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### Keywords:

• Compaction;
• density;
• grains;
• Janssen;
• loads storage

### Abstract

Janssen created a classical theory based on calculus to estimate static vertical and horizontal pressures within beds of bulk corn. Even today, his equations are widely used to calculate static loadings imposed by granular materials stored in bins. Many standards such as American Concrete Institute (ACI) 313, American Society of Agricultural and Biological Engineers EP 433, German DIN 1055, Canadian Farm Building Code (CFBC), European Code (ENV 1991-4), and Australian Code AS 3774 incorporated Janssen's equations as the standards for static load calculations on bins. One of the main drawbacks of Janssen's equations is the assumption that the bulk density of the stored product remains constant throughout the entire bin. While for all practical purposes, this is true for small bins; in modern commercial-size bins, bulk density of grains substantially increases due to compressive and hoop stresses. Over pressure factors are applied to Janssen loadings to satisfy practical situations such as dynamic loads due to bin filling and emptying, but there are limited theoretical methods available that include the effects of increased bulk density on the loadings of grain transmitted to the storage structures. This article develops a mathematical equation relating the specific weight as a function of location and other variables of materials and storage. It was found that the bulk density of stored granular materials increased with the depth according to a mathematical equation relating the two variables, and applying this bulk-density function, Janssen's equations for vertical and horizontal pressures were modified as presented in this article. The validity of this specific weight function was tested by using the principles of mathematics. As expected, calculations of loads based on the modified equations were consistently higher than the Janssen loadings based on noncompacted bulk densities for all grain depths and types accounting for the effects of increased bulk densities with the bed heights.