holes.
10. 检查法兰盘是否受压.
11. Repeat the flange checks for the second beam.
12. 检查腹板螺栓的详细限制.
13. 检查腹板螺栓组在剪切和轴向载荷作用下的滑移.
14. 检查腹板上的螺栓轴承是否受剪力, 轴向载荷及其相互作用.
15. Check bolt bearing on the beam web for shear, 轴向载荷及其相互作用.
16. 检查腹板的块剪力是否受剪力影响, 轴向载荷及其相互作用.
17. Check block shear of the beam web for axial load.
18. 检查腹板的剪切屈服和剪切断裂.
19. 检查腹板的张力屈服和断裂.
20. Check tension rupture of the beam web, 有剪切滞后.
21. 检查腹板的压缩情况.
22. Repeat the web checks for the second beam.

本示例的设计输入

设计代码为AISC 360-16 LRFD. 截面属性来自 AISC 手册. The left beam is the W27x84 and the right beam is the W27x94.

 

 

 

How the beam splice shares the load between flanges and web

Before any check, the splice has to decide which plates carry which load. The report proportions the axial load to the web by the web area over the total gross area of the beam, and gives the rest of the axial load and all of the moment to the flanges. The web also carries all of the shear.

The axial force on the web is:

[math] C_{web} = T_{web} = 135.34\,kip [math]

The flange force is half of the remaining axial load plus the moment divided by the distance between the flange centroids. [mathin] C_{bp} [mathin] is any compression carried by direct bearing between the beam ends. The beams are 1 in apart, so nothing bears and it is zero:

[math] C_{flange} = \frac{C_{u} – C_{bp} – C_{web}}{2} + \frac{M_{u}}{d_{c} – t_{fc}} [math]

[math] C_{flange} = \frac{(300\,kip) – (0\,kip) – (135.34\,kip)}{2} + \frac{(400\,kip\text{-}ft)}{(26.7\,in) – (0.64\,in)} = 266.52\,kip [math]

Tension and compression are both 300 基普, 所以 [mathin] T_{flange} [mathin] is the same, and the design flange force is:

[math] P_{flange} = \max\left( C_{flange},\, T_{flange} \right) = 266.52\,kip [math]

The report uses the W27x84’s depth and flange thickness for the moment arm on both sides. It is the shallower of the two beams, so its lever arm is shorter and the flange force is larger, which is conservative for the W27x94 side.

The web bolts see the shear and the web axial load together. Their resultant is:

[math] R_{u} = \sqrt{V_{u}^{2} + P_{web}^{2}} = \sqrt{(250\,kip)^{2} + (135.34\,kip)^{2}} = 284.28\,kip [math]

部分 1: the flange plate splice

脚步 1 至 10 check the flange plate and the W27x84 flange on the left side for the 266.52 kip flange force. 步 11 repeats them for the W27x94 on the right.

步 1: 法兰板螺栓的详细限制 (AISC 360-16 J3.3, J3.4, J3.5)

在进行任何力量检查之前, the bolt layout has to be buildable and match the assumptions behind the strength equations. Bolts that are too close tear between the holes, and edges that are too close tear out.

最小螺栓间距为 [mathin] 2\tfrac{2}{3} d_{b} [mathin] from J3.3, and the maximum here is 6 在. The minimum edge distance for a 1 in bolt is 1 1/4 in from Table J3.4, which is the limit on the beam flange, where the holes are standard. The flange plate has oversized holes, 因此表 J3.5 添加了 1/8 in and its edge distance limits are 1.375 在. The gage has its own minimum, so that the two bolt lines fit across the flange with room to install the bolts.

For a minimum limit the ratio is limit over actual, and for a maximum it is actual over limit. The governing row is the horizontal edge distance on the beam flange, from the end of the beam to the first bolt column:

[math] DCR = \frac{1.25\,in}{1.25\,in} = 1 [math]

DCR = 1.000 ≤ 1.0, 行

A ratio of 1.0 means the edge distance is at the code minimum, which is common in detailing. A short beam end distance also keeps the unbraced length of the flange plate short in Step 10.

步 2: Slip critical bolt strength at the flange (AISC 360-16 J3.8)

The flange plate bolts have to carry the flange force without slipping. These bolts are slip-critical because the flange plate has oversized holes, 哪个 AISC 360-16 J3.2 allows only in slip-critical connections.

在哪里 [mathin] \phi = 0.85 [mathin] is the resistance factor for oversized holes, [mathin] \mu = 0.5 [mathin] is the mean slip coefficient for Class B faying surfaces, [mathin] D_{u} = 1.13 [mathin] relates the mean installed pretension to the specified minimum, [mathin] h_{f} = 0.85 [mathin] is the filler factor, [mathin] T_{b} = 64\,kip [mathin] is the minimum pretension of a 1 in A490 bolt from Table J3.1, and there is [mathin] N_{s} = 1 [mathin] 滑移面:

[math] \phi R_{n} = \phi\, \mu\, D_{u}\, h_{f}\, T_{b}\, N_{s}\, n_{r}\, n_{c} [math]

[math] \phi R_{n} = (0.85) \times (0.5) \times (1.13) \times (0.85) \times (64\,kip) \times (1) \times (2) \times (6) [math]

[math] \phi R_{n} = 313.51\,kip [math]

DCR = 266.52 基普 / 313.51 基普= 0.850 < 1.0, 行

J3.8 sets the filler factor at 1.0 when there is no filler or one filler between the plies, 和 0.85 for two or more. The W27x84 is 0.2 in shallower than the W27x94, so its flanges sit inside the plane of the flange plates and need packing. The report designs that side for the 0.85 因素.

步 3: 法兰板上的螺栓轴承和撕裂口 (AISC 360-16 J3.10)

Slip-critical bolts must also work as bearing bolts, in case the joint does slip. Each bolt pushes on the edge of its hole in the plate. The plate either deforms at the hole (螺栓轴承, capped at 2.4 螺栓的剪切强度) or tears a strip out to the next hole or to the end of the plate (撕掉, 1.2 螺栓的剪切强度).

The clear distance for the end bolts, 与 [mathin] d_{h} = 1.25\,in [mathin] for the oversized holes, 是:

[math] l_{c1} = L_{eh,fp} – \frac{d_{h}}{2} = (2.875\,in) – \frac{(1.25\,in)}{2} = 2.25\,in [math]

Between the other bolts:

[math] l_{c2} = s_{c} – d_{h} = (3\,in) – (1.25\,in) = 1.75\,in [math]

The end bolt in each of the two lines uses [mathin] l_{c1} [mathin], and the other five in each line use [mathin] l_{c2} [mathin]:

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

[math] \phi R_{n} = (0.75) \times \left[ \min\left(1.2 \times 2.25\,in,\, 2.4 \times 1\,in\right)(0.75\,in)(65\,ksi)(2) + \min\left(1.2 \times 1.75\,in,\, 2.4 \times 1\,in\right)(0.75\,in)(65\,ksi)(2)(6 – 1) \right] [math]

[math] \phi R_{n} = 943.31\,kip [math]

DCR = 266.52 基普 / 943.31 基普= 0.283 < 1.0, 行

The end bolts are capped by bearing at 2.4 d, because their 2 7/8 in end distance is long. The inner bolts are limited by tear-out between the oversized holes.

步 4: Bolt bearing and tear-out on the beam flange (AISC 360-16 J3.10)

The same check applies to the beam flange, which has standard holes ([mathin] d_{h} = 1.125\,in [mathin]) 并且是 0.64 in thick on the W27x84. Its end bolts are only 1 1/4 in from the end of the beam, so tear-out governs them.

[math] l_{c1} = L_{eh,c} – \frac{d_{h}}{2} = (1.25\,in) – \frac{(1.125\,in)}{2} = 0.6875\,in [math]

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

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

[math] \phi R_{n} = (0.75) \times \left[ \min\left(1.2 \times 0.6875\,in,\, 2.4 \times 1\,in\right)(0.64\,in)(65\,ksi)(2) + \min\left(1.2 \times 1.875\,in,\, 2.4 \times 1\,in\right)(0.64\,in)(65\,ksi)(2)(6 – 1) \right] [math]

[math] \phi R_{n} = 753.48\,kip [math]

DCR = 266.52 基普 / 753.48 基普= 0.354 < 1.0, 行

步 5: 翼缘板块剪 (AISC 360-16 J4.3)

A block of the flange plate can tear out along the bolt lines: shear along a line of holes plus tension across the plate. With two bolt lines there are three ways for this to happen, and the weakest one governs. Each hole adds 1/16 in for damage during punching (B4.3), 和 [mathin] d_{h} = 1.25\,in [mathin] for the oversized holes.

L型: one shear plane, tension across the bolts to one edge

[math] A_{nt} = t_{fp} \left[ (n_{r} – 2)\, s_{r} + g_{a} + L_{ev,fp} – (n_{r} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] [math]

[math] A_{nt} = (0.75\,in) \times \left[ (2 – 2)(3\,in) + 5.5\,in + 2.25\,in – (2 – 0.5)(1.25\,in + 0.0625\,in) \right] = 4.3359\,in^{2} [math]

[math] A_{gv} = t_{fp} \left[ L_{eh,fp} + (n_{c} – 1)\, s_{c} \right] = (0.75\,in) \times \left[ 2.875\,in + (6 – 1)(3\,in) \right] = 13.406\,in^{2} [math]

[math] A_{nv} = t_{fp} \left[ L_{eh,fp} + (n_{c} – 1)\, s_{c} – (n_{c} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] = (0.75\,in) \times \left[ 2.875\,in + (5)(3\,in) – (5.5)(1.3125\,in) \right] = 7.9922\,in^{2} [math]

和 [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 7.9922 + 1 \times 65 \times 4.3359 \right) \le (0.75) \left( 0.6 \times 50 \times 13.406 + 1 \times 65 \times 4.3359 \right) [math]

[math] \phi R_{n} = 445.15\,kip [math]

U型: two shear planes, tension between the bolt lines

[math] A_{nt} = t_{fp} \left[ (n_{r} – 2)\, s_{r} + g_{a} – (n_{r} – 1)\left( d_{h} + 0.0625\,in \right) \right] = (0.75\,in) \times \left[ 0 + 5.5\,in – (1)(1.3125\,in) \right] = 3.1406\,in^{2} [math]

[math] A_{gv} = 2\, t_{fp} \left[ L_{eh,fp} + (n_{c} – 1)\, s_{c} \right] = 26.813\,in^{2} [math]

[math] A_{nv} = 2\, t_{fp} \left[ L_{eh,fp} + (n_{c} – 1)\, s_{c} – (n_{c} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] = 15.984\,in^{2} [math]

[math] \phi R_{n} = (0.75) \left( 0.6 \times 65 \times 15.984 + 1 \times 65 \times 3.1406 \right) \le (0.75) \left( 0.6 \times 50 \times 26.813 + 1 \times 65 \times 3.1406 \right) = 620.65\,kip [math]

2L型: two shear planes, tension from each bolt line to its edge

[math] A_{nt} = 2\, t_{fp} \left[ L_{ev,fp} – 0.5\left( d_{h} + 0.0625\,in \right) \right] = 2 \times (0.75\,in) \times \left[ 2.25\,in – 0.5 \times (1.3125\,in) \right] = 2.3906\,in^{2} [math]

[math] \phi R_{n} = (0.75) \left( 0.6 \times 65 \times 15.984 + 1 \times 65 \times 2.3906 \right) \le (0.75) \left( 0.6 \times 50 \times 26.813 + 1 \times 65 \times 2.3906 \right) = 584.09\,kip [math]

Governing block shear

[math] \phi R_{n} = \min\left( 445.15\,kip,\, 620.65\,kip,\, 584.09\,kip \right) = 445.15\,kip [math]

DCR = 266.52 基普 / 445.15 基普= 0.599 < 1.0, 行

The L pattern governs because it has only one shear plane.

步 6: Block shear of the beam flange (AISC 360-16 J4.3)

The beam flange can tear out the same way. The critical block is the 2L pattern: the two outer strips of flange shear along the bolt lines from the beam end and pull away in tension. The beam flange has standard holes, [mathin] d_{h} = 1.125\,in [mathin].

[math] A_{nt} = t_{f} \left[ b_{f} – g_{a} – (n_{r} – 1)\left( d_{h} + 0.0625\,in \right) \right] = (0.64\,in) \times \left[ 10\,in – 5.5\,in – (1)(1.125\,in + 0.0625\,in) \right] = 2.12\,in^{2} [math]

[math] A_{gv} = 2\, t_{f} \left[ L_{eh,c} + (n_{c} – 1)\, s_{c} \right] = 2 \times (0.64\,in) \times \left[ 1.25\,in + (5)(3\,in) \right] = 20.8\,in^{2} [math]

[math] A_{nv} = 2\, t_{f} \left[ L_{eh,c} + (n_{c} – 1)\, s_{c} – (n_{c} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] = 2 \times (0.64\,in) \times \left[ 16.25\,in – (5.5)(1.1875\,in) \right] = 12.44\,in^{2} [math]

[math] \phi R_{n} = (0.75) \left( 0.6 \times 65 \times 12.44 + 1 \times 65 \times 2.12 \right) \le (0.75) \left( 0.6 \times 50 \times 20.8 + 1 \times 65 \times 2.12 \right) [math]

[math] \phi R_{n} = 467.22\,kip [math]

DCR = 266.52 基普 / 467.22 基普= 0.570 < 1.0, 行

步 7: 法兰板的拉伸屈服和断裂 (AISC 360-16 J4.1)

On the tension flange, the flange plate is a short tension member. Its gross section must not yield, and its net section through the row of holes must not rupture.

Tension yielding (情商. J4-1)

[math] \phi R_{n,ty} = \phi\, F_{yp}\, t_{fp}\, b_{fp} = (0.9) \times (50\,ksi) \times (0.75\,in) \times (10\,in) = 337.5\,kip [math]

Tension rupture (情商. J4-2)

[math] \phi R_{n,tr} = \phi\, F_{up}\, t_{fp} \left[ b_{fp} – n_{r}\left( d_{h} + 0.0625\,in \right) \right] [math]

[math] \phi R_{n,tr} = (0.75) \times (65\,ksi) \times (0.75\,in) \times \left[ 10\,in – (2) \times (1.3125\,in) \right] = 269.65\,kip [math]

[math] \phi R_{n} = \min\left( 337.5\,kip,\, 269.65\,kip \right) = 269.65\,kip [math]

DCR = 266.52 基普 / 269.65 基普= 0.988 < 1.0, 行

This is the governing check for the flange plates. The oversized holes take 2.625 进出一个 10 在盘子里, so net section rupture controls well below gross yielding. A wider plate is not an option here because the plate already matches the 10 in flange width, so the fix is a thicker plate.

步 8: Tension rupture of the beam with shear lag (AISC 360-16 D3, J4.1)

The flange force has to get into the beam as well. Half the beam, a WT made of one flange and half the web, is treated as the tension member. The bolts connect only the flange, so the web lags behind in picking up stress, and the shear lag factor U reduces the effective net area.

From Table D3.1 case 2, 哪里 [mathin] \bar{y} = 3.5359\,in [mathin] is the distance from the flange to the centroid of the WT and l is the length of the connection, from the first bolt column to the last:

[math] U = 1 – \frac{\bar{y}}{l} = 0.76437 [math]

[math] \phi R_{n,tr} = \phi\, F_{u}\, U \left[ 0.5\, A – n_{r}\left( d_{h} + 0.0625\,in \right) t_{f} \right] [math]

[math] \phi R_{n,tr} = (0.75) \times (65\,ksi) \times (0.76437) \times \left[ 0.5 \times (24.7\,in^{2}) – (2) \times (1.125\,in + 0.0625\,in) \times (0.64\,in) \right] [math]

[math] \phi R_{n,tr} = 403.56\,kip [math]

DCR = 266.52 基普 / 403.56 基普= 0.660 < 1.0, 行

步 9: Flexural rupture of the beam at the flange bolt holes (AISC 360-16 F13.1)

The bolt holes take material out of the beam’s tension flange at the splice. F13.1 checks whether those holes reduce the beam’s flexural strength, and if they do, by how much.

Gross and net area of the tension flange

[math] A_{fg} = b_{f}\, t_{f} = (10\,in) \times (0.64\,in) = 6.4\,in^{2} [math]

[math] A_{fn} = A_{fg} – n_{r}\left( d_{h} + 0.0625\,in \right) t_{f} = (6.4\,in^{2}) – (2) \times (1.1875\,in) \times (0.64\,in) = 4.88\,in^{2} [math]

Does tensile rupture apply?

[math] \frac{F_{y}}{F_{u}} = \frac{50\,ksi}{65\,ksi} = 0.76923 \le 0.8 \;\Rightarrow\; Y_{t} = 1 [math]

[math] F_{u} A_{fn} = (65\,ksi) \times (4.88\,in^{2}) = 317.2\,kip [math]

[math] Y_{t} F_{y} A_{fg} = (1) \times (50\,ksi) \times (6.4\,in^{2}) = 320\,kip [math]

手动计算可用于静定梁 [mathin] F_{u} A_{fn} \lt Y_{t} F_{y} A_{fg} [mathin] by a small margin, the net flange ruptures before the gross flange yields and the limit state of tensile rupture applies.

Flexural strength at the holes (情商. F13-1)

[math] M_{n} = \frac{F_{u} A_{fn}}{A_{fg}}\, S_{x} = \frac{(65\,ksi) \times (4.88\,in^{2})}{(6.4\,in^{2})} \times (213.65\,in^{3}) = 882.4\,kip\text{-}ft [math]

As a flange force, to compare with [mathin] P_{flange} [mathin]:

[math] \phi R_{n} = \frac{\phi\, M_{n}}{d – t_{f}} = \frac{(0.9) \times (882.4\,kip\text{-}ft)}{(26.7\,in) – (0.64\,in)} = 365.69\,kip [math]

DCR = 266.52 基普 / 365.69 基普= 0.729 < 1.0, 行

步 10: 法兰板的抗压强度 (AISC 360-16 J4.4)

On the compression flange the flange plate is a short column across the gap between the beam ends. If it is stocky enough, it reaches its yield load without buckling, 和AISC 360-16 J4.4 lets you skip the full Chapter E column check.

The unbraced length is [mathin] L_{b} = 3.5\,in [mathin], the distance between the first bolt columns on either side of the joint: 1.25 边缘距离, 的 1 in gap, 和 1.25 in again. 和 [mathin] K = 1.2 [mathin] (Commentary Table C-A-7.1, rotation fixed at both ends, translation free at one) 和 [mathin] r = t_{fp} / \sqrt{12} [mathin] for a rectangular plate:

[math] \frac{K L}{r} = \frac{(1.2) \times (3.5\,in)}{(0.75\,in) / \sqrt{12}} = 19.4 \le 25 [math]

Since KL/r is no more than 25, 情商. J4-6适用:

[math] \phi R_{n} = \phi\, F_{yp}\, t_{fp}\, b_{fp} = (0.9) \times (50\,ksi) \times (0.75\,in) \times (10\,in) = 337.5\,kip [math]

DCR = 266.52 基普 / 337.5 基普= 0.790 < 1.0, 行

步 11: Flange plate splice on the W27x94 side

The right side of the splice carries the same 266.52 kip flange force through the same plate, but into a W27x94 with a thicker flange (0.745 在) and one fewer bolt column (五). Every check in Steps 1 至 10 is repeated with those values, and the detailing table is identical.

The slip check is the one that changes most. 报告使用 [mathin] h_{f} = 1 [mathin] on this side, the J3.8 value for no filler or one filler, and five bolt columns:

[math] \phi R_{n} = (0.85) \times (0.5) \times (1.13) \times (1) \times (64\,kip) \times (1) \times (2) \times (5) = 307.36\,kip [math]

DCR = 266.52 基普 / 307.36 基普= 0.867 < 1.0, 行

Flexural rupture uses the W27x94 flange and section modulus:

[math] A_{fg} = (10\,in)(0.745\,in) = 7.45\,in^{2}, \quad A_{fn} = 5.6806\,in^{2} [math]

[math] F_{u} A_{fn} = 369.24\,kip \lt Y_{t} F_{y} A_{fg} = 372.5\,kip [math]

[math] M_{n} = \frac{(65\,ksi) \times (5.6806\,in^{2})}{(7.45\,in^{2})} \times (242.89\,in^{3}) = 1003.2\,kip\text{-}ft [math]

[math] \phi R_{n} = \frac{(0.9) \times (1003.2\,kip\text{-}ft)}{(26.9\,in) – (0.745\,in)} = 414.24\,kip [math]

The other right side results:

The right side has five bolt columns against six on the left, so its slip and block shear ratios are higher. The beam checks are lower because the W27x94 flange is thicker. Flange plate tension is the same 0.988 两侧, since it depends only on the plate.

部分 2: the web plate splice

脚步 12 至 21 check the two web plates and the W27x84 web on the left side, 为了 250 kip shear and the 135.34 kip web axial force. 步 22 covers the W27x94 side. Because the web carries axial load as well as shear, the bearing and block shear checks are done in each direction and then combined.

步 12: 腹板螺栓的详细限制 (AISC 360-16 J3.3, J3.4, J3.5)

腹板螺栓布局必须满足与翼缘相同的间距和边距规则, and the web plates have to be deep enough to stabilise the beam web but fit between the flanges.

The horizontal short slots in the plate run perpendicular to the plate’s vertical end edge, 因此表 J3.5 添加了 1/8 in to the horizontal edge distance, 给予 1.375 在. The vertical edge distance stays at the Table J3.4 value of 1.25 在.

DCR = 1.000 ≤ 1.0, 行

Both plate edge distances sit at the code minimum. That keeps the web plates compact, which matters for the compression check in Step 21.

步 13: Slip critical bolt strength at the web (AISC 360-16 J3.8)

The web bolts carry the shear and the web axial force together, 所以滑动检查使用它们的结果, 284.28 基普. The bolts are slip-critical because the plates have short slots that run parallel to the axial load.

在哪里 [mathin] \phi = 0.85 [mathin] for short slots parallel to the load, [mathin] \mu = 0.3 [mathin] for Class A faying surfaces, [mathin] D_{u} = 1.13 [mathin], [mathin] h_{f} = 1 [mathin], [mathin] T_{b} = 64\,kip [mathin], 和 [mathin] N_{s} = 2 [mathin] 滑移平面，因为腹板的每个面上都有一个腹板:

[math] \phi R_{n} = \phi\, \mu\, D_{u}\, h_{f}\, T_{b}\, N_{s}\, n_{r}\, n_{c} [math]

[math] \phi R_{n} = (0.85) \times (0.3) \times (1.13) \times (1) \times (64\,kip) \times (2) \times (5) \times (2) [math]

[math] \phi R_{n} = 368.83\,kip [math]

DCR = 284.28 基普 / 368.83 基普= 0.771 < 1.0, 行

Two slip planes double the slip resistance of each bolt, so ten bolts are enough even with the lower Class A slip coefficient.

步 14: 腹板上的螺栓轴承 (AISC 360-16 J3.10)

腹板孔同时在两个方向上加载: down by the shear and along the beam by the axial force. Bolt bearing and tear-out are checked separately in each direction, using the clear distances that apply in that direction, and then combined. 两个板一起工作, 所以厚度是 [mathin] 2t_{wp} = 1\,in [mathin].

剪切方向

Across the slot, the hole dimension is [mathin] d_{h} = 1.125\,in [mathin]. The bottom bolt in each column tears toward the bottom edge of the plate, and the others toward the hole below:

[math] l_{c1} = L_{ev,wp} – \frac{d_{h}}{2} = (1.25\,in) – \frac{(1.125\,in)}{2} = 0.6875\,in, \quad l_{c2} = s_{r} – d_{h} = (3\,in) – (1.125\,in) = 1.875\,in [math]

The bracket sums one column of bolts, 和 [mathin] C / n_{r} [mathin] scales it to the whole group. The load is concentric, so the bolt group coefficient C is the number of bolts, 10:

[math] \phi R_{n} = \phi \left[ \min\left(1.2\, l_{c1},\, 2.4\, d_{b}\right) 2t_{wp} F_{up} + \min\left(1.2\, l_{c2},\, 2.4\, d_{b}\right) 2t_{wp} F_{up} \left( n_{r} – 1 \right) \right] \frac{C}{n_{r}} [math]

[math] \phi R_{n} = (0.75) \times \left[ \min\left(1.2 \times 0.6875\,in,\, 2.4\,in\right)(1\,in)(65\,ksi) + \min\left(1.2 \times 1.875\,in,\, 2.4\,in\right)(1\,in)(65\,ksi)(5 – 1) \right] \times \frac{10}{5} = 957.94\,kip [math]

DCR = 250 基普 / 957.94 基普= 0.261 < 1.0, 行

轴向方向

Along the slot, the hole dimension is [mathin] d_{h} = 1.3125\,in [mathin]. The outer bolt in each row tears toward the plate’s end edge:

[math] l_{c1} = L_{eh,wp} – \frac{d_{h}}{2} = (1.375\,in) – \frac{(1.3125\,in)}{2} = 0.71875\,in, \quad l_{c2} = s_{c} – d_{h} = (3\,in) – (1.3125\,in) = 1.6875\,in [math]

[math] \phi R_{n} = \phi \left[ \min\left(1.2\, l_{c1},\, 2.4\, d_{b}\right) 2t_{wp} F_{up} + \min\left(1.2\, l_{c2},\, 2.4\, d_{b}\right) 2t_{wp} F_{up} \left( n_{c} – 1 \right) \right] \frac{C}{n_{c}} [math]

[math] \phi R_{n} = (0.75) \times \left[ \min\left(1.2 \times 0.71875\,in,\, 2.4\,in\right)(1\,in)(65\,ksi) + \min\left(1.2 \times 1.6875\,in,\, 2.4\,in\right)(1\,in)(65\,ksi)(2 – 1) \right] \times \frac{10}{2} = 703.83\,kip [math]

DCR = 135.34 基普 / 703.83 基普= 0.192 < 1.0, 行

相互作用

The two directions are combined as a sum of squares, which treats the bearing strength as a circular interaction for a bolt loaded at an angle:

[math] \left( \frac{V_{u}}{\phi R_{n,v}} \right)^{2} + \left( \frac{P_{web}}{\phi R_{n,a}} \right)^{2} = \left( \frac{250}{957.94} \right)^{2} + \left( \frac{135.34}{703.83} \right)^{2} = 0.10508 [math]

DCR = 0.105 < 1.0, 行

步 15: 梁腹板上的螺栓轴承 (AISC 360-16 J3.10)

The beam web has standard holes, [mathin] d_{h} = 1.125\,in [mathin], and is only 0.46 in thick on the W27x84, so it is weaker in bearing than the pair of plates.

剪切方向

Below each web bolt there is either another hole or a long stretch of web down to the bottom flange, 所以每个螺栓都使用孔之间的净距离, [mathin] l_{c2} = 1.875\,in [mathin]:

[math] \phi R_{n} = \phi \min\left(1.2\, l_{c2},\, 2.4\, d_{b}\right) t_{w} F_{u}\, C = (0.75) \times \min\left(2.25\,in,\, 2.4\,in\right) \times (0.46\,in) \times (65\,ksi) \times (10) = 504.56\,kip [math]

DCR = 250 基普 / 504.56 基普= 0.495 < 1.0, 行

轴向方向

Along the beam, the bolt column nearest the beam end tears out toward it, 与 [mathin] l_{c1} = L_{eh,c} – d_{h}/2 = 0.6875\,in [mathin]:

[math] \phi R_{n} = \phi \left[ \min\left(1.2\, l_{c1},\, 2.4\, d_{b}\right) t_{w} F_{u} + \min\left(1.2\, l_{c2},\, 2.4\, d_{b}\right) t_{w} F_{u} \left( n_{c} – 1 \right) \right] \frac{C}{n_{c}} = 344.78\,kip [math]

DCR = 135.34 基普 / 344.78 基普= 0.393 < 1.0, 行

相互作用

[math] \left( \frac{250}{504.56} \right)^{2} + \left( \frac{135.34}{344.78} \right)^{2} = 0.39957 [math]

DCR = 0.400 < 1.0, 行

步 16: 腹板的块剪 (AISC 360-16 J4.3)

A block of the web plates can tear out under the shear, under the axial force, or under both. Each direction is checked with its own tear-out pattern, 两个比率的组合方式与轴承相同.

剪切载荷

The block shears along the inner bolt column to the bottom of the plates and tears in tension across the bottom row to the plate end. The tension area uses the slot length, [mathin] d_{h} = 1.3125\,in [mathin], and the shear area uses the slot width, 1.125 在:

[math] A_{nt} = 2t_{wp} \left[ (n_{c} – 1)\, s_{c} + L_{eh,wp} – (n_{c} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] = (1\,in) \times \left[ (1)(3\,in) + 1.375\,in – 1.5(1.375\,in) \right] = 2.3125\,in^{2} [math]

[math] A_{gv} = 2t_{wp} \left[ L_{ev,wp} + (n_{r} – 1)\, s_{r} \right] = 13.25\,in^{2} [math]

[math] A_{nv} = 2t_{wp} \left[ d_{wp} – L_{ev,wp} – (n_{r} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] = 7.9062\,in^{2} [math]

对于两个螺栓柱，块体上的拉应力不均匀, 所以 [mathin] U_{bs} = 0.5 [mathin], as the AISC Manual uses for multi-column bolt groups:

[math] \phi R_{n} = (0.75) \left( 0.6 \times 65 \times 7.9062 + 0.5 \times 65 \times 2.3125 \right) \le (0.75) \left( 0.6 \times 50 \times 13.25 + 0.5 \times 65 \times 2.3125 \right) = 287.62\,kip [math]

DCR = 250 基普 / 287.62 基普= 0.869 < 1.0, 行

轴向载荷

Under axial load, the report checks two patterns. 在L型图案中, the block tears in tension down the bolt rows and out the bottom edge, and shears along the top bolt row to the plate end:

[math] A_{nt} = 2t_{wp} \left[ (n_{r} – 1)\, s_{r} + L_{ev,wp} – (n_{r} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] = 7.9063\,in^{2} [math]

[math] A_{gv} = 2t_{wp} \left[ L_{eh,wp} + (n_{c} – 1)\, s_{c} \right] = 4.375\,in^{2} [math]

[math] A_{nv} = 2t_{wp} \left[ L_{wp} – L_{eh,c} – (n_{c} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] = (1\,in) \times \left[ 5.625\,in – 1.25\,in – 1.5(1.375\,in) \right] = 2.3125\,in^{2} [math]

[math] \phi R_{n,L} = (0.75) \left( 0.6 \times 65 \times 2.3125 + 1 \times 65 \times 7.9063 \right) \le (0.75) \left( 0.6 \times 50 \times 4.375 + 1 \times 65 \times 7.9063 \right) = 453.07\,kip [math]

在U (或C) 图案, the block between the top and bottom bolt rows pulls out, shearing along both outer rows:

[math] A_{nt} = 2t_{wp} \left[ (n_{r} – 1)\, s_{r} – (n_{r} – 1)\left( d_{h} + 0.0625\,in \right) \right] = 7.25\,in^{2} [math]

[math] A_{gv} = 2 \cdot 2t_{wp} \left[ L_{eh,wp} + (n_{c} – 1)\, s_{c} \right] = 8.75\,in^{2}, \quad A_{nv} = 2 \cdot 2t_{wp} \left[ (n_{c} – 1)\, s_{c} + L_{eh,wp} – (n_{c} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] = 4.625\,in^{2} [math]

[math] \phi R_{n,U} = 488.72\,kip [math]

[math] \phi R_{n} = \min\left( 453.07\,kip,\, 488.72\,kip \right) = 453.07\,kip [math]

DCR = 135.34 基普 / 453.07 基普= 0.299 < 1.0, 行

相互作用

[math] \left( \frac{250}{287.62} \right)^{2} + \left( \frac{135.34}{453.07} \right)^{2} = 0.84471 [math]

DCR = 0.845 < 1.0, 行

The shear term alone contributes 0.755 的 0.845.

步 17: Block shear of the beam web (AISC 360-16 J4.3)

Under axial load, a block of the beam web around the bolts can pull out of the beam end: tension between the top and bottom bolt rows, and shear along both rows to the end of the beam. 这是C模式.

[math] A_{nt} = t_{w} \left[ (n_{r} – 1)\, s_{r} – (n_{r} – 1)\left( d_{h} + 0.0625\,in \right) \right] = 3.335\,in^{2} [math]

[math] A_{gv} = 2t_{w} \left[ L_{eh,c} + (n_{c} – 1)\, s_{c} \right] = 3.91\,in^{2} [math]

[math] A_{nv} = 2t_{w} \left[ (n_{c} – 1)\, s_{c} + L_{eh,c} – (n_{c} – 0.5)\left( d_{h} + 0.0625\,in \right) \right] = 2.2713\,in^{2} [math]

[math] \phi R_{n} = (0.75) \left( 0.6 \times 65 \times 2.2713 + 1 \times 65 \times 3.335 \right) \le (0.75) \left( 0.6 \times 50 \times 3.91 + 1 \times 65 \times 3.335 \right) = 229.02\,kip [math]

DCR = 135.34 基普 / 229.02 基普= 0.591 < 1.0, 行

步 18: 腹板的剪切屈服和剪切断裂 (AISC 360-16 J4.2)

两个腹板承载完整的 250 接头上的斜切剪切力. 它们的总截面不得因剪切而屈服, 其穿过螺栓孔的净截面不得破裂.

剪切屈服 (情商. J4-3)

[math] A_{gv} = d_{wp} \times 2t_{wp} = (14.5\,in) \times (1\,in) = 14.5\,in^{2} [math]

[math] \phi R_{n,sy} = \phi\, 0.6\, F_{yp}\, A_{gv} = (1) \times 0.6 \times (50\,ksi) \times (14.5\,in^{2}) = 435\,kip [math]

剪切断裂 (情商. J4-4)

[math] A_{nv} = 2t_{wp} \left[ d_{wp} – n_{r}\left( d_{h} + 0.0625\,in \right) \right] = (1\,in) \times \left[ 14.5\,in – 5 \times (1.1875\,in) \right] = 8.5625\,in^{2} [math]

[math] \phi R_{n,sr} = \phi\, 0.6\, F_{up}\, A_{nv} = (0.75) \times 0.6 \times (65\,ksi) \times (8.5625\,in^{2}) = 250.45\,kip [math]

[math] \phi R_{n} = \min\left( 435\,kip,\, 250.45\,kip \right) = 250.45\,kip [math]

DCR = 250 基普 / 250.45 基普= 0.998 < 1.0, 行

This is the governing check of the whole beam splice. Five holes remove 41% of the plate depth, so shear rupture of the net section is far below shear yielding. Another bolt row or a deeper plate would add net area directly.

步 19: 腹板的张力屈服和断裂 (AISC 360-16 J4.1)

在轴向拉力下, 腹板承载 135.34 作为受拉构件，kip 跨接头的腹板力.

[math] \phi R_{n,ty} = \phi\, F_{yp}\, 2t_{wp}\, d_{wp} = (0.9) \times (50\,ksi) \times (1\,in) \times (14.5\,in) = 652.5\,kip [math]

[math] \phi R_{n,tr} = \phi\, F_{up}\, 2t_{wp} \left[ d_{wp} – n_{r}\left( d_{h} + 0.0625\,in \right) \right] = (0.75) \times (65\,ksi) \times (1\,in) \times \left[ 14.5\,in – 5 \times (1.1875\,in) \right] = 417.42\,kip [math]

DCR = 135.34 基普 / 417.42 基普= 0.324 < 1.0, 行

步 20: Tension rupture of the beam web with shear lag (AISC 360-16 D3, J4.1)

The web axial force also has to get into the beam. Here the bolts connect only the web, 因此法兰在承受应力方面滞后. The whole wide flange section is the tension member, and the shear lag factor uses [mathin] \bar{x} = 1.3614\,in [mathin], the distance from the web to the centroid of half the section, over the 3 连接长度:

[math] U = 1 – \frac{\bar{x}}{l} = 0.54639 [math]

[math] \phi R_{n} = \phi\, F_{u}\, U \left[ A – n_{r}\left( d_{h} + 0.0625\,in \right) t_{w} \right] = (0.75) \times (65\,ksi) \times (0.54639) \times \left[ 24.7\,in^{2} – 5 \times (1.1875\,in) \times (0.46\,in) \right] = 585.17\,kip [math]

DCR = 135.34 基普 / 585.17 基普= 0.231 < 1.0, 行

步 21: 腹板的抗压强度 (AISC 360-16 J4.4, E3)

Under axial compression the web plates span the gap between the beam ends as short columns. 每个板都可以自行弯曲, 所以回转半径为一 1/2 在盘子里, while the area is that of both plates.

和 [mathin] K = 1.2 [mathin] 和 [mathin] L_{b} = 3.5\,in [mathin], the same unbraced length as the flange plates:

[math] \frac{K L}{r} = \frac{(1.2) \times (3.5\,in)}{(0.5\,in) / \sqrt{12}} = 29.098 \gt 25 [math]

KL/r 以上 25, so J4.4 sends the plates to Chapter E. 细长如下 [mathin] 4.71\sqrt{E/F_{y}} = 113.43 [mathin], 所以方程. E3-2适用:

[math] F_{e} = \frac{\pi^{2} E}{\left( KL/r \right)^{2}} = \frac{\pi^{2} \times (29000\,ksi)}{(29.098)^{2}} = 338.03\,ksi [math]

[math] F_{cr} = 0.658^{F_{y}/F_{e}} F_{y} = 0.658^{(50/338.03)} \times (50\,ksi) = 46.998\,ksi [math]

[math] \phi R_{n} = \phi\, F_{cr}\, 2t_{wp}\, d_{wp} = (0.9) \times (46.998\,ksi) \times (1\,in) \times (14.5\,in) = 613.33\,kip [math]

DCR = 135.34 基普 / 613.33 基普= 0.221 < 1.0, 行

的 1/2 in web plates are thinner than the 3/4 in flange plates, so they cross the KL/r = 25 limit over the same 3.5 in length. Buckling only takes about 6% off the yield strength at this slenderness.

步 22: Web plate splice on the W27x94 side

The web plates and bolt layout are the same on the right, 所以板检查 (承载在板上, 板块剪切, 剪力, 张力和压缩) give the same results as on the left. The beam web checks change because the W27x94 web is 0.49 在厚, and the slip check uses [mathin] h_{f} = 0.85 [mathin] on this side:

[math] \phi R_{n} = (0.85) \times (0.3) \times (1.13) \times (0.85) \times (64\,kip) \times (2) \times (5) \times (2) = 313.51\,kip [math]

DCR = 284.28 基普 / 313.51 基普= 0.907 < 1.0, 行

设计检查总结

法兰板拼接

腹板拼接

The beam splice passes every check. Shear rupture of the web plates governs at 0.998 两侧, and tension rupture of the flange plates is next at 0.988. Both are net section checks through the bolt holes, so the plates, not the bolts or the beams, are what limit this splice. The detailing ratios of 1.000 mean the edge distances are at the code minimum, not that the connection is overstressed.

如果检查失败要更改什么

• 腹板剪切破裂或块剪切: add a bolt row and make the web plates deeper, 或者使用较厚的板材.
• Flange plate tension rupture: use a thicker flange plate. The plate is already as wide as the beam flange, so width is not available.
• Slip of the flange or web bolts: add a bolt column, change to a Class B faying surface on the web, or reduce the number of fillers so the filler factor goes up to 1.0.
• Block shear or bearing on the beam flange or web: increase the edge distance at the beam end, or add bolt columns to lengthen the shear planes.
• Beam tension or flexural rupture at the holes: these depend on the beam and the hole layout, so use fewer holes across the flange, or move the splice to a point of lower moment.
• 板压缩: shorten the unbraced length by tightening the gap or the beam edge distance, 或者使用更厚的板来降低 KL/r.

经常问的问题

How is the load shared between the flange plates and the web plates in a beam splice?

腹板承受所有剪力. The axial load is split by area: 网络占据了总面积的份额, 这里 135.34 基普的 300 基普, 其余部分由法兰承担, 各半. 力矩完全传递到法兰作为张力和压力偶. 在此示例中，每个法兰板都带有 266.52 基普.

为什么拼接螺栓的滑动至关重要?

The flange plates have oversized holes and the web plates have short slots parallel to the axial load. Both give the erector room to fit the beams together, 和AISC 360-16 J3.2 allows those holes only in slip-critical connections. Slip-critical bolts also keep the splice from moving when the moment or axial force reverses, so the beam behaves as continuous.

Why does the web plate check combine shear and axial results?

The web bolts are loaded diagonally, by the vertical shear and the horizontal axial force at the same time. The report checks bearing and block shear in each direction on its own, then adds the squares of the two ratios. A result below 1.0 means the combined load is inside the circular interaction curve. The slip check uses the resultant force directly.

Why is there a gap between the beam ends?

的 1 in gap gives erection tolerance, so the beams do not have to be cut to an exact length. Because the ends do not touch, no compression passes by direct bearing and all of it goes through the splice plates. The gap also sets the unbraced length of the plates for the compression check.

What happens when the two beams have different depths?

The flanges of the shallower beam sit inside the plane of the flange plates, so fillers or shims are packed in to make up the difference. Fillers reduce slip resistance, 这就是为什么 AISC 360-16 J3.8 uses a filler factor of 0.85 when there are two or more. This example also uses the shallower beam’s lever arm to find the flange force, which gives the larger force.

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. AISC 第 16 版手册与后续版本配对 360-22 规范. 条款编号和一些规定, 包括滑动关键螺栓的填充系数, 新版本中发生了变化, 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, 因此翼缘和腹板力较低.

Design a beam splice connection for free

此页上的每个数字都来自一个解决方案. Pick the beam splice configuration, enter your two beams, 盘子, 螺栓, 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.

免费设计连接

SkyCiv Connection Design 模块是本示例背后的连接设计软件. 它为您提供完整的计算报告，其中包含每个方程和您的数字, 就像上面的步骤一样, 加上每个容量和 DCR, 对于AISC 360-16 (LRFD 和 ASD) 并作为 4100:2020. 的 螺栓计算器 涵盖螺栓组自行检查.

购买连接设计模块

参考资料

• AISC 360-16, 钢结构建筑规范: B4.3, D3 (表D3.1), E3 (情商. E3-2, E3-4), F13.1 (情商. F13-1), J3.2, J3.3, J3.4 (表J3.4), J3.5 (表 J3.5), J3.8 (情商. J3-4, Table 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), J4.3 (情商. J4-5), J4.4 (情商. J4-6); Commentary Table C-A-7.1.
• AISC 钢结构手册, 15第版: 部分 1 截面属性.
• 使用 AISC 进行钢连接设计 360-16
• 螺栓 SkyCiv 连接设计