Free Structural Analysis Calculator

Generate bending moment diagrams, shear force diagrams and deflection for a 2D frame.

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Theory & FAQ

Node	X Coord	Y Coord	Restraint
1	m	m
2	m	m

Element ID	Start node	End node
1

ID	Applied to type	Applied to Node	Position on element	Load (x) magnitude	Load (y) magnitude
1			%	kN	kN

Load ID	Element ID	UDL X magnitude	End X magnitude	UDL Y magnitude	End Y magnitude	Start position	End position
1		kN	kN	kN	kN	%	%

Bending moment result

Worst case predicted: kNm

Shear force result

Worst case predicted: kN

Axial force result

Worst case predicted: kN

Support reactions result

Worst case predicted (x): kN

Worst case predicted (y): kN

Displacement result

This analysis assumes the same stiffness is applied to all elements

Edit the stiffness below & re-analyse.

Young's Modulus GPa

Area cm²

2nd Moment of Area cm⁴

Worst case displacement: mm

Analysis validation

Method & theory

How the frame analysis is solved

The frame is solved using the direct stiffness method: nodes and members are assembled into a global stiffness matrix and solved for nodal displacements and rotations under the applied load vector, from which bending moment, shear force, axial force and reactions are recovered member-by-member.

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What's this calculator used for?

This free Structural Analysis calculator can be used by Civil Engineers to design 2D frame structures. This tool will generate and find the bending moment, shear force, deflection and reaction forces on the structure. Add nodes and members with stiffnesses before applying point loads or distributed loads to the frame and calculating results. The frame can also be analysed as a truss structure rather than a pin jointed frame.

Common questions

Most Engineering problems are 3D problems. Engineers however frequently simplify 3D problems into 2D or planar analysis. In the case of structural frame analysis often Engineers will perform 2D frame analysis along the x and y axis of the structure. If there are bi-axial effects which need to be considered on members resulting from this analysis, then these members can be analysed in isolation. 3D analysis is frequently on required for detailed design of complex models and often includes some element of dynamic analysis. Most analysis is usually simplified into 2D.

Determinate structures can be analysed using the simple equations of statics. For 2D structures this means that we can have no more than three unknown reactions since we only have three equations for 2D statics. Most problems found in Civil Engineering are indeterminate problems. Indeterminate problems require approaches such as Moment Redistribution Theory.

Static analysis considers forces applied to a structure which do not vary with time. In Dynamic analysis loads applied to the structure could vary in magnitude, location at which they are applied or both. Dynamic loading considers the inertia and damping of a structure.

Linear analysis assumes that the applied load and deflection are proportional to one another. Most structures behave linearly within a certain range of loading. Non-linearity can result from material or geometric non-linearity or a combination of both.

Finite element analysis is used to break a complex shape into a mesh of smaller interconnected elements which when combined represent the complete shape. Finite element analysis uses partial differential equations describing stress and strain relationships between the elements of the mesh. The calculations performed on each element are polynomial and involve interpolating the values. Determination of values starts at the boundaries of elements, known as nodal points. The calculations then propagate across all the elements in the mesh to arrive at estimated stress and strain values.

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