Mechanical calculators

Beams & Deflection Calculators

51 tools

Euler–Bernoulli closed forms and station queries. Workspace: /workspace/beam. Tools may appear in more than one topic.

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Beam Deflection Calculator Midspan deflection of a simply supported span with one concentrated load. δ = P L³/(48 E I). I is an input. Runs locally.
Cantilever Deflection Calculator Free-end deflection of a cantilever with one concentrated load at the tip. δ = P L³/(3 E I). I is an input. Runs locally.
Uniform Load Deflection Calculator Midspan deflection of a simply supported span with a uniform load. δ = 5 w L⁴/(384 E I). I is an input. Runs locally.
Shear and Moment Calculator Shear and bending moment at a cut in a simply supported span. Point forces and concentrated moments only. Runs locally. Not beam deflection.

All Beams & Deflection

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Beam Deflection Calculator Midspan deflection of a simply supported span with one concentrated load. δ = P L³/(48 E I). I is an input. Runs locally.
Beam Moment Deflection Calculator Midspan deflection of a simply supported span with one end moment. δ = M L²/(16 E I). I is an input. Runs locally.
Beam Moment Maximum Deflection Calculator Largest deflection of a simply supported span with one end moment. δ = M L²/(9√3 E I) at x = L/√3. I is an input. Runs locally.
Cantilever Deflection Calculator Free-end deflection of a cantilever with one concentrated load at the tip. δ = P L³/(3 E I). I is an input. Runs locally.
Cantilever Intermediate Deflection Calculator Deflection at a concentrated load on a cantilever. δ = P a³ / (3 E I). a is measured from the fixed end. Runs locally.
Cantilever Load at a Station Calculator Deflection at station x for a cantilever load at a. x = a is the load page. x = L is the free-end page. Runs locally.
Cantilever Moment at the Couple Calculator Deflection at a concentrated moment on a cantilever. δ = M a² / (2 E I). a is measured from the fixed end. Runs locally.
Cantilever Moment Deflection Calculator Free-end deflection of a cantilever with one concentrated moment. δ = M L²/(2 E I). I is an input. Runs locally.
Cantilever Outer Uniform Calculator Tip deflection when a uniform load starts away from the wall. δ = w [3 L⁴ − a³ (4L − a)] / (24 E I). Runs locally.
Cantilever Partial Load Calculator Deflection where a uniform load that starts at the wall stops. δ = w a⁴ / (8 E I). Runs locally.
Cantilever Tip Deflection Calculator Free-end deflection of a cantilever with an intermediate point load. δ = P a² (3L − a) / (6 E I). Runs locally.
Cantilever Tip-Peak Deflection Calculator Tip deflection of a cantilever whose triangular load peaks at the free end. δ = 11 w0 L⁴ / (120 E I). Runs locally.
Cantilever Triangular Deflection Calculator Tip deflection of a cantilever whose triangular load peaks at the fixed end. δ = w0 L⁴ / (30 E I). Runs locally.
Cantilever Uniform Deflection Calculator Free-end deflection of a cantilever with a uniform load. δ = w L⁴/(8 E I). I is an input. Runs locally.
Cantilever Uniform Load at a Station Calculator Deflection at distance x from the wall. δ = w x² (6 L² − 4 L x + x²) / (24 E I). Runs locally.
Center-Peaked Triangle at a Station Calculator Deflection at station x when the triangle is 0 at both supports and w0 at midspan. x = L/2 is the midspan page. Runs locally.
Center-Peaked Triangle Calculator Midspan deflection when a triangular load peaks at midspan. δ = w0 L⁴ / (120 E I). Runs locally.
Center-Peaked Triangle plus End Moment Calculator Deflection at station x for a center-peaked triangle plus a sagging moment at the right end. x = L/2 is the sum of the two midspan pages. Runs locally.
End Moment at a Station Calculator Deflection at station x for one end moment. x is measured from the unloaded end. Runs locally.
End-Peaked Triangle at a Station Calculator Deflection at station x when the triangle is w0 at both supports and 0 at midspan. x = L/2 is the midspan page. Runs locally.
End-Peaked Triangle Calculator Midspan deflection when a triangular load peaks at both supports. δ = 3 w0 L⁴ / (640 E I). Runs locally.
End-Peaked Triangle plus End Moment Calculator Deflection at station x for an end-peaked triangle plus a sagging moment at the right end. x = L/2 is the sum of the two midspan pages. Runs locally.
Equal End Moments at a Station Calculator Deflection at station x for equal sagging end moments. x = L/2 is the midspan page. Runs locally.
Equal End Moments Calculator Midspan deflection of a simply supported span with equal sagging end moments. δ = M L² / (8 E I). Runs locally.
Midspan Load at a Station Calculator Deflection at station x when the load is at midspan. δ = P c (3 L² − 4 c²) / (48 E I). Runs locally.
Offset Load at a Station Calculator Deflection at station x for one offset load. x = a is the under-load page. x = L/2 is the midspan page. Runs locally.
Offset Load Deflection Calculator Deflection under a concentrated load that is not at midspan. δ = P a² b² / (3 E I L). I is an input. Runs locally.
Offset Load Maximum Calculator Largest deflection of a simply supported span with an offset point load. δ = P c (L² − c²)^(3/2) / (9 √3 E I L). Runs locally.
Offset Load Midspan Calculator Midspan deflection when one concentrated load is not at midspan. δ = P c (3 L² − 4 c²) / (48 E I). Runs locally.
One-Sided Triangle plus End Moment Calculator Deflection at station x for a one-sided triangle plus a sagging moment at the right end. x = L/2 is the sum of the two midspan pages. Runs locally.
One-Sided Triangle plus Equal End Moments Calculator Deflection at station x for a one-sided triangle plus equal sagging end moments. x = L/2 is the sum of the two midspan pages. Runs locally.
Outer Uniform Load at a Station Calculator Deflection at distance x from the wall when the uniform load starts at a and runs to the tip. x = L is the tip page. a = 0 is the full uniform curve. Runs locally.
Overhang Arm at a Station Calculator Deflection at station z on the overhang, measured from the right support out to the load. z = a is the load page. Runs locally.
Overhang End Deflection Calculator Deflection at a load beyond a simply supported span. δ = P a² (L + a) / (3 E I). Runs locally.
Overhang Span at a Station Calculator Deflection at station x on the span when a load sits at the end of an overhang. x = L/2 is the span-midspan page. Runs locally.
Overhang Span Deflection Calculator Midspan of the span moves opposite a load on the overhang. δ = −P a L² / (16 E I). Runs locally.
Paired Load at the Load Calculator Deflection under either of two equal loads. δ = P a² (3L − 4a) / (6 E I). Runs locally.
Paired Load Deflection Calculator Midspan deflection of two equal loads, each at distance a from the nearer support. δ = P a (3 L² − 4 a²) / (24 E I). Runs locally.
Paired Loads at a Station Calculator Deflection at station x for two equal loads, each at distance a from the nearer support. x = L/2 is the midspan page. x = a is the under-load page. Runs locally.
Paired Point Loads plus End Moment Calculator Deflection at station x for two equal point loads plus a sagging moment at the right end. x = L/2 adds the paired midspan page. Runs locally.
Partial Uniform Load at a Station Calculator Deflection at distance x from the wall when a uniform load runs from the wall to a. x = a is the loaded-end page. x = L is the tip page. Runs locally.
Shear and Moment Calculator Shear and bending moment at a cut in a simply supported span. Point forces and concentrated moments only. Runs locally. Not beam deflection.
Tip Load at a Station Calculator Deflection at distance x from the wall under a tip load. δ = P x² (3L − x) / (6 E I). Runs locally.
Tip Moment at a Station Calculator Deflection at distance x from the wall for a moment at the free end. δ = M x² / (2 E I). Runs locally.
Tip-Peak Triangle at a Station Calculator Deflection at distance x from the wall when the triangle peaks at the tip. x = L is the tip page. Runs locally.
Triangular Load at a Station Calculator Deflection at station x for a triangular load that is zero at the left support. x = L/2 is the midspan page. Runs locally.
Triangular Load Deflection Calculator Midspan deflection of a simply supported span with a triangular load. δ = 5 w0 L⁴ / (768 E I). Intensity is 0 at the left support. Runs locally.
Triangular Load Maximum Calculator Largest deflection of a simply supported span with a triangular load. The peak is not at midspan. Runs locally.
Uniform Load at a Station Calculator Deflection at station x on a simply supported uniform load. δ = w x (L³ − 2 L x² + x³) / (24 E I). Runs locally.
Uniform Load Deflection Calculator Midspan deflection of a simply supported span with a uniform load. δ = 5 w L⁴/(384 E I). I is an input. Runs locally.
Wall-Peak Triangle at a Station Calculator Deflection at distance x from the wall when the triangle peaks at the wall. x = L is the tip page. Runs locally.