Engineering guide
Module BULK calculates bulk solids loads in silos to DIN EN 1991-4 (Eurocode 1, Part 4). It determines the wall pressures from the stored bulk solid — horizontal pressure, wall frictional traction and vertical pressure — for the filling state and as the basis for the discharge states, supplemented by patch loads and additional circumferential pressures from seismic action in the barrel and in the hopper.
To calculate silo loads to EN 1991-4 means applying Janssen theory with characteristic bulk solid properties: the unit weight, the lateral pressure ratio K and the wall friction coefficient μ are each applied via conversion factors as upper and lower characteristic values, because different combinations are unfavourable for different verifications (wall pressure, frictional load, base load). From the cross-sectional area, the internal perimeter and the filling height follows the pressure distribution over the depth below the equivalent bulk solid surface.
The results are the load basis for designing the silo barrel, the hopper and the supporting structure — in steel construction typically as input for buckling and ring-stiffener verifications. The slenderness of the silo determines which load pattern applies.
Scope
- Bulk loads in silos
Typical workflow
Define bulk solid properties
The unit weight, the lateral pressure ratio K and the wall friction coefficient μ are entered as characteristic values; via the conversion factors the module forms the upper and lower characteristic values, which are combined unfavourably depending on the verification objective.
Enter silo geometry
From the characteristic cross-sectional dimension, the height of the vertical silo barrel, the cross-sectional area and the internal perimeter, the module determines the slenderness of the silo and the Janssen characteristic depth for the pressure distribution.
Calculate filling loads
For the depth below the equivalent bulk solid surface, the horizontal pressure, the wall frictional traction and the vertical pressure in the filled state are determined from the Janssen relationship.
Apply the patch load
Asymmetries during filling and discharge are captured via the patch load with the load magnification factor derived from the bulk solid properties; it acts locally on the silo wall and is often design-relevant for thin-walled metal silos.
Determine additional seismic pressures
From the ratio of seismic to gravitational acceleration at height z, the reference pressures and additional circumferential pressures for the barrel and the hopper are calculated — depending on the angle between the point considered and the direction of seismic action.
Frequently asked questions
Why are upper and lower characteristic values of K and μ needed?
Bulk solid properties scatter widely. For the maximum horizontal pressure, a high K with low wall friction is unfavourable; for the maximum wall frictional load (axial compression in the barrel), a high μ; and for the base load, low K and μ. EN 1991-4 therefore requires each load quantity to be calculated with the respective unfavourable combination of upper and lower characteristic values — using mean values leads to systematic underestimation.
What is the equivalent bulk solid surface?
The real bulk solid surface is conical after filling. For the load calculation it is replaced by a plane surface of equal volume; the depth z in the pressure formulas is measured from this equivalent surface. For eccentric filling or large repose cones this must be taken into account when determining the governing filling height.
Are discharge loads higher than filling loads?
Yes, as a rule. During discharge, dynamic pressure amplifications occur, which EN 1991-4 captures via discharge factors applied to the filling pressures; with eccentric discharge (funnel flow beside the axis) unsymmetrical load patterns are added, which are frequently decisive for the design of metal silos. The Janssen filling loads are the starting point, not the end result, of silo design.
For which silo geometries does the method apply?
EN 1991-4 classifies silos by the slenderness hc/dc into slender, intermediate and squat silos with correspondingly adapted load patterns; the action assessment class (based on capacity and eccentricity) also controls the required calculation effort. Outside the geometric limits of the standard — for example for strongly unsymmetrical cross-sections — separate investigations are required.
Worked example
For a slender cylindrical steel silo (inside diameter 5 m, barrel height 20 m), the Janssen filling loads at the base of the barrel are to be calculated — a worked example of silo pressure calculation to EN 1991-4. Assumed characteristic bulk solid properties of a grain-like material are applied.
Given
| Inside diameter dc | 5.0 m |
|---|---|
| Height of the vertical barrel hc | 20.0 m |
| Characteristic unit weight γ | 9.0 kN/m³ |
| Lateral pressure ratio K | 0.54 |
| Wall friction coefficient μ | 0.38 |
| Depth below equivalent bulk solid surface z | 20.0 m |
Solution
Cross-sectional values and Janssen characteristic depth
A = π·dc²/4 = π·5.0²/4 = 19.63 m²; U = π·dc = 15.71 m
z0 = A / (K · μ · U) = 19.63 / (0.54 · 0.38 · 15.71) = 6.09 m
Asymptotic horizontal pressure
ph0 = γ · K · z0 = 9.0 · 0.54 · 6.09 = 29.6 kN/m²
Pressures at the barrel base (z = 20 m)
Depth function: 1 − e−z/z0 = 1 − e−20/6.09 = 0.962
Horizontal pressure: phf = 29.6 · 0.962 = 28.5 kN/m²
Wall frictional traction: pwf = μ · phf = 0.38 · 28.5 = 10.8 kN/m²
Vertical pressure: pvf = phf/K = 28.5/0.54 = 52.8 kN/m²
Result
| Horizontal pressure phf at the barrel base | 28.5 kN/m² |
|---|---|
| Wall frictional traction pwf | 10.8 kN/m² |
| Vertical pressure pvf | 52.8 kN/m² |
Technical content source: LV-Solved-Problems-Content 628d313247e7