Calculator Inputs
Use magnitude and angle, or enter horizontal and vertical components.
Example Data Table
These examples show how different force directions change axial and shear demand.
| Load | Load Angle | Member Angle | Members | Area | Axial Force | Shear Force | Comment |
|---|---|---|---|---|---|---|---|
| 20 kN | 90° | 35° | 1 | 800 mm² | 11.47 kN | 16.38 kN | Inclined member with large transverse action. |
| 12 kN | 0° | 0° | 1 | 600 mm² | 12.00 kN | 0.00 kN | Load is aligned with the member. |
| 30 kN | 180° | 0° | 2 | 1000 mm² | -15.00 kN | 0.00 kN | Compression is shared by two members. |
| 15 kN | 45° | 20° | 1 | 750 mm² | 13.59 kN | 6.34 kN | Mixed axial and shear response. |
Formula Used
The calculator first converts all inputs into SI units. It then resolves the applied force along and across the member axis.
Relative angle = Load angle - Member angle
Axial force = Factored force × cos(relative angle) ÷ parallel members
Shear force = Factored force × sin(relative angle) ÷ parallel members
Axial stress = Axial force ÷ Area
Shear stress = |Shear force| ÷ Area
Equivalent stress = √(axial stress² + 3 × shear stress²)
Strain = Axial stress ÷ Elastic modulus
Elongation = Axial force × Length ÷ (Area × Elastic modulus)
Euler critical load = π² × E × I ÷ (K × L)², where I = Area × r².
How to Use This Calculator
- Select the force input mode.
- Enter either force magnitude and angle, or enter Fx and Fy.
- Add the member angle measured from the horizontal axis.
- Enter how many parallel members share the load.
- Add area, length, elastic modulus, and allowable stress.
- Enter radius of gyration and K factor for compression checks.
- Press the calculate button.
- Review the result, then export CSV or PDF.
Forces on a Member Guide
What the Calculator Does
A structural member usually carries load in more than one way. A force may pull along the member. It may push across the member. It may also create both effects at once. This calculator separates an angled load into axial and shear parts. That makes the result easier to read. It also helps you see whether the member is in tension or compression.
Why Direction Matters
Direction changes everything. A load parallel to the member creates mostly axial force. A load perpendicular to the member creates mostly shear force. An inclined load creates both. The calculator uses the angle between the load and the member. It then applies sine and cosine rules. This gives a clear force split for design review.
Stress and Deformation
Force alone is not enough. A small member may be stressed more than a large member under the same load. The tool divides force by area to estimate stress. It also uses elastic modulus to estimate strain and elongation. This is useful when checking service behavior. Large elongation may cause alignment issues. It may also affect connected parts.
Safety and Buckling
The calculator compares stress with allowable stress. It also estimates a combined stress value from axial and shear stress. Compression members need extra care. Slender members can buckle before the material stress becomes high. For this reason, the tool includes radius of gyration and effective length factor. These values support a simple Euler buckling check.
Practical Use
Use the results for early checks, teaching, comparisons, and report drafts. Always confirm final structural design with the correct code, connection behavior, load cases, and professional judgment. Real structures may include eccentricity, bending, dynamic effects, and local failure modes.
Frequently Asked Questions
1. What is axial force?
Axial force acts along the member axis. Positive axial force is treated as tension. Negative axial force is treated as compression.
2. What is shear force in this calculator?
Shear force is the part of the applied force that acts perpendicular to the member axis. It can affect joints, connectors, and local behavior.
3. Why do I need the member angle?
The member angle defines the member direction. The calculator compares it with the load angle to split the load into axial and shear components.
4. What does a negative axial force mean?
A negative axial force means compression. Compression members may need a buckling check, especially when they are long and slender.
5. What is combined utilization?
Combined utilization compares equivalent stress with allowable stress. A value under 100 percent suggests the selected stress check is within the limit.
6. When should I enter radius of gyration?
Enter radius of gyration when checking a compression member for buckling. Use zero when you only want force, stress, strain, and elongation results.
7. Can this replace structural design software?
No. It is best for quick checks and learning. Final design should follow applicable codes, load combinations, connection details, and professional review.
8. Why are CSV and PDF downloads included?
CSV helps with spreadsheets and record keeping. PDF gives a clean result summary for reports, reviews, and project notes.