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I need some help. Anyone can help me out in this.
I have applied only a constant axial load on the column and tip load on the beam's tip. The top-end column has two DoFs (Rz&Dx) and the bottom end has one DOF (Rz). Screenshot of the window is also attached.

I receive the following error when I run the analysis:
WARNING SuperLU::solve(void)- Error 17 returned in factorization dgstrf()
WARNING AcceleratedNewton::solveCurrentStep() -the LinearSysOfEqn failed in solve()
StaticAnalysis::analyze() - the Algorithm failed at iteration: 0 with domain at load factor 0.1
OpenSees > analyze failed, returned: -3 error flag
Press any key to continue . . .

You should give more details about the boundary conditions. From what you wrote, I understand that you are doing a 2D analysis, 3 DOFs per node (Ux, Uy, Rz) and you said that the bottom node has Ux+Rz fixed, while the top node has only Rz fixed. This means that your model has an un-constrained rigid body motion in Uy. Thus the error saing that your system is singular.

Dear sir,
Initially, I defined the model as given below:
I defined the dimension of ZeroLength Element as 3D used for the zero-length rotational spring at the end of the column by assigning the hysteresis material to mat4 (along the x-axis). This because the column spring is to include the contribution of column rotation along the X-axis.
Similarly, I also defined the zero-length rotational spring at the end of the beam with 3D and by assigning the hysteresis material to mat6 (along the z-axis).
2. Boundary condition includes, Column bottom end support allows only rotation along the z-axis due to pin support at the bottom,
Now I changed the dimension from 3D to 2D along with the following:
1. Constraints: Bottom end support with 1 DoF only i.e. Rz, Column top end with roller support and with 1 DoF of Uy, All rotational-spring assigned at the joint interface with 1DoF of Rz only, and beam end is free without any constraint.
2. Physical properties: 2D element for beam-column elements and rotational spring.
3. In physical properties, the dimension of the zero-length springs are also changed to 2D with the corresponding materials model assigned at mat3 and other mats i.e. mat1 and mat2 are kept rigid.
Now, when I run analysis I receive the following error( also shown in the attached screenshot):

LinearCrdTransf2d::computeElemtLengthAndOrien: 0 length
ForceBeamColumn2d::setDomain(): Error initializing coordinate transformationPress any key to continue . . .

Dear Asad, that error means that some beam element has a length = 0. Therefore the linear coordinate transformation raises the error.
Please, post your file here so we can have a look.
However I think that you modelled your example in a plane other than the XY plane. Note that in 2D problems opensees only considers the X-Y coordinates.

I am not finding the option to attach the STKO format file.
Can I send it via email?
Here the picture is only able to be sent as an attachment when I tried to attach a file.

Yup, I modelled it in plane other than X, Y plane. I am remodelling it in X,Y plane only. Thanks

Dear sir,
I tried to model it in XY plane, by using x, y coordinates (keeping z=0) for each member but at the end when I checked the same error of linear transformation prevails.
Although I entered the dimensions for the members in the proper format (x,y,z "12 30 0") when I checked the geometry of the model, the Y coordinates were transferred to the Z. Should I send the model via "[email protected]"?
I tried to attach it here with the post but its impossible to be attached due to format difference.

Of course, send it. However I am pretty sure you are typing your coordinates correctly, but maybe you are using a wrong workplane. Note that workplanes in STKO work like in AutoCAD:
If you have a workplane in the XZ plane (for example if you moved ot the front view) and then you type "10.0 10.0 0.0", the vector you input is in the local x-y-z system of the workplane, but in the global system it is 10.0 0.0 10.0.

Please switch to the 3D view point, and you will see that your model is actually in 3D. By the way, if so, there is no need to redraw the model from the beginning, you can select everything and use the rotate command.

More than thanks for your assistance. The problem of the transformation error is solved.

Dear sir/madam,
I sent yesterday the model via email for ur kind scrutiny. I am waiting for your kind help. Thank you