Hello,

I am trying to analyze a 3-hinge arch to find the buckling load. I have attached the SAP file here, which has the modeling done correctly. I suspect I am not doing to P-delta analysis correctly.

My objective is to apply equal value point loads at the two knees and the top ridge, starting with P1=P2=P3 =36 kips and trying to determine at what equal value load the arch would buckle. The answer should be P1=P2=P3 = 43.1 kips. Other checks can be:
1. At P1 (left knee) = P2 (at ridge) = P3 (right knee)=36 kips, the downward deflection at the ridge should be 1.8189 in.
1. At P1 = P2 = P3 =40 kips, the downward deflection at the ridge should be 3.1909 in.

May I ask if someone could take a look and tell me what is not being done correctly? Thanks.

I am unsure if I attachment is uploaded. Here are the geometry and material properties.
Left support : 0,0
Left knee : 50 ft, 30 ft
Ridge (hinge) : 100 ft, 40 ft
Right knee : 150 ft, 30 ft
Right support : 200 ft, 0

Cross-section of the arch member: 5.5" x 30.25"
E = 1800 ksi

Hi,

Attached is the 3-hinged arch I want to analyze to determine at what value of P, the arch will buckle.
Cross-section of the arch member: 5.5" x 30.25", E = 1800 ksi

I have been using non-linear P-delta analysis and applying P in small increments. Is there an easier way to obtain Pcr?

Thanks.

• http://files.engineering.com/getfile.aspx?folder=b640a789-2570-41b9-9f16-4d

What would be the suggested procedure in SAP2000 for determining the buckling load Pcr for this particular 3-hinged arch with loads as indicated in my previous message?

Here's my SAP file. I will appreciate any help.

• http://files.engineering.com/getfile.aspx?folder=9f01e3be-5859-4b91-9ac3-4c

catenary, first, you have a 2D model, so set analysis options parameters to run as a 2D with XZ plane unless you are able to change the supports/restraints to fixed.. in which case you could run as 3D. Second, you do not have a buckling load case defined, only a P-delta case. Buckling case is eigen buckling which, unless you add a small imposed displacement or load to perturb the structure to simulate construction tolerance imperfections (out of plumbness), it will otherwise assume an idealized perfectly symetrical structure and may therefore calculate a theoretical buckling load that is an artificially high critical buckling load. In buckling analysis, as with modal analysis, in some cases you will want to base the buckling analysis on a "prestressed" nonlinear p-delta load case instead of assuming Unstressed state which is the default.

There is also an option to run large deformation snap through buckling analysis, but you would need to change the P-Delta case option to P-Delta plus large displacements and switch 'Results saved' to Multiple steps