EQUITRUSS – frequently asked questions

EquiTruss calculates axial forces in members by solving the truss using the method of joints (∑Fx=0, ∑Fy=0) , either after first determining the support reactions or without explicitly doing so in advance. The result is the force value in each member together with information on whether the member is in tension or compression.

• Assumption of an ideal truss: loads are applied at joints, connections are pinned, and members carry axial force only.
• Method of joints: for successive joints, the equations ∑Fx=0 and ∑Fy=0 are written, with the unknowns being the member forces connected to the joint.
• Member geometry: member forces are resolved according to the member directions, so the result depends directly on the angles within the structure.
• Sign interpretation: N>0 → tension, N<0 → compression (according to the adopted convention).
• Feature development: Ritter’s method (method of sections) and Cremona’s method are planned for quick determination of forces in selected members and for learning graphical statics.

In practice, this allows the student to follow the classical solution path, e.g. reactions → joints with a small number of unknowns → successive members until the entire truss is solved.

Axial_forces_analysis in EquiTruss application

Yes. EquiTruss analyzes equilibrium at a truss joint, because this is the basis of the method of joints. For each joint, it formulates the equations and determines the member forces connected to that joint.

• Joint equations: the program writes ∑Fx=0  and ∑Fy=0  for the selected joint.
• Member forces as unknowns: the equations include the axial forces in the members connected to the joint.
• Components from geometry: each member contributes to the balance through the components  and  according to its direction.
• Inclusion of loads and reactions: external forces and support reactions are added to the joint if it is a support joint.
• Step-by-step solution: the program selects successive joints, usually those with a small number of unknowns, and solves them one by one until the full system is resolved.

This makes it easy to check whether “the forces at the joint are in equilibrium” and to see where errors in signs or force directions in the members most often occur.

Truss joint equilibrium in EquiTruss app

EquiTruss solves the system of equations for member forces by proceeding joint by joint, starting with those that have the fewest unknowns. If such an order cannot be established, the program builds a coupled system of equations and solves it as a whole while showing the calculation procedure.

• Sequential strategy: it selects a joint where there are at most 2 unknowns and writes ∑Fx=0, ∑Fy=0 to determine the member forces.
• Propagation of results: the calculated forces values become “known” in adjacent joints, which unlocks the next equations.
• Detection of missing sequence: when joints have too many unknowns at once, the program switches to a coupled solution.
• Coupled system: it creates a larger set of equilibrium equations for several joints at the same time and solves it as a linear system.
• Full calculation path: it presents the successive steps: joint selection → equation formulation → elimination/substitution → final member force values.

Thanks to this, the truss is solved just as it is done manually in class, and in more difficult cases the program “ties together” several joints into one system instead of stopping at a dead end.

System of equations solution: method of joints in EquiTruss app

EquiTruss analyzes the effect of a concentrated load on truss members by including that force in the global equilibrium equations (for reactions) and in the joint equilibrium equations through which the load “passes.” As a result, the program shows how a given force changes the axial force in specific members (tension/compression).

• Support reaction stage: the concentrated force enters the equations ∑Fx=0, ∑Fy=0, ∑M=0, so it affects the reaction values.
• Assignment to a joint: the load is attached to a specific joint; if it is inclined, the program decomposes it into Fx and Fy.
• Joint equilibrium: the force appears directly in the equations ∑Fx=0, ∑Fy=0 for the loaded joint.
• Propagation through the truss: solving successive joints transfers the influence of the load to the following members all the way to the supports.
• Reading the effect on a member: for each member, you obtain the axial force and its sign (tension/compression), so it is easy to compare loading cases such as a change in the position or direction of P.

This works exactly like a manual solution: first, the system of equations for member forces can be simplified by calculating reactions, and then the load enters the joint balance and is distributed into axial forces in the members.

Force load on joint in EquiTruss app

No. EquiTruss does not determine support reactions for space trusses (3D), and for now we are not planning to add such a feature. The module is focused on plane trusses (2D), where reactions are calculated from the equations ∑Fx=0, ∑Fy=0, ∑M=0.

• 2D scope: joints and loads in a plane are supported, as well as support types typical for 2D analysis.
• 3D reactions require a different set of equations: in space, equilibrium also includes ∑Fz=0 the moments ∑Mx, ∑My, ∑Mz, along with a different definition of restraints.
• Geometry and member directions: in 3D, spatial            direction cosines are required, together with support for loads in the Z-direction when formulating the joint equations.

If someone has a space truss, at the moment it needs to be calculated with another tool (FEM / 3D solver), while EquiTruss should be treated as a solution strictly for 2D student problems.

Planar truss 2D in EquiTruss app

EquiTruss calculates axial forces using the method of joints by writing the equations ∑Fx=0  and ∑Fy=0 for successive joints and solving them step by step until the member forces are determined. Support reactions may be calculated first from global equilibrium, or they may “appear along the way” as part of solving the joint equations — depending on how the equation system is arranged.

• Choosing the starting joint: the program selects joints with the smallest number of unknowns (typically ≤2) and starts “untangling” the system from there.
• Joint equilibrium: for a given joint, it writes ∑Fx=0 and ∑Fy=0 .
• Member geometry: member forces enter as the components and , according to member directions.
• Loads and supports: the equations include external forces at the joint and known/unknown reactions if the joint is a support.
• Two ways of handling reactions:
• Variant A: it first calculates reactions from global equilibrium(∑Fx, ∑Fy, ∑M), and then treats them as known values at support joints,
• Variant B: it determines reactions as unknowns within the joint equations when such a solution sequence is possible.
• Step-by-step solution and propagation: after determining the member forces at one joint, it transfers them to adjacent joints and solves the next ones.
• When a sequential approach is not possible: it creates a coupled system of equations for several joints and solves it as a whole, while showing the calculation procedure.
• Interpretation of the result: it reports the value and sign of N (tension/compression according to the adopted convention).

As a result, the student sees both the classical joint equilibrium approach and the fact that reaction analysis can be treated either as a preliminary calculation step or as part of the same system of joint equilibrium equations.

Method of joints in EquiTruss app

EquiTruss helps users understand the method of joints because it solves the truss exactly as it is done in class: it builds the joint equilibrium equations and guides the user through successive steps until the member forces are obtained. This allows the student to see how the result from one joint “passes on” to the next ones.

• Direct joint equilibrium: for each joint, the program writes ∑Fx=0 and ∑Fy=0, with the unknowns being the axial member forces.
• Geometry matters: member components are calculated from the directions  and , so the effect of member angles on the result is clearly visible.
• Step-by-step solution: it selects joints with the smallest number of unknowns and solves them one after another, showing the elimination/substitution process.
• Reactions depending on the scenario: reactions may be calculated first from global equilibrium or may “appear” during joint equilibrium solving, depending on the solution order.
• Correctness control: it is easy to compare the joint balance and catch mistakes in your own calculations, such as sign errors, incorrect decomposition of forces into components, or wrong member directions.
• Clear interpretation: the program immediately shows which members are in tension and which are in compression (based on the sign of the axial force).

It works like an interactive “class notebook”: you get the joint equations, the solution sequence, and the final member forces, so you can compare everything step by step with your handwritten solution.

Truss calculations in EquiTruss