Calculator inputs
Example data table
This example illustrates typical inputs and computed outputs at the base.
| H (m) | P (kN) | a (m) | w (kN/m) | q (kN/m²) | b (m) | V (kN) | e (m) | Service M (kN·m) | Factored M (kN·m) |
|---|---|---|---|---|---|---|---|---|---|
| 12 | 5 | 10 | 0.30 | 0.90 | 0.60 | 20 | 0.10 | — | — |
Formulas used
- MP = P · a (point lateral load at height a)
- MUDL = w · H² / 2 (uniform lateral load over full height)
- wwind = q · b (convert pressure to line load)
- MWIND = (q · b) · H² / 2 (uniform wind along height)
- MECC = V · e (vertical load with eccentricity)
- Mtotal,service = MP + MUDL + MWIND + MECC
- Mtotal,factored = γP·MP + γUDL·MUDL + γWIND·MWIND + γV·MECC
These equations provide a practical base-moment estimate for preliminary design and checks. For final design, include code-specific distributions, second-order effects, connection flexibility, and dynamic amplification where applicable.
How to use this calculator
- Enter mast height H and all applicable loads.
- Use P and a for any concentrated lateral action.
- Use w for continuous lateral effects (cables, ice, services).
- Enter wind pressure q and projected width b to model wind as a line load.
- Add eccentric vertical moment using V and e when gravity is offset.
- Select a load combination or set custom factors, then calculate.
- Download CSV or PDF for documentation after calculating.
Professional notes for mast bending moment checks
1) Purpose and scope
This calculator estimates the bending moment at the mast base, combining common construction-stage actions: a concentrated lateral force, a uniform lateral line load, wind pressure converted to a line load, and a vertical load acting with eccentricity. It is intended for quick sizing, review, and reporting before detailed analysis. Typical outputs support base-plate selection, anchor checks, and preliminary foundation reaction coordination.
2) Load inputs and units
Enter height H in meters and forces in kilonewtons. Wind pressure q is entered in kN/m² and multiplied by projected width b (m) to form a wind line load wwind (kN/m). For example, q = 0.90 and b = 0.60 give wwind = 0.54 kN/m.
3) Component moments at the base
A point load P applied at height a produces MP = P·a. A uniform lateral load over the full height produces M = w·H²/2, which applies to both the UDL and the wind line load. An eccentric vertical action produces MECC = V·e, often governing when attachments offset the gravity line.
4) Reading service and factored results
The service total is a direct sum of the component base moments and is useful for operational checks and comparisons. The factored total applies load factors to each component for design verification. If you select “Wind governing,” the wind factor increases while other components remain near unity, which highlights wind-sensitive mast geometries and attachments.
5) Practical tips and limitations
Use conservative projected width when antennas, ladders, cable trays, or signage are present. If wind varies with height or shielding applies, split the mast into segments and sum segment moments. Final design should include code-specific wind profiles, dynamic effects, second-order amplification, connection flexibility, and foundation interaction as required by your standard.
FAQs
1) What moment location does the tool report?
All moments are reported about the mast base. The calculator sums individual base moments from each load type to provide service and factored totals.
2) How do I choose the wind pressure input?
Use the design wind pressure from your governing code or project basis. Enter it in kN/m², then confirm your projected width represents the exposed face area per meter height.
3) Can I model wind that increases with height?
Yes, approximate it by segmenting the mast into zones, computing each zone’s equivalent line load, and summing the individual zone base moments. This tool provides the uniform-height baseline.
4) What does the UDL lateral load represent?
It can represent continuous horizontal effects such as cable drag, ice accretion load converted to lateral, or distributed equipment drag. Apply it over the full mast height for a conservative estimate.
5) Why include a vertical load eccentricity?
Vertical actions can create bending when the gravity line is offset from the mast centroid, such as bracketed equipment or offset platforms. The term V·e captures that first-order effect.
6) Which result should I use for design checks?
Use the factored moment for strength checks when your standard requires load factors. Use the service moment for operational or comparison checks, unless your design basis specifies otherwise.
7) Does the calculator account for deflection or buckling?
No. It only computes base bending moments. Deflection, buckling, P-Δ effects, and vibration require additional analysis and section properties not included in this simplified tool.