BIZOMAT MAKEOS · Strength
Overhang Beam with Tip Load (Uplift, Anchor Bolts, Tip Deflection)
For a beam on two supports with a load out on an overhang, how hard does the back support have to hold the beam down, are the anchor bolts enough, and how far does the tip drop?
Check of a beam on two supports with a point load at the tip of an overhang (a runway extension, a jib on a frame, a cantilevered platform beam): the reactions, including the uplift at the back support, the moment over the front support, bending stress and tip deflection (as the overhanging beam tool), the tension per anchor bolt at the back support, and checks against the allowable stress, bolt capacity, front support capacity and tip deflection limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Span between supports | mm | Distance between the back and front supports. |
| Overhang length | mm | Length of the overhang beyond the front support. |
| Point load at the tip | N | Load at the end of the overhang (include an allowance for dynamic effects). |
| Elastic modulus | GPa | Elastic modulus. |
| Second moment of area | mm⁴ | Second moment of area about the bending axis. |
| Distance to extreme fibre | mm | Distance from the neutral axis to the extreme fibre. |
| Allowable bending stress | MPa | Allowable bending stress. |
| Supports | ||
| Anchor bolts at the back support | Number of anchor bolts holding the back support down. | |
| Allowable tension per bolt | kN | Allowable tension of each anchor bolt and its anchorage. |
| Capacity of the front support | kN | Load the front support can carry. |
| Tip deflection limit (overhang ÷ …) | Tip deflection limit as the overhang length divided by this number. | |
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: Span between supports
- What it is
- The distance between the back support and the front support, measured centre to centre of the bearings or anchor points.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 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 span lowers the uplift at the back support and the front reaction, but increases tip deflection; it does not change bending stress.
- Get it right
- Measure between support centres, not to the end of the beam; the overhang is entered separately.
What this means: Overhang length
- What it is
- The length of beam that projects beyond the front support, from that support to the point where the tip load acts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 800 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 and uplift rise in proportion to the overhang; tip deflection rises faster, with roughly its square.
- Get it right
- Measure to the line of action of the load, such as the hook or trolley position, not just to the end of the steel.
What this means: Point load at the tip
- What it is
- The point load hanging from or resting on the tip of the overhang, such as a hoist with its rated load or a platform load.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Reactions, stress, bolt tension and tip deflection all rise in direct proportion to the load.
- Get it right
- Enter newtons, not kilonewtons or kilograms (1 kg weighs about 9.81 N), and include any dynamic allowance your standard requires.
What this means: Elastic modulus
- What it is
- The elastic (Young’s) modulus of the beam material, which sets how much the beam bends under load.
- 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.
- Effect on the result
- A higher modulus reduces tip deflection in proportion; it does not change stress or reactions.
- Get it right
- Enter gigapascals, not megapascals. Take it from the material data sheet or standard.
What this means: Second moment of area
- What it is
- The second moment of area of the beam section about the axis it bends around, from a section table or a section-properties calculation.
- Units and format
- Enter a number in mm⁴: millimetres to the fourth power (second moment of area). The form accepts 0.000001 mm⁴ or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8000000 mm⁴ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress and tip deflection both fall in direct proportion as I increases.
- Get it right
- Use mm⁴, not cm⁴ (1 cm⁴ = 10 000 mm⁴), and the value for the axis the load bends about, normally the strong axis.
What this means: Distance to extreme fibre
- What it is
- The distance from the neutral axis of the section to its outermost fibre, where bending stress is highest; half the depth for a symmetric section.
- 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 50 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 in direct proportion to this distance.
- Get it right
- For an unsymmetric section use the larger distance to the extreme fibre so the highest stress is checked.
What this means: Allowable bending stress
- What it is
- The highest bending stress your design code or company rule permits for this beam, against which the stress at the front support is checked.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 MPa 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 applicable structural code for the material and load case; do not use the yield strength itself.
Supports
What this means: Anchor bolts at the back support
- What it is
- The number of anchor bolts at the back support that together hold the beam down against the uplift from the tip load.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 100. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The tension per bolt is the uplift divided by this number.
- Get it right
- Count only bolts that actually resist uplift at the back support; bolts at the front support do not share it.
What this means: Allowable tension per bolt
- What it is
- The allowable tension of one anchor bolt together with its anchorage into concrete or steel, from the bolt and anchor supplier’s data or your design code.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the capacity per bolt in kilonewtons, while the tip load is in newtons; check that the anchorage, not just the bolt, can carry it.
What this means: Capacity of the front support
- What it is
- The load the front support can safely carry, such as a column, bracket or bearing rating, from its design or the supplier.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 1000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The front reaction is larger than the tip load, because it also resists the uplift at the back; compare with that reaction, in kilonewtons.
What this means: Tip deflection limit (overhang ÷ …)
- What it is
- The number the overhang length is divided by to set the largest tip deflection you accept, as used in deflection limits written as length ÷ n.
- Units and format
- Enter a plain number with no unit. The form accepts 20 to 5000. 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.
- Effect on the result
- A larger number gives a stricter, smaller deflection limit.
- Get it right
- Enter only the divisor; the tool works out the limit in millimetres from the overhang length.
Method and formulas
- Back reaction R₁ = −P a ÷ L (uplift); front reaction R₂ = P (L + a) ÷ L; moment at the front support = P a (as the overhanging beam tool).
- Stress = P a c ÷ I; tip deflection = P a² (L + a) ÷ 3EI (as the overhanging beam tool).
- Bolt tension = uplift ÷ number of bolts.
- Example: the back support is pulled up with 1,066.7 N (533.33 N per bolt); the tip drops 2.0267 mm; stress 20 MPa.
Limitations
- Prismatic beam, rigid supports; support flexibility adds to the tip deflection.
- Static load; moving hoists need a dynamic allowance in P.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a beam extended past its support to carry a hoist
- Size hold-down bolts for an overhanging platform
- Check tip deflection of an overhang
Who it is for
- Structural designers
- Design engineers
- Maintenance engineers
What you get
- Reactions and uplift
- Bending stress and tip deflection
- Anchor bolt tension
Interpreting the result
- A short back span makes the uplift large: lengthen the span or add holding-down weight.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 257–262. Topic reference; no source tables or recommended settings are reproduced.
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Open the Overhang Beam with Tip Load (Uplift, Anchor Bolts, Tip Deflection) calculator