Calculator Input
Example Data Table
| Beam Length | Load 1 | Load 1 Position | Load 2 | Load 2 Position | E | I | Use Case |
|---|---|---|---|---|---|---|---|
| 6 m | 12 kN | 2 m | 8 kN | 4 m | 200 GPa | 85,000,000 mm4 | Steel beam service check |
| 18 ft | 1800 lb | 6 ft | 1200 lb | 12 ft | 29,000,000 psi | 120 in4 | Floor beam review |
| 4200 mm | 5 kN | 1400 mm | 7 kN | 3100 mm | 210 GPa | 42,000,000 mm4 | Machine frame beam |
Formula Used
This calculator assumes a simply supported beam. Two downward concentrated loads act at measured positions from the left support.
Left reaction:
RA = [P1(L - a1) + P2(L - a2)] / L
Right reaction:
RB = P1 + P2 - RA
Moment at any point x:
Mx = RAx - P1<x - a1> - P2<x - a2>
Deflection equation:
EIy = RAx³ / 6 - P1<x - a1>³ / 6 - P2<x - a2>³ / 6 + C1x
The bracket term is zero before the load position. It becomes active after the load position.
How to Use This Calculator
Enter the total beam span first. Then select the matching length unit. Add the first and second concentrated loads. Enter each load position from the left support. Add the analysis point where you want shear, moment, slope, and deflection.
Enter the elastic modulus and second moment of area. These values control stiffness. A larger stiffness gives lower deflection. Add a load factor when service loads need adjustment. Use one for unfactored service checks.
Press Calculate. The result appears above the form. Use the CSV button for spreadsheet work. Use the PDF button for a compact report.
Article: Calculating Deflection With Two Concentrated Loads
What This Calculator Does
A beam can bend under point loads. This bending is called deflection. Two concentrated loads make the shape more complex. Each load affects shear, moment, slope, and vertical movement. This calculator handles both loads together. It also checks the beam at any selected point.
Why Beam Deflection Matters
Strength is not the only design concern. A beam may be strong, yet still feel weak. Too much deflection can crack finishes. It can jam doors. It can harm machinery alignment. It can also reduce user comfort. That is why serviceability checks are important.
Important Inputs
The span is the clear distance between supports. The load values describe vertical point forces. The load positions show where forces act. Elastic modulus describes material stiffness. The second moment of area describes section stiffness. These two stiffness values work together as EI.
How the Method Works
The calculator first finds support reactions. It uses static equilibrium. The sum of vertical forces must balance. The sum of moments must also balance. Then the tool evaluates shear and bending moment along the span. It integrates the moment equation to estimate slope and deflection.
Maximum Deflection
The maximum deflection may not occur at the center. It depends on load size and load position. The calculator scans the full span. It finds the largest absolute deflection. This helps when the two loads are unequal or placed away from the center.
Deflection Limit Check
Many projects use a span ratio. A common service limit is L over 360. Some cases need a tighter value. Others allow more movement. This calculator compares maximum deflection with the selected limit. The result gives a quick pass or review status.
Use With Care
This tool is for simple beam checks. It assumes simple supports. It does not replace a full structural design. Real beams may have lateral effects, connection flexibility, vibration, or load combinations. Use verified material data. For final work, consult a qualified engineer.
FAQs
What is a concentrated load?
A concentrated load is a force applied at one point. In real structures, the force may spread slightly. For beam calculations, it is treated as acting at a single position.
Can I enter loads in different units?
The calculator uses one force unit for both loads. Convert loads first when they use different units. Then select the correct shared force unit before calculating.
What beam condition is assumed?
This calculator assumes a simply supported beam. That means one support at each end. The beam can rotate at supports, but vertical movement is restrained there.
Why is my deflection negative?
The sign shows direction based on the selected convention. Downward bending often appears negative. The magnitude is usually most important for serviceability comparison.
What is EI?
EI is flexural stiffness. E is elastic modulus. I is the second moment of area. A larger EI usually means a stiffer beam and smaller deflection.
Where should I set the analysis point?
Set it where you need local results. Common points include midspan, under each load, or at a machine support. Maximum deflection is still scanned separately.
What does L over 360 mean?
It means allowable deflection equals span divided by 360. A longer span allows more absolute movement. Project rules may require another ratio.
Can this replace engineering design?
No. It is a calculation aid. It does not include every code rule, support detail, or load combination. Use professional review for final structural decisions.