Masters Theses


“Theoretical stress analysis in mine structures begins with the assumption that the structural elements are homogeneous, isotropic and perfectly elastic. It is this writers belief that stresses in a mine roof supported by barrier pillars may be compared to those stresses which may be found in a thin plate supported and restrained in the manner similar to such a mine roof. Therefore the stress and moment equations developed for plates are herein applied to mine roofs of limited thickness.

A thin roof bed which is stressed with evenly distributed lateral load and supported with barrier pillars will be regarded as a large rectangular plate clamped at the two longitudinal ends and with the other edges simply supported.

Figure 1a shows the free body diagram or such a plate. AB and CD are built-in or clamped edges, and AD and BC are simply supported edges. My is the bending moment along the built-in edges, and q is the unit load on the mine roof bed. The weight of the bed per unit area may be included into the q. The moment My will be considered positive and when it produces compression at the top of the bed.

The most convenient method to analyze the stresses in such a plate will be to find a general equation for the deflection of a rectangular plate which is loaded similar to the mine roof bed.

To determine the general equation of bending for such a plate it is necessary to take two general cases of bending of plates: One of which is the bending of a plate by moments along the edges of the plate as shown in Figure 1c, and the other one is the bending of the plates by evenly distributed load, Figure 1b, and then superimpose them to apply for a plate which is subjected to evenly distributed loads and contains bending moments along two parallel edges.

First, the relations between the bending moments and the curvature in pure bending of plates will be determined”—Introduction, pages 1-2.


Vine, William A.


Mining Engineering

Degree Name

M.S. in Mining Engineering


Missouri School of Mines and Metallurgy

Publication Date



v, 36 pages

Note about bibliography

Includes bibliographical references (page 35).


© 1951 Sahap Sakip Aybat, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Pillaring (Mining) -- Design and construction
Strains and stresses -- Mathematical models
Mine buildings

Thesis Number

T 948

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