BIZOMAT MAKEOS · Strength
Cantilever Rack Arm Check (Arm Section, Bending Stress, Tip Deflection, Column Bolts)
For a cantilever racking arm carrying a uniform load, are its bending stress and tip deflection within limits, and can the bolts at the column take the pull?
Check of a cantilever rack arm or bracket with a uniformly spread load: the section properties of an I, T, channel or angle arm (as the section shapes tool), the moment at the column and the tip deflection for a cantilever with a uniform load (as the beam cases tool), the bending stress, and the tension in the top bolts of the moment connection from the lever arm to the bottom bearing point, against your allowable stress, deflection limit and bolt capacity.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Total load on the arm (spread evenly) | N | Total load on the arm, taken as spread evenly along it. |
| Arm length from the column face | mm | Length of the arm from the column face. |
| Arm section | ||
| Shape | choice | Shape of the arm section. |
| Overall depth (vertical leg) | mm | Depth of the section. |
| Overall width | mm | Width of the section. |
| Flange thickness | mm | Flange thickness. |
| Web thickness | mm | Web thickness. |
| Modulus of elasticity | GPa | Modulus of elasticity. |
| Allowable bending stress | MPa | Allowable bending stress. |
| Tip deflection limit (length ÷) | Largest tip deflection as a fraction of the arm length. | |
| Column connection | ||
| Lever arm, top bolts to bottom bearing point | mm | Distance from the top bolts down to the point where the arm bears on the column. |
| Top bolts in tension | bolts | Bolts in the top row taking the moment as tension. |
| Allowable tension per bolt | N | Allowable tension in each bolt. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Total load on the arm (spread evenly)
- What it is
- The total load on one cantilever arm, taken as spread evenly from the column face to the tip.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stress, deflection and bolt tension rise in direct proportion.
- Get it right
- Enter newtons for one arm, not the whole rack level; a load concentrated at the tip is more severe.
What this means: Arm length from the column face
- What it is
- The length of the arm from the face of the column to its tip.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 900 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress rises with length; tip deflection with its cube.
- Get it right
- Measure from the column face, not from the column centre.
Arm section
What this means: Shape
- What it is
- The cross-section shape of the arm, which sets how the tool builds it from flange and web rectangles.
- Units and format
- Choose one of 4 options from the list: I or H section (symmetrical); T section; Channel; Angle.
- Example
- The form opens with “I or H section (symmetrical)” selected as a worked example. Choose the option that matches your case.
- Get it right
- For an angle, the vertical leg is the depth and the horizontal leg is the width.
What this means: Overall depth (vertical leg)
- What it is
- The overall depth of the arm section from top to bottom, or the length of the vertical leg for an angle.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deeper sections are much stiffer and stronger in bending.
- Get it right
- Take it from the steel table for the section.
What this means: Overall width
- What it is
- The overall width of the arm section, or the length of the horizontal leg for an angle.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the steel table for the section.
What this means: Flange thickness
- What it is
- The thickness of the horizontal flange or flanges, or of the horizontal leg for an angle.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the steel table value; tapered flanges are listed as a mean thickness.
What this means: Web thickness
- What it is
- The thickness of the vertical web, or of the vertical leg for an angle.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the steel table for the section.
What this means: Modulus of elasticity
- What it is
- The elastic modulus of the arm material, used for tip deflection.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter it in GPa, not MPa.
What this means: Allowable bending stress
- What it is
- The bending stress you allow in the arm.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 160 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set it from the arm material and the racking or structural design code.
What this means: Tip deflection limit (length ÷)
- What it is
- The divisor of the arm length that sets the largest tip deflection you accept: allowed deflection = arm length ÷ this number.
- Units and format
- Enter a plain number with no unit. The form accepts 10 to 100000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- A larger number is stricter; take it from the racking standard or your design rules.
Column connection
What this means: Lever arm, top bolts to bottom bearing point
- What it is
- The vertical distance from the top bolts of the arm connection down to the point where the arm bracket bears on the column. It is the lever arm resisting the moment.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer lever arm reduces the bolt tension.
- Get it right
- Measure from the bolt centres to the bottom bearing edge.
What this means: Top bolts in tension
- What it is
- The number of bolts in the top row of the connection that take the bending moment as tension.
- Units and format
- Enter a number in bolts: bolts. The form accepts 1 bolts to 100 bolts. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 bolts as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More bolts share the tension equally.
- Get it right
- Count only the top row; lower bolts carry little tension.
What this means: Allowable tension per bolt
- What it is
- The tension each top bolt may carry, compared with the tension from the arm moment.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the bolt standard or design code for the bolt size and grade.
Method and formulas
- A, I and Z of the section about its horizontal axis (as the section shapes tool).
- Cantilever with a uniform load: M = P L ÷ 2 at the column, tip deflection = P L³ ÷ 8EI (as the beam cases tool).
- Bolt tension = M ÷ lever arm ÷ top bolts.
- Example: 42.054 MPa and 0.56773 mm at the tip; each top bolt carries 15,000 N.
Limitations
- Uniform load and a rigid column; point loads at the tip double the moment for the same total.
- Bending about the section’s main axis; channels and angles also twist under load.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check cantilever racking for bar or pipe storage
- Size a wall bracket arm
- Check bolts of a cantilever arm to its column
Who it is for
- Design engineers
- Warehouse engineers
- Fabricators
What you get
- Arm section properties
- Moment, stress and tip deflection
- Bolt tension at the column
Interpreting the result
- Loads placed at the arm tip are the worst case; marking a safe working load per arm prevents overloading.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 234–246, 257–277, 1535. Topic reference; no source tables or recommended settings are reproduced.
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