1. What is the P-Delta Effect?
The P-Delta effect refers to the additional moment generated in vertical structures such as columns when lateral displacement occurs under vertical loads. This means that the displacement caused by the primary load induces a secondary force, which is a nonlinear geometric effect.
(AISC Steel Design Guide - 28. Fig. A-4 First-and second-order effects - cantilever column)
The P-Delta effect is generally divided into two categories: Big P-Delta effect and Small P-Delta effect.
1) Big P-Delta Effect
This occurs when a horizontal load causes a displacement difference between the top and bottom of a column, and an additional moment is generated due to the vertical load on this displacement difference.
2) Small P-Delta Effect
This occurs when the geometric stiffness of a vertical member changes due to a vertical load, resulting in an additional moment.
In Korean Road Bridge Design Standards, the P-Delta effect is considered using the moment magnification factor method or the system P-Delta analysis method.
(General Bridges - Limit State Design Method)
Recent bridge piers are becoming thinner and longer, indicating a need for design considerations that adequately reflect the P-Delta effect due to potentially larger horizontal displacements.
2. P-Delta Analysis Function in midas Civil
midas Civil is a structural analysis software for the civil engineering field. It includes features to account for the P-Delta effect.
Figure 3. P-Delta function in midas Civil
In fact, the P-Delta function in midas Civil is an approximate analysis that considers relative displacement and stiffness deformation within elastic analysis. It cannot fully reflect the true nonlinear behavior of the P-Delta effect but is recognized as a sufficient approximation.
Figure 4: P-Delta analysis within the elastic range
3. Verification to Understand the principle of P-Delta Analysis in midas Civil
Comparison 1: Modeling Without Applying the P-Delta Function
→ The final displacement and bending moment do not change with or without the vertical load, indicating that the midas Civil does not inherently consider the secondary moment due to displacement from horizontal forces.
Comparison 2: Result Comparison With and Without P-Delta Function Application
→ With the application of the P-Delta function, the displacement at the top of the column increased from 0.1343m to 0.1365m, and the bending moment at the bottom of the column increased from 10,000.0 kN·m to 10,136.5 kN·m.
→ Here, 10,136.5 kN·m includes the secondary moment of 136.5 kN·m (1,000.0 kN x 0.1365m) due to displacement added to the initial 10,000.0 kN·m.
4. Conclusion
The P-Delta effect is a type of nonlinear geometric effect where a secondary moment is generated due to vertical loads and displacements, leading to secondary displacements and increased member forces. However, the P-Delta function supported in midas Civil only increases the member forces considering the primary displacement due to elastic deformation. According to design standards, this approach sufficiently reflects the approximate behavior due to the P-Delta effect.
References
American Institute of Steel Construction. (2013). AISC Steel Design Guide - 28: Stability Design of Steel Buildings.
Korea Bridge and Structural Engineering Association, Bridge Design Core Technology Research Group. (2015). Commentary on Road Bridge Design Standards (Limit State Design Method).
Ministry of Land, Infrastructure, and Transport. (2016). Road Bridge Design Standards (Limit State Design Method).
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I have been involved in various types of structural design work, including bridges, underpasses, and sound barriers, for over 10 years.
I am a user of various Midas software programs, such as midas Civil for structural analysis, as well as midas FEA and midas CIM.
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