AISC 360: 力矩连接设计实例

如果您阅读我们之前的文章, AISC 360: 剪力连接设计, you would have a good sense of how simple connections are designed under AISC 360. A shear connection only has to deliver the beam end reaction. A moment connection has to deliver that reaction and the end moment with it, which brings the supporting column into the problem. In this article we work through an example moment connection between two I-shaped members and go through the design criteria that have to be satisfied. We can also get to the same results directly through the SkyCiv连接设计 模块, which checks these connections to AISC 360-16 在 ASD 或 LRFD 中.

As in the shear connection example, the calculations here use the Allowable Stress Design (自卫队) 方法. 如果你不熟悉 ASD 和 LRFD 在结构设计上的区别, 确保 看看我们的视频 解释这个.

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在这个例子中, we evaluate the capacity of a Bolted Flange-Plated Fully-Restrained (阻燃剂) Moment connection between a W18x50 beam and a W14x99 column, using the dimensions, welds and loads shown below. The connection has to support the beam end vertical reaction and the developed end moment. Compared with a shear connection, the difference is the pair of plates carrying the beam flange forces onto the supporting column flange.

The flange plates turn the beam end moment into a tension and compression couple. The top plate pulls, the bottom plate pushes, and both forces land on the column flange as concentrated forces. That is why a moment connection needs the column local checks that a shear connection does not.

给定的:

服务水平负载 & 材料:

静载的垂直剪力 (虚拟机) = 7.0 ps
活荷载的垂直剪力 (VL) = 21.0 ps

静载力矩 (医学博士) = 42.0 基普英尺
来自活荷载的力矩 (机器学习) = 126.0 基普英尺

板材材质: ASTM A36, 风 = 36 KSI, Fu = 58 KSI
梁柱材料: ASTM A992, 风 = 50 KSI, Fu = 65 KSI

梁柱几何:

光束: W18x50; BF = 7.50 在, tf = 0.570 在, d = 18.0 在, tw = 0.355 在, X = 88.9 在^3
柱: W14x99; BF = 14.6 在, tf = 0.780 在, d = 14.2 在, tw = 0.485 在, kdes = 1.38 在
法兰盘: 3/4 在厚; 7.0 在x 12.5 在维度上
腹板: 3/8 在厚; 5.0 在x 9.0 在维度上

灯具 (螺栓和焊缝):
法兰: (8) – 7/8-在.-diameter ASTM F3125 Grade A325-N bolts in standard holes
腹板: (3) – 7/8-在.-diameter ASTM F3125 Grade A325-N bolts in standard holes

70-ksi 电极圆角. A325 和 A490 是 ASTM F3125 范围内的牌号, which consolidated the older standalone bolt specifications.

负载计算:

LRFD 负荷 (仅供参考):

终极垂直反应 ([R_ü) = 1.2 (7.0 ps) + 1.6 (21.0 ps) = 42.0 ps
终极时刻 (m_ü) = 1.2 (42.0 基普英尺) + 1.6 (126.0 基普英尺) = 252.0 基普英尺

自卫队 负荷:

允许垂直反应 ([R_一个) = 7.0 ps + 21 基普 = 28.0 ps
容许力矩 (m_一个) = 42.0 基普英尺 + 126 基普英尺 = 168.0 基普英尺

Everything below is checked against the ASD loads. Keep the two methods apart: ASD compares service loads to allowable strength, LRFD compares factored loads to design strength, and the LRFD figures above are carried only so you can compare the two.

基于 SkyCiv 连接设计软件的解决方案:
勘误表: 本例中的法兰盘宽度为 7.0 在 但计算中使用的宽度是 7.50 在, 因此价值的差异.

 

法兰力
Every check that follows is driven by one number, the force in the flange plate. The end moment is resolved into a couple acting at the plate centroids, so the lever arm is the beam depth plus one plate thickness:
P_的 = [ 168.0 基普英尺 (12 英寸/英尺) ] / (18.0 在 + 0.75 在) = 107.5 ps

 

法兰盘到 W14x99 法兰, 焊接强度
角焊缝强度, Ω = 2.0
焊缝尺寸, t = 0.375 在
F_净重 = 0.6 F_埃克斯 [ 1.0 + 0.5 没有^1.5 (θ) ]
在哪里, θ = 载荷与焊缝轴线的夹角
= 90, 用于横向加载的焊缝
= 0, 用于纵向受力焊缝

单位尺寸焊缝强度:
允许焊接应力, F_啊 = 0.6 (70KSI) / 2.0 = 21 KSI
横向长度, 升_Ť = 7 在
纵向长度, 升_升 = 0 在
总有效长度, 升 = 升_Ť (1.5) + 升_升 (1.0) = 10.5 在
的 1.5 on the transverse length is the directional strength increase, 1.0 + 0.5 没有^1.5(90).
([R_一个 / 一个) = 21 KSI (10.5 在) = 220.5 ps / 在

有效尺寸 (喉) 角焊缝, 一个:
0.707 = 的余弦或正弦 45 度数
a = (0.707) t = 0.265 在

Two welds, one each side of the plate:
[R_一个 = ([R_一个 / 一个) 一个 (2) = 220.50 (0.265 在) 2 = 116.9 ps
设计容量比, 直流电:
所需负载, R = 107.5 ps
总容量, [R_一个 = 116.9 ps
DCR = (107.5 / 116.9) = 0.919, 行

 

色谱柱局部检查
These four checks ask whether the W14x99 can accept the flange force without local stiffening. All of them are compared against the same flange force:

法兰力, P_的 = 107.5 ps

• 网络本地收益, Ω = 1.5
  [R_ñ / Ω = [ F_是 Ť_w (5ķ + 升_b) ] / Ω = 50ksi (0.485在) [ 5(1.38在) + 0.75在 ] / 1.5 = 123.7 ps
  这里 Ť_w is the column web thickness and 升_b the bearing length, taken as the flange plate thickness.
  设计容量比, 直流电:
  法兰力, P_的 = 107.5 ps
  总容量, [R_一个 = 123.7 ps
  DCR = (107.5 / 123.7) = 0.869, 行

• 法兰局部弯曲, Ω = 1.67
  [R_ñ / Ω = [ 6.25 F_和 Ť_F² ] / Ω = [ 6.25 (50KSI) (0.78在)² ] / 1.67 = 113.8 ps
  设计容量比, 直流电:
  法兰力, P_的 = 107.5 ps
  总容量, [R_一个 = 113.8 ps
  DCR = (107.5 / 113.8) = 0.944, 行

• 网络本地瘫痪, Ω = 2.0
  [R_ñ / Ω = 0.8 Ť_w² [ 1 + 3 ( 升_b / d ) ( Ť_w / Ť_F )^1.5 ] ( EF_和 Ť_F / Ť_w)^0.5 / Ω
  = 0.8 (0.485在)² [ 1 + 3 (0.05) (0.62)^1.5 ] [ (29000KSI) (50KSI) (0.78在) / 0.485在 ] ^0.5 / 2.0
  = 154.8 ps
  设计容量比, 直流电:
  法兰力, P_的 = 107.5 ps
  总容量, [R_一个 = 154.8 ps
  DCR = (107.5 / 154.8) = 0.694, 行

• 腹板压缩屈曲, Ω = 1.67
  [R_ñ / Ω = [ 24 Ť_w³ ( EF_和 )^0.5 / H ] / Ω
  = 24 (0.485在)³ [ (29000KSI) (50KSI) ] ^0.5 / 14.2在 (1.67)
  = 139.0 ps
  The full column depth is used here in place of H, the clear distance between flanges less the fillets, which is conservative.
  设计容量比, 直流电:
  法兰力, P_的 = 107.5 ps
  总容量, [R_一个 = 139.0 ps
  DCR = (107.5 / 139.0) = 0.773, 行

None of the four column local checks governs, so the W14x99 takes the flange force without transverse stiffeners for these limit states. Had any of them exceeded 1.0, the fix would be stiffeners or a doubler plate rather than a larger flange plate, because the capacity that ran out belongs to the column.

 

W18x50 法兰, 法兰盘拉伸屈服
元素抗拉强度, Ω = 1.67

[R_ñ / 它们不会带来与矩连接相同的设计挑战_和 一个_G / Ω = (36KSI) (7.5在) (0.75在) / 1.67 = 121.3 ps

设计容量比, 直流电:
法兰力, P_的 = 107.5 ps
总容量, [R_一个 = 121.3 ps
DCR = (107.5 / 121.3) = 0.887, 行

 

W18x50 法兰, 法兰盘压缩屈服
压缩元素的强度, Ω = 1.67

[R_ñ / 它们不会带来与矩连接相同的设计挑战_和 一个_G / Ω = (36KSI) (7.5在) (0.75在) / 1.67 = 121.3 ps

The compression plate is checked on the gross section because the bolt holes are filled in bearing. It matches the tension yielding value because the plate is short enough between the column face and the first bolt line for slenderness not to reduce it.

设计容量比, 直流电:
法兰力, P_的 = 107.5 ps
总容量, [R_一个 = 121.3 ps
DCR = (107.5 / 121.3) = 0.887, 行

 

W18x50 法兰, 法兰盘拉伸断裂
断裂中的元素强度, Ω = 2.0
剪切滞后因子, ü 来自 AISC 规范表 D3.1: 1.0

[R_ñ / 它们不会带来与矩连接相同的设计挑战_ü 一个_Ë / Ω = (58KSI) [ 7.5在 – 2 (1在) ] (0.75在) (1.0) / 2.0 = 119.6 ps

Two holes are deducted across the plate width. 的 1 in deduction is the 7/8 in bolt diameter plus 1/8 在, which is the standard hole allowance used for net area.

设计容量比, 直流电:
法兰力, P_的 = 107.5 ps
总容量, [R_一个 = 119.6 ps
DCR = (107.5 / 119.6) = 0.899, 行

 

所有检查结果汇总表
以下是为此连接完成的所有必要设计检查的 SkyCiv 连接设计模块汇总表. 并非所有这些检查都显示在本文中，但可以通过 PDF 获取，您可以在此处下载: 连接设计报告示例 II.B-1-ASD

Of the checks worked through above, flange local bending governs at 0.944. That is the one to watch if the beam end moment grows, and it is a column property, so a heavier flange plate would not help.

相似地, LRFD 版本示例可以在此链接中找到: 连接设计报告示例 II.B-1-LRFD

Run This Example Yourself
Enter the W18x50, the W14x99 and the flange plates, and the module returns every check above with its utilization ratio and the clause behind it. 它在浏览器中运行, 无需安装任何东西.

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参考资料

• AISC 360-16, 钢结构建筑规范
• AISC 设计实例 v14.1 (示例 II.B-1, 第IIB-2页到 13)
• SkyCiv连接设计软件: https://skyciv.com/structural-software/connection-design/
• Flange plate connection calculator: https://skyciv.com/structural-software/connection-design/flange-plate-connection-calculator/