Plane Frame Analyzer

You can access the full source code and documentation on GitHub:

🔗github.com/Samson-Mano/Plane_frame_analyzer

The Static Plane Frame Analysis Software is a powerful tool designed for engineers and structural analysts to perform comprehensive structural analysis of plane frames. The software utilizes classical methods of structural analysis to determine member forces, displacements, reactions, and other important parameters.

This project was developed as part of my BEng (Bachelor of Engineering) final year project back in 2010. Its aim is to provide an efficient and user-friendly platform for analyzing static plane frames, allowing engineers to gain insights into the behaviour and performance of various structural configurations.

Plane Frame Analysis

For all member, young’s modulus E = 210000, moment of Inertia I = 0.0002, cross sectional area = 0.01, spring stiffness = 10

Solution:

Degree of Freedom Matrix

Nodal support condition can be classified into following irrespective of its inclination in the global axis. Support inclination had taken into consideration later by redistributing it into global stiffness matrix.

1 – Free to displace or rotate,

0 – Restrained from displacement and rotation.

Spring support is taken as rigid joint criteria; however the stiffness of spring is distributed in global stiffness matrix. Later the nodal resultant force is calculated by multiplying spring stiffness and the vertical displacement at that node.

DOF Matrix

Member:1 ( 0 ---> 1 ) => [0 0 1 1 1 1]

Member:2 ( 1 ---> 2 ) => [1 1 1 1 1 1]

Member:3 ( 2 ---> 3 ) => [1 1 1 1 0 1]

Support Inclination Transformation Matrix [SI_T]

Element Stiffness Matrix

Stiffness matrix, combing the axial, shear and bending effects for the bar element in the global coordinates is given by

Stiffness matrix in Local Coordinate system

Stiffness Matrix (Local Coordinate System) [K~]

Element Direction Cosine Matrix [DC_T]

Stiffness Matrix (Global Coordinate System) (after applying transformation from element direction cosine matrix [K^] = [DC_T]T [K~] [DC_T]

Stiffness Matrix (Global Coordinate System) (after applying transformation from support inclination

transformation matrix [K] = [SI_T]T [K^] [SI_T]

Fixed End Reaction Matrix

Fixed reaction is calculated by the numerical method shown in the figure below. The force vector in the member is distributed as force vector along the lateral and longitudinal direction of the member. Longitudinal force is Fx which taken as the axial load applied on the member.

Support settlement is redistributed as additional force in the fixed end reaction matrix. New force matrix = [F] + [K][Settlement].

Above Picture and Formula Credit:  TURAN   BABCAN 

Global Stiffness Matrix

Global stiffness matrix after curtailment (removing the elements which are restrained from displacement

Solve for displacement [U] ([K][U] = [F])

Result Matrix (after applying Gauss elimination method)

Nodal Reaction

[N] = [K][U] – [F]

Since spring support is allowed to displace and rotate in all directions we have to find the reaction under the spring support by

Reaction under spring = – spring stiffness x displacementY

Result matrix (Force at the element end nodes, Fx, Fy and Mxy)

End resultant in each member is easily calculated by back computation

[U^] = [SI_T]T [U]

[U~] = [DC_T]T [U]

[N~] = [K~][U~] – [F~}

Shear Force Plot

Bending Moment Plot

Deflection Plot

Axial Force and Reaction Force Plot

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