Portal (Approximate) Method of Analysis: Superposition

In summary, the conversation discusses using the Portal Frame Method to calculate the shear force, axial load, and bending moment diagrams for a given portal frame geometry and factored loading. The homework statement also notes that the dimensions are in meters and that ASTM A992 steel with a grade of 345MPa should be used. The equations for this method come from simple statics, and the solution involves combining the dead load and live load and using the principle of superposition for gravity and lateral load effects. The student also mentions some difficulties with this particular question and asks for clarification on the correct approach.
  • #1
JulianEng
1
0

Homework Statement


For the portal frame geometry and factored loading shown in the figure below, calculate the shear
force, axial load and bending moment diagrams using the Portal Frame Method. You may use the
principle of superposition for gravity and lateral load effects.

Note:
• all dimensions in meters
• use ASTM A992 steel, grade 345MPa;

Homework Equations


If you understand the portal method you know that there are no equations specifically designed to answer this question. The equations come from simple statics

The Attempt at a Solution


Attached is the problem. My solution was to combine the DL and LL, which gave me a total of w = 50 kN/m and I solved the problem using that assumption. I have never completed a Portal Method question with a uniformly distributed load on top of the frame, nor one that required me to do a gravity analysis and/or use the superposition method. Please let me know if I have gone about this question the right way and if NOT, what are the steps involved in order to successfully answer this question.

Thank you
 

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  • #2
Dimensions appear to be in mm, rather than m.
 

FAQ: Portal (Approximate) Method of Analysis: Superposition

1. What is the "Portal (Approximate) Method of Analysis: Superposition"?

The Portal (Approximate) Method of Analysis: Superposition is a structural engineering method used to analyze portal frames, which are commonly used in buildings to resist lateral loads such as wind or earthquakes.

2. How does the "Portal (Approximate) Method of Analysis: Superposition" work?

The method uses the principle of superposition, which states that the total response of a structure to multiple loads can be obtained by summing the individual responses to each load acting alone. In this case, the loads are divided into two separate cases: the fixed-base case and the free-base case.

3. What are the advantages of using the "Portal (Approximate) Method of Analysis: Superposition"?

One of the main advantages of this method is that it simplifies the analysis process by breaking down the structure into two separate cases. This allows for easier calculations and can save time compared to other analysis methods.

4. Are there any limitations to the "Portal (Approximate) Method of Analysis: Superposition"?

Yes, this method is only an approximate analysis technique and may not accurately represent the behavior of the structure in all cases. It is best used for simple portal frames with regular shapes and loading patterns.

5. How is the "Portal (Approximate) Method of Analysis: Superposition" different from other analysis methods?

Compared to other methods such as the moment distribution method or the finite element method, the Portal (Approximate) Method of Analysis: Superposition is simpler and requires less computational power. However, it is also less accurate and may not be suitable for more complex structures.

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