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構造3Dで偏心点荷重を適用する方法

An introduction to eccentric point loads in structural 3D modeling and analysis

When modeling a structure in SkyCiv Structural 3D, メンバーと接続は、メンバーのノードとラインで簡素化されます. ノード間のこれらの線は、単純さと連続性のために、常に各メンバーの重心を通過します. 実際には, メンバーに作用する荷重がその重心によって正当化できない場合に状況が発生します, これは偏心荷重です. Engineers need to think about eccentric loads when designing members because the addition of cross-sectional rotation, または ねじれ, できる, そしておそらくそうなるでしょう, 断面の限界状態に影響を与える.

例えば: a point load on top of a cantilevered floor from above, または補強材に取り付けられた梁の側面からぶら下がっている荷重. 偏心荷重とその解釈方法の簡単な図を図に示します。 1.

eccentric beam load

図 1: Example of eccentric load on an I-shaped cross-section

ソース: http://manual.midasuser.com

Lets take a look at an example in SkyCiv Structural 3D and apply an eccentric point load two different ways. 最初, lets assume we have a W14x22 beam that is 15 feet long with an eccentric point load at midspan of 10 キップ, 演技 12 inches away from the centroid. We will assume that the load is acting downward (-Y direction) and to the left side (+Z direction) of the member. また, 自重がオフであると仮定します, 簡単にするために.

単一のメンバーをモデル化する場合, make sure that your supports are correct when modeling an eccentric load. The analysis wont run with both supports of your beam set as 3D pins because neither support will be resisting rotation of the cross section. 私たちの場合には, the support further from the origin is only a 2D pin allowing rotation in the X and Y direction, coming from vertical and horizontal deflection. Lets take a look at our example member in the 3D modeling space:

スクリーンショット 2019-07-11 で 1.01.02 午後

今, lets looks at the two methods of accounting for the eccentricity of our load. Referring to Figure 1, in our case:

\({P} = {10} キップ)

\({e} = 12 inches = 1 foot\)

方法 1: Accounting for eccentricity by applying a Moment

図に示すように 1, we can account for the eccentricity of the load by applying an additional moment at the centroid of the member. This moment is found by taking the point load multiplied by the moment arm, または “e”. We still need to account for the point load itself, so there will be (2) loads at the identified location.

私たちの場合には:

\({M} = {P}*{e}\)

\({M} = 10 キップ * 1 foot = 10 kip-ft\)

述べたように, this moment is now applied at the same location along the member as the eccentric point load. SkyCiv recognizes positive moment as counter-clockwise around the axis that is being applied, which is around the global X-axis in our case. 図を参照 3 of these loads applied in SkyCiv 3D:

スクリーンショット 2019-07-11 で 1.12.30 午後

図 3: Modeling eccentric load by applying an additional moment

方法 2: Using rigid links

Another method is to use rigid links. リジッドリンク are thought of as imaginary members that rotate and translate with whatever its connected to. They do not deflect between their nodes and are entirely stiff. Rigid Links are identified in the 3D modeling space as light grey and have a “R” next to them, 図に示すように 4. Because they are used more for connecting elements and loads, they do need a size or section ID.

私たちの例では, ノード 6 is at midspan on the member. ノード 5 is at the same X-coordinate, だが 1.0 feet in the +Z direction; ノード 5 偏心荷重の実際の位置.

2 つのノード間のメンバーを作成/描画する, それをリジッド リンクとして割り当てます. You can do this by pressing the 高度な switch in the member window, その後に行きます タイプ and changing it to リジッドリンク. 適用後, the member should look as described above. With one end signifying the actual location of the eccentric load and the other end connected to the member in the perpendicular direction, the load can finally be applied. This is shown in Figure 4; the red arrow is pointing to the Rigid Link:

スクリーンショット 2019-07-11 で 1.26.58 午後

図 4: Using a rigid link to account for eccentricity of a point load

Final Comparison and Analysis:

Lets run a Linear Static Analysis and look at the results. We should be seeing the downward force of 10 kips in addition to a torsional component at the loading location. 両方

スクリーンショット 2019-07-11 で 1.30.17 午後

図 5: Both loading conditions for eccentric load

最初, lets look at the reaction and moment results (図 6):

スクリーンショット 2019-07-11 で 4.09.16 午後

図 6: Reactions and Moment results for both methods

As expected we see what we would expect from the same magnitude load and location along the member, but through the centroid.

その後, due to the eccentricity, we can observe that both members give the same result and show that the member is ALSO experiencing torsion (図 7):

スクリーンショット 2019-07-11 で 1.31.05 午後

図 7: Torsion analysis results for both methods

Trevor Solie構造エンジニア
トレバーソリー
構造エンジニア
ベン (民事)
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