Tables For The Analysis Of Plates Slabs And Diaphragms Based On The Elastic Theory - Pdf

By the 1990s, institutions like the U.S. Forest Products Laboratory, the Portland Cement Association (PCA), and European steel construction institutes began scanning their out-of-print table collections. Today, sites like Archive.org, Engineering Toolbox, and academic repositories host high-quality PDFs. However, due to copyright, many are still circulated privately or via university libraries.

Given: ( a = 5m, b = 6m, h = 0.2m, E = 30 GPa, \nu = 0.2, p = 10 kPa )

First compute ( D = \frac30\times10^9 \cdot 0.2^312(1-0.04) = \frac30e9 \cdot 0.00812\cdot0.96 = \frac240e611.52 \approx 20.83 \times 10^6 , Nm )

Maximum deflection ( w_max = 0.00192 \cdot \frac10,000 \cdot 5^420.83e6 ) By the 1990s, institutions like the U

( 5^4 = 625 ), numerator ( 10,000 \cdot 625 = 6.25e6 )

( w_max = 0.00192 \cdot \frac6.25e620.83e6 = 0.00192 \cdot 0.30 \approx 0.000576 , m = 0.58 , mm )

Maximum moment ( M_max = 0.045 \cdot 10,000 \cdot 5^2 = 0.045 \cdot 250,000 = 11,250 , Nm/m ) Given: ( a = 5m, b = 6m, h = 0

This value is used directly for reinforcement design per meter width.

The elastic behavior of thin plates (where thickness is less than 1/10th of the smallest span) is described by the biharmonic equation:

[ \nabla^4 w = \fracpD ]

Where:

Unlike slabs, diaphragms (shear walls, floor diaphragms) are analyzed using plane stress elasticity. Tables provide:

Tables allow rapid exploration of aspect ratio effects. For a square plate, ( M_max ) occurs at center; as ( a/b ) increases, moments shift—visible instantly from tabulated values. Given: ( a = 5m