	Applies To
	Product(s):	AutoPIPE,
	Version(s):	All
	Area:	Report
	Original Author:	Bentley Technical Support Group

Logged Nov 2014, AutoPIPE V8i 09.06.01.10

Problem:

Can you please explain the forces and moments, specifically, why in the middle of a segment the magnitude of the forces flip from (-)ve to (+)ve at the same node point.

Solution:

Before reading this article, please see the following AutoPIPE help section:

Help > Contents> Contents Tab> Reference Information> Results Interpretation> Pipe Forces and Moments: Global Option, read this entire document.

Key points to remember:

Key Points to Keep in Mind When Reviewing Forces and Moments Reports in AutoPIPE

Start with the Coordinate System
- Reports can be in Global or Local coordinates. Always confirm the system by checking the report header.
- Unless otherwise noted, this article uses Global coordinates..
Understand Segment Direction and Node Faces
- Every pipe segment has a defined direction, which is critical for interpreting forces and moments.
- Each node has two faces:
  - Negative (-) side: immediately before the node point
  - Positive (+) side: immediately after the node point
Cross-Section Concept
- Forces and moments act on the exposed cross-section created by “cutting” the pipe at each of the node points two faces.
- The reported values represent loads acting on that exposed face after removing the segment up to that point.
Sign Convention
- Positive forces and moments act in the positive X, Y, Z directions of the chosen coordinate system (Global or Local).
Result Reporting Rules
- If forces and moments are identical on both faces of a node, only one set of results is shown (e.g., A01).
- If values differ, two sets are reported (e.g., A01 - and A01 +).
Excluded Loads
- Pipe weight, contents weight, pressure, and thermal loads will be ignored in this KB article.

Example #1:

Consider a cantilever beam modeled as a single pipe segment E, with three node points:

- E00 – the anchor point at the origin
- E02 – the free end of the segment
- Segment direction – along the positive Z-axis (to the right)
- A concentrated force of 1000 is applied at the free end (E02) in the +Z-axis direction.

Important Note:
The applied force does not remain localized at the point of application E02. Instead, it is transmitted through the connected piping system along the load path until it reaches a point of restraint, such as an anchor or rigid support. In this example, the force propagates toward the anchor at E00.

Forces and Moments at E00(+):

What are the forces and moments acting at node point E00(+)?

To understand the forces and moments acting on the positive face of node point E00, imagine starting at the beginning of the segment and moving in the segment direction toward E00. At this point, remove all piping up to just beyond E00, leaving the exposed cross-section immediately after the node (as shown in the red box in the referenced image below). This exposed face represents the cut section where AutoPIPE calculates the reported forces and moments.

Since a concentrated force of +1000 units was applied at the free end (E02) in the positive Z-axis direction, the remaining piping system must stay in equilibrium. To achieve this, the exposed cross-section at E00 (+) must resist the applied load with an equal and opposite force. Therefore, AutoPIPE reports a Global Force of 1000 in the -ve Z-axis direction for E00 (+), shown as the red arrow. Because there are no rotational restraints or applied moments in this simple model, no moments are calculated or reported for this face.

Finally, note that E00 is the start of the segment, so there is no -ve face associated with this node. As a result, only one set of results is generated and displayed for E00 (+) in the Forces and Moments report.

Forces and Moments at E01(-):

What are the forces and moments acting at node point E01(-)?

Next, consider node point E01. Starting from the beginning of the segment (E00), move in the segment direction to E01. To evaluate the forces acting on the negative face of this node, remove all piping up to just before E01, leaving the exposed cross-section immediately preceding the node (highlighted in red in the image below). This cut face represents the section where AutoPIPE calculates the reported forces and moments.

For the remaining piping system to remain in equilibrium, this exposed cross-section must resist the applied load at the free end (E02). Since a 1000 force acts in the +ve Z-axis direction at E02, the cut face at E01 (-) must provide an equal and opposite reaction. Therefore, AutoPIPE reports a Global Force of 1000 in the -ve Z-axis direction for E01 (-), shown as the red arrow. As with the previous example, there are no rotational restraints or applied moments in this model, so no moments are calculated or reported for this node.

Forces and Moments at E01(+):

What are the forces and moments acting at node point E01(+)?

Now consider the positive face of node point E01. Starting from the beginning of the segment (E00), move in the segment direction past E01. To evaluate the forces acting on this face, remove all piping up to just after E01, leaving the exposed cross-section immediately beyond the node (highlighted in red in the image below). This cut face represents the section where AutoPIPE calculates the reported forces and moments.

For the remaining piping system to remain in equilibrium, this exposed cross-section must resist the applied load at the free end (E02). Since a 1000 force acts in the +ve Z-axis direction at E02, the cut face at E01 (+) must provide an equal and opposite reaction. Therefore, AutoPIPE reports a Global Force of 1000 in the -ve Z-axis direction for E01 (+), shown as the red arrow. As with the negative face, there are no rotational restraints or applied moments in this model, so no moments are calculated or reported for this node.

Forces and Moments at E02(-):

What are the forces and moments acting at node point E02(-)?

Finally, consider node point E02 (-). Starting from the beginning of the segment (E00), move in the segment direction to E02. To evaluate the forces acting on the -ve face of this node, remove all piping up to just before E02, leaving the exposed cross-section immediately preceding the node (highlighted in red in the image below). This cut face represents the section where AutoPIPE calculates the reported forces and moments.

For the remaining piping system to remain in equilibrium, this exposed cross-section must resist the applied load at the free end. Since a force of 1000 acts in the +ve Z-axis direction at E02, the cut face at E02 (-) must provide an equal and opposite reaction. Therefore, AutoPIPE reports a Global Force of 1000 in the -ve Z-axis direction for E02 (-), shown as the red arrow. As with previous nodes, there are no rotational restraints or applied moments in this model, so no moments are calculated or reported.

Printed Forces and Moments report:

Conclusion

The applied force of 1000 at the free end propagates through the segment toward the anchor at E00, and AutoPIPE reports reactions at each node face to maintain equilibrium.

This illustrates how AutoPIPE distributes forces along the segment and reports them based on cut faces and sign conventions.

Since Forces and Moments results are the same on both sides of a node point (+ve and -ve) only one set of results are printed per node point.

Example #2:

Building on Example #1, only change is the segment direction is now -ve Z-axis direction.

Remember, the concentrated force of 1000 acts at the free end (F02) in the +ve Z-axis direction. As mentioned, this force does not remain localized; it propagates through the segment toward the anchor at F00.

Forces and Moments at F02(+):

What are the forces and moments acting at node point F02(+)?

Using the same approach as in Example #1, start from the segment origin (F02) and move in the segment direction to the node in question, F02 (+). Remove all piping up to just after this node, leaving the exposed cross-section immediately beyond F02 (highlighted in red in the image below).

After defining the cut face at F02 (+), note that there are no additional loads acting on the remaining portion of the model. Therefore, unlike Example #1, no balancing force is required to keep the piping in equilibrium. However, remember the principle: “a force does not remain localized; it propagates through the segment toward the anchor at F00.” This means the concentrated load applied at F02 still propagates through the segment to the anchor. As a result, AutoPIPE reports a force of 1000 in the +ve Z-axis direction at F02 (+). Again, since there is only one set of results, the report shows F02 = 1000 (Z-axis).

Forces and Moments at F01 and F00:

What are the forces and moments acting at node points F01 and F00?

Similar to F02, the cut faces at F01 (-), F01 (+), and F00 (+) report forces based on the same principle: the applied load of 1000 in the +ve Z-axis direction propagates through the segment toward the anchor. Therefore, AutoPIPE reports 1000 in +ve Z-axis for each of these faces, with no moments calculated.

Printed Forces and Moments report:

Conclusion

By reversing the segment, the magnitude of the force remains exactly the same. However, direction of the force changes. This demonstrates how segment direction and cut-face definitions influence the Forces and Moments report.

Example #3

Building on Example 1 and 2, suppose the piping was composed of 2 segments, Segment L, origin at anchor node point L00, progressing in the +ve Z-axis direction to node point L01, node point L01 is the split point between segments L and M, segment M continues in the same axis direction to node point M01. Again, at the end, 1000 force acting in the +ve Z-axis direction, as imaged below.

Keep in mind, the concentrated force will not remain localized at the point of application. Instead, it propagates through the connected piping system along the load path until it reaches a point of restraint, such as an anchor or a rigid support. In this case towards the anchor at L00:

Forces and Moments at all node points

Question: What are the forces and moments going to be at all node point?

Will the forces act all to the LEFT, all to the right, split half to the LEFT and half to the RIGHT?

Answer:

For those who voted, half the moment would act in the +ve Z-axis and the half the moments would act in the -ve Z-axis, you are correct?

Why?

Correct, because of how the forces and moments are determined in examples 1 and 2. Segment L node points L00 and L01 (-ve) would be processed as shown in example #1, meanwhile segment M node points M01 and L01 (-ve) would be processed as explained in example #2. These values are substantiated by reviewing the Forces and Moments output reports.

Printed Forces and Moments report:

Conclusion

This example demonstrates how AutoPIPE calculates and reports forces when two segments share a common node and have opposite segment directions. The applied force at M01 in the +ve Z-axis direction generates reactions at connected node points based on the segment direction for segments L and M. The force at each node point was determined using the same cut-face philosophy as in previous examples, applied across the shared node L01.

Note, understanding segment progression and direction is critical for interpreting the Forces and Moments report. The sign of reported forces depends on the orientation of each segment relative to given load.

If you have concerns about how the forces and moments are calculated in this 3rd example, reverse one of the segments (A or B but not both), so that both segments are progressing in the same direction. Again, generate a new forces report, this should be akin to example #1 or #2 above.

Example #4

Building on Example 1, same exact model except a new node point (Jxx) and concentrated force = 750 was added (imaged below). What are the forces and moments at Node points Jxx and J01?

Remember, the concentrated forces will not remain localized at their points of application. Instead, they will propagate through the connected piping system along the load path until it reaches a point of restraint, such as an anchor or a rigid support. In this case towards the anchor at J00

Forces and Moments at Jxx(-):

What are the forces and moments acting at node point Jxx(-)?

Using the same approach as in previous examples, start at the segment origin (J00) and move in the segment direction to the node of interest (Jxx). Remove all piping from the beginning of the segment up to just before Jxx, leaving the exposed cross-section immediately preceding the node (highlighted in red in image below).

For the remaining piping to stay in equilibrium, this cut face must resist the net load acting on the rest of the segment. In this case, the required force is 250 (calculated as 1000 – 750) acting in the -ve Z-axis direction (shown by the red arrow). This is the force reported by AutoPIPE for Jxx (-). Since the model has no rotational restraints, no moments are calculated or reported at this node point.

Forces and Moments at Jxx(+):

What are the forces and moments acting at node point Jxx(+)?

Repeat the same process as before: start at the segment origin (J00) and move in the segment direction to the node of interest (Jxx). Remove all piping from the beginning of the segment up to just after Jxx, leaving the exposed cross-section immediately beyond the node (highlighted in red in the image below).

For the remaining piping to stay in equilibrium, this cut face must resist the total applied load on the rest of the segment. In this case, the required force is 1000 acting in the -ve Z-axis direction (shown by the red arrow). This is the force reported by AutoPIPE for Jxx (+). Since the model has no rotational restraints, no moments are calculated or reported.

Forces and Moments at J01 and J02:

What are the forces and moments acting at node point J01 and J02?

The results at these node points would be exactly the same as mentioned in Example #1.

Printed Forces and Moments report:

Conclusion

This example reinforces the concepts learned in previous scenarios and shows how they apply to a more complex case. By following the same general procedure established earlier—identifying segment direction, defining cut faces, and applying equilibrium principles—it becomes straightforward to determine the forces and moments reported at each node point.

Example #5

Given the following piping arrangement (imaged below), concentrated forces acting in opposite directions and anchor on tee branch (2 units long), calculate the forces and moments at A02.

Note:

This is a completely different scenario in comparison to examples above. However, by applying the principles and methods demonstrated earlier, one can systematically investigate this piping system to understand how AutoPIPE calculates forces and moments.

The concentrated forces will not remain localized at their points of application. Instead, they will propagate through the connected piping system along the load path until it reaches a point of restraint, such as an anchor or a rigid support. In this case towards the anchor at B01

Forces and Moments at A02 (-) segment A:

What are the forces and moments acting at node point A02 (-) on segment A?

Starting at the segment origin (A00), move in the segment direction to the node of interest (A02). Remove all piping from the beginning of the segment up to just before A02, leaving the exposed cross-section immediately preceding the node (highlighted in red in the image below).

As explained earlier, concentrated forces do not remain localized, they propagate through the piping system until they reach a point of resistance. In this case, the point of resistance is the anchor at B01 and the branch piping between the anchor and the header. Therefore, the only load acting on the cut face just before A02 is 750 in the -ve Z-axis direction (shown by the red arrow). This is the force reported by AutoPIPE for A02 (-). Since there is no rotational restraint or loads causing a moment at this node, no moments are calculated or reported.

Forces and Moments at A02 (+) segment A:

What are the forces and moments acting at node point A02 (+) on segment A?

Once again, start at the segment origin (A00) and move in the segment direction to the node of interest (A02). Remove all piping from the beginning of the segment up to just after A02, leaving the exposed cross-section immediately beyond the node (highlighted in red in the image below).

As noted earlier, concentrated forces do not remain localized, they propagate through the piping system until they reach a point of resistance. In this case, the point of resistance is the anchor at B01 and the branch piping between the anchor and the header. Therefore, the only load acting on the cut face just after A02 is 1000 in the -ve Z-axis direction (shown by the red arrow). This is the force reported by AutoPIPE for A02 (+). Since there is no rotational restraint or loads causing a moment at this node, no moments are calculated or reported.

Forces and Moments at A02, segment B:

What are the forces and moments acting at node point A02 on segment B ?

Pay close attention to this explanation. Starting at the segment origin (A02 on Segment B), move in the segment direction to the node of interest (A02 on Segment B). Remove all piping from the beginning of the segment up to just after this node, leaving the exposed cross-section immediately beyond A02 (highlighted in red in the image below).

As noted earlier, concentrated forces do not remain localized, they propagate through the piping system until they reach a point of resistance. In this case, the point of resistance is the anchor at B01. Therefore, the only load acting on the cut face just after A02 is 250 (calculated as 1000 – 750) in the +ve Z-axis direction (shown by the red arrow). This is the force reported by AutoPIPE for this face. While no moments are calculated at this node because there is no rotational restraint, this load will generate a moment of 500 (calculated as 250 × 2) acting in the +ve X-moment direction (right hand rule) on the anchor at B01, as shown in the report below.

Printed Forces and Moments report:

Understanding Node point sign convention

In a new example model below with output reports, answer these 2 basic questions:

1. Why are all of the reported forces at A00 and A01 +ve?

2. Why are the anchor restraint loads all -ve for A00, however all +ve for A01?

Model details:

Press = 300 PSI

Temp = 150 Deg F

Amb. Temp = 70 deg F

Analysis Set:

Pressure Stiff= P1

Hot modulus = T1

Pressure Extent. = Yes

Ignore Friction GR = Yes

Question:

What is driving the sign convention for the forces at A00 and A01, why are all of the forces +ve?

Answer:

In this particular example model, with this piping arrangement, support system, loading, segment direction (Segment started at A00 and ended at A01), and Results Interpretation for Pipe Forces and Moments: Global Option. All of the results are +ve.

To further help answer this question, ask yourself; what side of the node point are the anchors on when the free body diagram is applied for calculating Forces and moments?

Note, review AutoPIPE help... Help > Contents> Contents> Reference Information> Results Interpretation> Pipe Forces and Moments: Global Option.

Now knowing these details of how forces and moments are calculated, plus segment direction, and understanding Anchor A00 is located on the upstream side while Anchor A01 is located on the downstream side of their respective node points.. This is very important information. The calculated forces report are on the downstream side, unless the values are different, then 2 sets of results (+ve and -ve) are printed at each node point.

Again, what is driving the sign convention for the forces at A00 and A01?

For A00, due to the laws of equilibrium, the upstream results are equal and opposite of the downstream side results. Conversely, Anchor A01 is located on the downstream side, thus the reported forces and moments will match both values and direction.

There are 3 good exercises that should aid with understanding the results and drive home the concept of how the results are reported in AutoPIPE:

1. Animate load case, see animate shape below:

From this vantage point see how the piping is responding to load case GT1P1. Now it is easy to understand what is happening at the anchors. Per this load case, thermal and pressure loadings is pushing the elbow A05 piping in the -X-dir, thus causing the -ve loading on downstream side of Anchor node point A00. Conversely, thermal and pressure loadings is pushing the piping against the upstream side of anchor node point A01 (+X-dir), thus causing the elbow displacement at A03.

2. Reverse Segment command (Home > Operations > Segments > Reverse Segment(s)),

Segment now starts at A01 and progresses towards A00.

Again, notice how all of the results are now equal and opposite that of the original segment direction. All of the forces results are -ve, and the restraint load still have opposite signed values.

3. Rotate the entire model 180 about A00, and review the results

Note, if the model was rotated 180 deg then you will see the same values but in opposite direction, see image below (note, vertical direction is not rotated, therefore vertical results has the same directional sign as before rotation).

Question:

What is driving the sign convention for the restraint loads at A00 and A01?, Why are the anchor restraint loads all -ve for A00, however all +ve for A01?

Answer:

Very similar to the concepts mentioned above, ask yourself, what side of the node point are the anchor on when the free body diagram is applied? Next, determine the segment direction....etc...

Again, the reason for the signed results is based upon how the model is constructed, applied loads, etc.. In this case, GrT1P1 is applying a -ve X-dir load on the Anchor at node point A00 and exerting a +ve X-dir load on the Anchor at node point A01

05. Forces and Moments output Results appear to have both (+)ve and (-)ve at the same point in AutoP

Problem:

Solution:

Key Points to Keep in Mind When Reviewing Forces and Moments Reports in AutoPIPE

Example #1:

Example #2:

Example #3

Example #4

Understanding Node point sign convention

See Also