StructuralEngineerLab · TOOL-007

Beam Deflection Calculator

Deflection-focused analysis for the two frozen TOOL-001 support models. E and I are required. Reaction, shear, and moment are read-only context.

Simply Supported: x = 0 left support · x = L right support · v(0)=0 · v(L)=0

Beam, stiffness & loads

Support Type

Span L

Young's modulus E (required)

Second moment of area I (required)

Point Loads

Enter downward loads as positive magnitudes.

Point 1 magnitude

Point 1 position x (m)

Uniform Distributed Loads

Use start = 0 and end = L for a full-span UDL.

Ready.

Primary result

Deflection

Deflection unit

Calculate to view the inherited TOOL-001 deflection result.

Example

Simply Supported: L = 6 m, downward Point Load = 12 kN at x = 3 m, E = 200 GPa and I = 8 cm⁴. TOOL-007 reports the inherited TOOL-001 Deflection Series, extrema, and Critical Locations.

Assumptions

Only Simply Supported and Cantilever Fixed-Left support models are allowed.
Point Loads and uniform distributed loads only.
E and I are mandatory.
Deflection is the primary TOOL-007 result.
Reaction/Shear/Moment are read-only TOOL-001 context.

Warnings

No multi-span analysis.
No triangular or trapezoidal loads.
No material-strength or code-design conclusion.
No utilization or PASS/FAIL conclusion.
Critical Locations are intentionally non-exhaustive.

Method & assumptions

TOOL-007 is a deflection-focused interface over the verified TOOL-001 beam mechanics. It supports only simply_supported and cantilever_fixed_left. E and I are mandatory.

Support type is limited to simply_supported or cantilever_fixed_left.
Supported loads are point loads and uniform distributed loads only.
Young's modulus E is required.
Second moment of area I is required.
Deflection is the primary TOOL-007 result.
Reaction, Shear and Moment are read-only TOOL-001 context.
All inputs are normalized to canonical SI before the frozen TOOL-001 mechanics are called.

Primary result: Deflection

TOOL-007's primary result is Deflection: Deflection Series, maximum deflection, minimum deflection, their locations, and Critical Locations.

Reaction, Shear and Moment are read-only Context inherited from TOOL-001. They are not independently recalculated and are not promoted to TOOL-007 primary results.

TOOL-001 sign convention

x increases from left to right.
Downward applied loads are entered as positive magnitudes.
Sagging internal bending moment is positive.
Downward deflection is negative.

Boundary conditions

Simply Supported

v(0)=0 and v(L)=0.

Cantilever Fixed-Left

v(0)=0 and θ(0)=0. The zero-slope condition is inherited from TOOL-001; TOOL-007 does not add slope or rotation as a separate output.

Critical Locations

criticalLocationsM is intentionally non-exhaustive. It contains beam boundaries, Point Load positions, UDL start/end breakpoints, and inherited TOOL-001 deflection extrema. It is not every analytical root, every slope-zero point, or every one-sided limit.

Limitations

No multi-span or continuous-beam analysis.
No fixed-fixed or propped cantilever mode.
No triangular or trapezoidal distributed loads.
No applied concentrated moments.
No material-strength or allowable-stress calculation.
No code-based design verification.
No utilization ratio or PASS/FAIL conclusion.
No independent slope output.
criticalLocationsM is non-exhaustive.

Worked examples

Simply Supported Midspan Point Load

Inputs: L = 6 m, P = 12 kN at x = 3 m, E = 200 GPa, I = 8×10⁻⁶ m⁴

Deflection is zero at both supports, the downward deflection is negative, and the maximum-magnitude deflection occurs at or near midspan under the inherited TOOL-001 solution.

Simply Supported Full-span UDL

Inputs: L = 10 m, w = 4 kN/m from x = 0 to x = 10 m, E and I supplied

The deflection field is symmetric, both support deflections are zero, and the maximum-magnitude downward deflection occurs at or near midspan.

Cantilever Free-end Point Load

Inputs: L = 4 m, P = 10 kN downward at x = 4 m, E and I supplied

The fixed-end deflection is zero, θ(0)=0 is inherited from TOOL-001, and the free-end deflection is negative with the free end as the standard critical location.

Frequently asked questions

Which beam support types does TOOL-007 support?

TOOL-007 supports only the two frozen TOOL-001 support models: simply_supported and cantilever_fixed_left.

Which loads are supported?

TOOL-007 supports one or more point loads and one or more uniform distributed loads, including full-span and partial-span UDLs.

Are E and I required?

Yes. Young's modulus E and second moment of area I are mandatory because TOOL-007 is a deflection-focused tool and has no statics-only mode.

What is the primary result?

Deflection is the primary result: Deflection Series, maximum deflection, minimum deflection, their locations, and Critical Locations.

What are Reaction, Shear and Moment used for?

They are read-only engineering context inherited from TOOL-001. TOOL-007 does not independently recalculate them and does not promote them to primary results.

What boundary conditions are used?

Simply Supported uses v(0)=0 and v(L)=0. Cantilever Fixed-Left uses v(0)=0 and inherits θ(0)=0 from TOOL-001.

Does TOOL-007 output slope?

No. Cantilever θ(0)=0 is an inherited TOOL-001 boundary condition, but TOOL-007 does not add slope or rotation as a separate output field.

Are criticalLocationsM exhaustive?

No. criticalLocationsM is a practical review set containing beam boundaries, point-load positions, UDL breakpoints, and inherited TOOL-001 deflection extrema. It is not every analytical root, slope-zero point, or one-sided limit.