# Beam Deflection and Bending Stress Calculator for Steel and Aluminum

> Source: https://netray.co/tools/beam-deflection-and-bending-stress-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Compute midspan or tip deflection, peak bending moment and bending stress for a simply supported or cantilever beam in steel, stainless, aluminum or titanium.

## Category

engineering-plm

## Audience

- Design engineer
- Fabricator
- Buyer

## Tool

**Kind:** calculator

**Inputs:**

#### Load case

**Key:** case_id

**Type:** select

**Default:** 1

**Options:**

##### Simply supported, uniform load

**Value:** 1

##### Cantilever, point load at free end

**Value:** 2

##### Simply supported, point load at center

**Value:** 3

**Help:** For the uniform case enter the total load, which is w x L.

#### Total load W

**Key:** load_n

**Type:** number

**Default:** 20000

**Min:** 0

**Max:** 5000000

**Step:** 100

**Unit:** N

**Help:** Total applied load in newtons. 1 kgf is about 9.81 N.

#### Span or length L

**Key:** span_mm

**Type:** number

**Default:** 2000

**Min:** 50

**Max:** 20000

**Step:** 50

**Unit:** mm

**Help:** Support-to-support span, or cantilever length.

#### Material

**Key:** e_gpa

**Type:** select

**Default:** 200

**Options:**

##### Carbon steel (E = 200 GPa)

**Value:** 200

##### Stainless 304 (E = 193 GPa)

**Value:** 193

##### Aluminum 6061 (E = 69 GPa)

**Value:** 69

##### Titanium Ti-6Al-4V (E = 114 GPa)

**Value:** 114

**Help:** Young's modulus. Stiffness depends on E, not on strength.

#### Second moment of area I

**Key:** i_cm4

**Type:** number

**Default:** 1943

**Min:** 0.1

**Max:** 500000

**Step:** 1

**Unit:** cm4

**Help:** Section property about the bending axis. An IPE 200 steel beam is about 1,943 cm4.

#### Distance to extreme fibre c

**Key:** c_mm

**Type:** number

**Default:** 100

**Min:** 1

**Max:** 1000

**Step:** 1

**Unit:** mm

**Help:** Half the section depth for a symmetric section.

**Outputs:**

#### Deflection coefficient

**Key:** coef

**Expr:** if(eq(case_id,1),5/384,if(eq(case_id,2),1/3,1/48))

**Format:** decimal

#### Maximum deflection

**Key:** defl_mm

**Expr:** coef * load_n * pow(span_mm,3) / (e_gpa * 1000 * i_cm4 * 10000)

**Format:** decimal

**Primary:** true

**Description:** Midspan for simply supported cases, tip for the cantilever.

#### Span to deflection ratio (L/x)

**Key:** ratio

**Expr:** if(gt(defl_mm,0),span_mm / defl_mm,0)

**Format:** integer

**Description:** Many designs target L/250 to L/500 depending on the application.

#### Maximum bending moment

**Key:** moment_nm

**Expr:** if(eq(case_id,1),1/8,if(eq(case_id,2),1,1/4)) * load_n * span_mm / 1000

**Format:** decimal

#### Maximum bending stress

**Key:** stress_mpa

**Expr:** moment_nm * 1000 * c_mm / (i_cm4 * 10000)

**Format:** decimal

**Primary:** true

**Description:** sigma = M x c / I in MPa.

**Chart:**

#### Maximum deflection (mm) vs span (mm)

**Type:** line

**X:** span_mm

**From:** 500

**To:** 4000

**Steps:** 30

**Series:**

- defl_mm

**Disclaimer:** Elastic, small-deflection formulas for prismatic beams. Does not include shear deflection, self-weight unless added to the load, lateral-torsional buckling or connection flexibility.

## Content

**Intro:** Check how much a beam, shaft, rail or frame member will bend and how hard the material is working. Pick a load case, enter the span, material and section, and read deflection, moment and bending stress.

**Sections:**

#### How to use it

**Body:** Choose the load case that matches the arrangement, enter the total load, span and the second moment of area from your section table, then select the material. For symmetrical sections, c is half the depth. The span chart shows how fast deflection grows with length, since it rises with the cube of the span for point loads and with the cube for the uniform total load as entered. That makes length the first thing to shorten when a member is too flexible.

**Bullets:**

- Use I about the bending axis, not the weak axis
- Add self-weight to the load for long spans
- Compare L/x against your design standard limit
- Compare stress to allowable stress with a safety factor

#### The formulas

**Body:** For a simply supported beam with a uniform total load W, midspan deflection is 5 x W x L^3 divided by 384 x E x I. A cantilever with an end load deflects by W x L^3 divided by 3 x E x I, and a simply supported beam with a center load by W x L^3 divided by 48 x E x I. Peak moment is WL/8, WL and WL/4 respectively, and bending stress is M x c / I. Deflection depends on E and I only, so swapping to a stronger steel does not stiffen the beam.

#### Worked example

**Body:** A 2 m steel beam with I of 1,943 cm4 carries 20 kN spread uniformly. Deflection is about 0.54 mm, which is L/3,700, very stiff. The peak moment is 5 kNm and the bending stress about 26 MPa. Replace the steel with aluminum 6061 at E of 69 GPa and the same section, and deflection rises to roughly 1.6 mm because stiffness scales with E. Aluminum needs about three times the I to match steel stiffness, though it weighs about one third as much.

#### Common mistakes and ERP notes

**Body:** Frequent errors are mixing cm4 and mm4, forgetting that the uniform load is entered as a total, and checking stress while ignoring deflection on machine bases and gantries. For buyers, a substitution from steel to aluminum or from one profile to another changes stiffness, so route it through engineering change control. In ERP the approved material and profile sit on the item master and BOM, and substitutions should be controlled by an ECN rather than a purchasing note.

**Bullets:**

- Check units on I before trusting the result
- Include dynamic or impact factors for moving loads
- Treat this as a screening check, not a code design

**Cta:** If material substitutions bypass engineering review today, we can help build a controlled change flow connected to your BOMs.

**Faq:**

#### Why does a stronger steel not reduce deflection?

**Answer:** Elastic deflection depends on Young's modulus E and the section's second moment of area I. Almost all steels share about 200 GPa, so higher strength does not stiffen the member. Increase I by using a deeper section or reduce the span.

#### What deflection limit should I use?

**Answer:** It depends on the application and the governing code. General floor members often use L/360, while machine tool structures and precision gantries can need L/2000 or better. Use the limit your design standard specifies.

#### How do I get I for my section?

**Answer:** Take it from the manufacturer's section tables, a CAD mass-properties report or a formula such as b x h^3 / 12 for a rectangle. Make sure it is about the correct bending axis and entered in cm4.

#### Does it include the beam weight?

**Answer:** No. Add the beam's own weight to the total load for long spans. Steel weighs about 7.85 g/cm3, so a heavy section can contribute meaningfully to both deflection and stress.

## Search terms

beam deflection calculator, simply supported beam deflection, cantilever deflection formula, bending stress calculator, 5wL4/384EI, aluminum vs steel beam stiffness, span to deflection ratio, moment of inertia deflection

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