Composite Element Forces
- mert.goktas (Unlicensed)
What is Composite Element Forces?
In Finite Element Analysis (FEA) the area of a slab being analyzed is often divided into smaller parts called shell elements. Each shell element is subject to forces, which are collectively known as Composite Element Forces. However, during the design process, it may become necessary to determine the forces and moments acting on the entire composite structure (e.g., girder and slab), rather than on individual elements.
The Composite Element Force method can be used to calculate the resultant forces and moments on the composite structure. To do so, the Building Design System (BDS) follows a specific procedure. First, a slicing plane is created on the structure, and any selected element that intersects this plane is included in the calculation. The BDS then records the forces reported by each element and its intersection position on the plane, along with a new combined center of gravity (COG) of the elements. The collected forces are then converted into the new COG and summed. Finally, for each slicing plane, the BDS generates a list of intersecting elements, the new combined COG of those elements , and the new combined forces and moments acting on the COG in the global system.
How Calculate Composite Element Forces for Shell Elements?
Element End Forces (External-Global)
To access the Local FE Analysis model of the last analyzed floor in the OpenBrIM App, simply open the app and navigate to the relevant section. The app automatically saves the model in the Building Design System (BDS) for easy access. From there, you can easily navigate to the FEA Local analysis of the floor you are currently working on.
To view the "Element End Forces (External-Global)" and Composite Element Forces (Sectional) values of the shell elements, start a new analysis in the app. Once the analysis is complete, you can view these values for each element in the results section.
To illustrate how to calculate the Composite Element Forces let's consider an example. First, select the S4 Shell element from the model. This element consists of four points in the coordinate system. Next, open the data spreadsheet in the app and navigate to the "Element End Forces (External-Global)" page using the tree view. From there, select "Self Weight" as the analysis result.
The Force and Moment values for the S4 Shell element can be found in the figure below.
Element | Node | Analysis Case | Force X (kip) | Force Y (kip) | Force Z (kip) | Moment X (kip - ft) | Moment Y (kip - ft) | Moment Z (kip - ft) | |
|---|---|---|---|---|---|---|---|---|---|
| 1 | S4 | 1.0000 | Self Weight | -0.2069 | 0.2268 | 7.8712 | -1.4319 | 4.7893 | -0.0962 |
| 2 | S4 | 2.0000 | Self Weight | -0.6147 | 0.5203 | -2.0810 | -0.0168 | 3.1735 | 0.0836 |
| 3 | S4 | 3.0000 | Self Weight | 0.0061 | -0.1601 | 0.2911 | 0.1141 | -0.8927 | -0.0254 |
| 4 | S4 | 4.0000 | Self Weight | 0.8156 | -0.5870 | -5.9260 | -1.2442 | -0.6435 | 0.0379 |
Element End Forces (External-Global)
Node | X (in) | Y (in) | |
|---|---|---|---|
| 1 | 1 | -307.78 | 1240.53 |
| 2 | 2 | -307.78 | 1223.96 |
| 3 | 3 | -321.28 | 1223.96 |
| 4 | 4 | -321.28 | 1240.53 |
Shell Elements Node Coordinates
Composite Element Forces (Sectional)
To view the Composite Element Forces (Sectional) values for the S4 Shell element in, navigate to the relevant page in the data spreadsheet using the tree view in the OpenBrIM App. To filter the results by element, click on the "Elements" column and select the S4 Shell Element. This will show you that there are four Composite Element Forces passing over the S4 Shell Element, named FEComp1 and FEComp115.
Assuming we want to capture the values for FEComp115, we can use the Element End Forces (External-Global) value by Composite Element Forces calculation method. To do so, select the values in row 4 corresponding to FEComp115 in the Composite Element Forces (Sectional) table. These values can then be read in the spreadsheet after calculation.
Elements | Force X (kip) | Force Y (kip) | Force Z (kip) | |
S4 | -0.8217 | -0.7471 | -5.7672 | |
Composite Object | Position | Moment X (kip-ft) | Moment Y (kip-ft) | Moment Z (kip-ft) |
FEComp115 | 5.0000 | 5.4225 | -7.0103 | -0.1695 |
Analysis Case | Position (ft) | c.o.g. X (global) ft | c.o.g. X (global) ft | c.o.g. X (global) ft |
Self Weight | 1.9583 | -25.8151 | 102.6871 | 0.0000 |
Composite Element Forces Calculation Method
fx=Fx
fy=Fy
fz=Fz
mx = Mx - (Fy * d.Z) + (Fz * d.Y)
my = My + (Fx * d.Z) - (Fz * d.X)
mz = Mz - (Fx * d.Y) + (Fy * d.X)
Start - End Condition
Ss= Start Condition Parameters
Se= Start-End Condition Parameters
Force or Moment Conversion | fx | fy | fz | Mx | My | Mz |
Start Node | -fx | fy | fz | -Mx | My | -Mz |
End Node | fx | -fy | -fz | Mx | -My | Mz |
As previously mentioned, the S4 Shell Element is composed of four points in the coordinate system. However, in order to use the Composite Element Forces Calculation method, we must identify two start nodes and two end nodes. To do so, we first need to determine the direction of the FEComp115 we have selected.
To find out the direction of FEComp115, we can go to the "Model" section of the OpenBrIM App. Based on our observation, we can see that the direction of FEComp115 goes from "-X" to "+X" in the Global coordinate system. Therefore, Node 3 and Node 4 will be the start nodes, while Node 1 and Node 2 will be the end nodes.
Once we have identified the start and end nodes, we can use the Composite Element Forces calculation method to calculate the force and moment for the S4 Shell Element. The resulting values will then be modified according to the start and end node status.
Force and Moment Calculation
Force X = (Fx1 + Fx2) * Se or (Fx3 + Fx4) * Se
Force X = (Fx1 + Fx2) * Se = (-0.2069 + -0.6147) * 1 = -0.8217 * 1 = -0.8217
Force X = (Fx3 + Fx4) * Ss = (0.0061 + 0.8156) = 0.8217 * -1 = -0.8217
Force Y = (Fx1 + Fx2) * Se or (Fx3 + Fx4) * Se
Force Y = (Fx1 + Fx2) * Se = (0.2268 + 0.5203) * -1 = 0.7471 * -1 = -0.7471
Force Y = (Fx3 + Fx4) * Ss = (-0.1601 + -0.5870) * 1 = -0.7471 * 1 = -0.7471
For X direction → De = Node1 X - c.o.g X = -307.78 - (-25.8151 * 12) = 2 in
Distance End= De = 2 in = 0.1667 ft
For X direction → Ds = c.o.g X - Node4 X = (-25.8151 * 12) - - 321.28 = 11.5 in
Distance Start= Ds =11.5 in = 0.9583 ft
Distance Iteration = 0.9583 ft / ( 0.9583 ft + 0.1667 ft ) = 0.85
Force Z = (Force Zs - Force Ze) * (Ds/ Ds+De) + Force Ze
Force Ze = (Fx1 + Fx2) * Se = (7.8712 + -2.0810) * -1 = 5.7902 * -1 = -5.7902
Force Zs= (Fx3 + Fx4) * Ss = (0.2911 + -5.9260) * 1 = -5.6349 * 1 = -5.6349
Force Z = (-5.6349 - -5.7902) * (0.9583 / ( 0.9583+0.1667 ) ) + -5.6349 = -5.7672
In order to calculate the Force Z, we need to determine the total Fz force of the Start Nodes and the total Fz force of the End Nodes. This calculation has already been performed using the procedures described earlier.
What are Force Negative & Positive Zones?
To calculate the mx, my, and mz moments, we first need to determine the moment value of each node individually. Once we have obtained these values, we must then collect the moment values separately for the start and end nodes.
After calculating Mstart and Mend moments, we need to iterate the results, taking into account their distance from the center of the shell element.
In case where Node 2 and Node 3 fall within the force negative zone, it is important to note that the results obtained from the force-related operations should be converted into negative values.
For Example
mx = Mxtotal + ( -Fy * d.Z ) + ( Fz * d.Y)
Mx2= -0.0168 + ( -0.5203 * 0 ) + ( -2.0810 * (8.285/12) ) * -1 . 1 = 1.4200
In the previous calculation, the value "0" is because there is no distance in the Z direction in the shell element.
In the previous calculation, the value of "-1" is attributed to the fact that "Node 2" is situated within the Force Negative Zone.
In the previous calculation, the value of "1" is assigned due to the positioning of "Node 2" as the End node in the FeComp115 direction of the local coordinate system.
After calculating the moment in all directions (x, y, z) for Node 2 and Node 3, the result of force values will be multiplied by -1.
Moment X
mx = Mxtotal + ( -Fy * d.Z ) + ( Fz * d.Y)
For X direction → De = Node1 X - c.o.g X = -307.78 - (-25.8151 * 12) = 2 in
Distance End= De = 2 in = 0.1667 ft
For X direction → Ds = c.o.g X - Node4 X = (-25.8151 * 12) - - 321.28 = 11.5 in
Distance Start= Ds =11.5 in = 0.9583 ft
Distance Iteration = Di = 0.9583 ft / ( 0.9583 ft + 0.1667 ft ) = 0.85
Mytotal = (Mend - Mstart) * Di + Mstart = (5.4225 - 5.4225) * 0.85 + 5.4225 = 5.4225 kip-ft
Moment | Node Location | Mx | (-Fy*d.Z) | (+Fz*d.Y) | Mx | Node start-end Con. | (1+2)<->(3+4) Result Iteration kip-ft | |
Mx1= | End | -1.4319 | 0 | 5.4344 | 4.0025 | 4.0025 | M(1+2) kip - ft | 5.4225 kip - ft |
Mx2= | End | -0.0168 | 0 | 1.4368 | 1.4200 | 1.4200 | ||
Mx3= | Start | 0.1141 | 0 | -0.2010 | -0.0869 | 0.0869 | M(3+4) kip - ft | 5.4225 kip - ft |
Mx4= | Start | -1.2442 | 0 | -4.0914 | -5.3356 | 5.3356 | ||
Mytotal | 5.4225 | kip-ft |
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Moment Y
my = Mytotal + ( -Fy * d.Z ) + ( Fz * d.Y)
For X direction → De = Node1 X - c.o.g X = -307.78 - (-25.8151 * 12) = 2 in
Distance End= De = 2 in = 0.1667 ft
For X direction → Ds = c.o.g X - Node4 X = (-25.8151 * 12) - - 321.28 = 11.5 in
Distance Start= Ds =11.5 in = 0.9583 ft
Distance Iteration = Di = 0.9583 ft / ( 0.9583 ft + 0.1667 ft ) = 0.85
Mytotal = (Mend - Mstart) * Di + Mstart = (-7.96 - (-1.54) ) * 0.85 + (-1.54) = -7.0107 kip-ft
Moment | Node Location | My | (+Fx*d.Z) | (-Fz*d.X) | Mx | Node start-end Con. | (1+2)<->(3+4) Result Iteration kip-ft | |
My1= | End | 4.7893 | 0.0 | 0.0 | 4.7893 | -4.7893 | M(1+2) kip - ft | -7.9628 kip - ft |
My2= | End | 3.1735 | 0.0 | 0.0 | 3.1735 | -3.1735 | ||
My3= | Start | -0.8927 | 0.0 | 0.0 | -0.8927 | -0.8927 | M(3+4) kip - ft | -1.5362 kip - ft |
My4= | Start | -0.6435 | 0.0 | 0.0 | -0.6435 | -0.6435 | ||
Mytotal | -7.0107 | kip-ft |
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Moment Z
mz = Mztotal + ( -Fx * d.Y ) + ( Fy * d.X)
For X direction → De = Node1 X - c.o.g X = -307.78 - (-25.8151 * 12) = 2 in
Distance End= De = 2 in = 0.1667 ft
For X direction → Ds = c.o.g X - Node4 X = (-25.8151 * 12) - - 321.28 = 11.5 in
Distance Start= Ds =11.5 in = 0.9583 ft
Distance Iteration = 0.9583 ft / ( 0.9583 ft + 0.1667 ft ) = 0.85
Mztotal = (Mend - Mstart) * Di + Mstart = (-0.2942 - 0.5464) * 0.85 + (0.5464) = -0.1695 kip-ft
Moment | Node Location | Mz | (-Fx*d.Y) | (+Fy*d.X) | Mz | Node start-end Con. | (1+2)<->(3+4) Result Iteration kip-ft | |
Mz1= | End | -0.0962 | 0.1428 | 0 | 0.0466 | 0.0466 | M(1+2) kip - ft | -0.2942 kip - ft |
Mz2= | End | 0.0836 | -0.4244 | 0 | -0.3408 | -0.3408 | ||
Mz3= | Start | -0.0254 | 0.0042 | 0 | -0.0212 | 0.0212 | M(3+4) kip - ft | 0.5464 kip - ft |
Mz4= | Start | 0.0379 | -0.5631 | 0 | -0.5252 | 0.5252 | ||
Mytotal | -0.1695 | kip-ft |
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As evident from the data, we have derived the Composite Element Forces (Sectional) values by utilizing the values obtained from the Element end Force (External - Global).
Please proceed to the next page.