When considering the use of perforated metal, the ability to provide a desired level of strength and elasticity can be of great importance. Realizing that perforated metal is neither stronger nor stiffer than unperforated metal, strength and elasticity levels can be established by comparing the two forms of metal. This comparison is referred to as the Equivalent Solid Material Concept.
In an effort to provide designers with the information they need to make decisions about strength and elasticity of perforated metal, solid material equivalent tests were performed. The tests compared the strength and elasticity of 26 different perforated metal samples to the equivalent solid metal. Because they account for more than half of the perforating industry's production, due to their inherent strength and wide range of open areas, the tests were performed on round hole 60° staggered patterns ranging from .020" to 3/4".
The direction of the stagger is the short distance or width of the sheet and the straight row runs parallel to the long dimension or length of the sheet as illustrated in Figure 1 below. This is the standard formation for 60° staggered patterns and is often referred to as an Actual Center Pattern. In some cases the hole orientation in relationship to the length and width dimensions may be reversed. This 60° pattern formation is often referred to as Reverse Actual Center.
The strength and elasticity tests were
performed by O'Donnell & Associates and
are courtesy of the Industrial Perforators Association.
Strength
In this test, the equivalent strength of the perforated material is used in place of the strength of the solid material. By evaluating the effect of the perforations on the yield strength of the material, S*, can be obtained as a function of the yield strength of the solid or unperforated material, S. Thus, the designer is able to determine safety margins for the perforated material for any geometry of application and any loading conditions. The S*/S ratios are the same for bending and stretching of the material. Having the S*/S ratio for the particular penetration pattern of interest, it is therefore easy for the designer to determine what thickness of the perforated material will provide strength equal to that of unperforated material.
Perforated material has different strengths depending on the direction of loading. Values of S*/S are given for the width (strongest) and the length (weakest) directions. The values for the length direction have been calculated conservatively. Refer to Figure 1 (left) for the length and width directions corresponding to the directional results given in the Tables.
| IP # |
Hole Dia. |
Centers |
Holes Per sq. in. |
Open Area |
Width Direction |
Length Direction |
| 100 |
.020" |
.043" |
625 |
20% |
.530 |
.465 |
| 106 |
1/16" |
1/8" |
73.9 |
23% |
.500 |
.435 |
| 107 |
5/64" |
7/64" |
96.5 |
46% |
.286 |
.225 |
| 108 |
5/64" |
1/8" |
73.9 |
35% |
.375 |
.310 |
| 109 |
3/32" |
5/32" |
47.3 |
33% |
.400 |
.334 |
| 110 |
3/32" |
3/16" |
32.8 |
23% |
.500 |
.435 |
| 112 |
1/10" |
5/32" |
47.3 |
38% |
.360 |
.296 |
| 113 |
1/8" |
3/16" |
32.8 |
40% |
.333 |
.270 |
| 114 |
1/8" |
7/32" |
24.1 |
30% |
.428 |
.363 |
| 115 |
1/8" |
1/4" |
18.5 |
23% |
.500 |
.435 |
| 116 |
5/32" |
7/32" |
24.1 |
46% |
.288 |
.225 |
| 117 |
5/32" |
1/4" |
18.5 |
35% |
.375 |
.310 |
| 118 |
3/16" |
1/4" |
18.5 |
51% |
.250 |
.192 |
| 119 |
3/16" |
5/16" |
11.8 |
33% |
.400 |
.334 |
| 120 |
1/4"" |
5/16" |
11.8 |
58% |
.200 |
.147 |
| 121 |
1/4" |
3/8" |
8.2 |
40% |
.333 |
.270 |
| 122 |
1/4" |
7/16" |
6.0 |
30% |
.428 |
.363 |
| 123 |
1/4" |
1/2" |
4.6 |
23% |
.500 |
.435 |
| 124 |
3/8" |
1/2" |
4.6 |
51% |
.250 |
.192 |
| 125 |
3/8" |
9/16" |
3.6 |
40% |
.333 |
.270 |
| 126 |
3/8" |
5/8" |
3.0 |
33% |
.400 |
.334 |
| 127 |
7/16" |
5/8" |
3.0 |
44% |
.300 |
.239 |
| 128 |
1/2" |
11/16" |
2.4 |
48% |
.273 |
.214 |
| 129 |
9/16" |
3/4" |
2.1 |
51% |
.250 |
.192 |
| 130 |
5/8" |
13/16" |
1.7 |
54% |
.231 |
.175 |
| 131 |
3/4" |
1" |
1.2 |
51% |
.250 |
.192 |
Elasticity (Stiffness)
In this test, the equivalent stiffness of the perforated material is used in place of the stiffness of the solid material. By evaluating the effect of the perforations, the equivalent effective elastic modulus of the perforated material, E*, is obtained as a function of the elastic modulus of the solid or unperforated material, E. In addition, the effective Poisson's Ratio, v*, of the perforated material is obtained. This Poisson's Ratio may be used in cases where correction for load biaxiality is important.
The effective elastic constants presented herein are for plane stress conditions and apply to the in-plane loading of the thin perforated sheets of interest. The bending stiffness of such perforated sheets is somewhat greater. However, most loading conditions involve a combination of bending and stretching, and it is more convenient to use the same effective elastic constants for the combined loading conditions. The plane stress effective elastic constants given herein can be conservatively used for all loading conditions. Using these effective elastic properties, the designer is able to determine the deflections of the perforated sheet for any geometry of application and any loading conditions using available elastic solutions. It is, therefore, easy for the designer to determine what additional thickness of the perforated material will provide stiffness equal to that of unperforated material.
| IP Numbers |
Hole Dia. |
Centers |
Holes Per sq. in. |
Open Area |
E*/E |
| 100 |
.020" |
.043" |
625 |
20% |
.565 |
| 106 |
1/16" |
1/8" |
73.9 |
23% |
.529 |
| 107 |
5/64" |
7/64" |
96.5 |
46% |
.246 |
| 108 |
5/64" |
1/8" |
73.9 |
35% |
.362 |
| 109 |
3/32" |
5/32" |
47.3 |
33% |
.395 |
| 110 |
3/32" |
3/16" |
32.8 |
23% |
.529 |
| 112 |
1/10" |
5/32" |
47.3 |
38% |
.342 |
| 113 |
1/8" |
3/16" |
32.8 |
40% |
.310 |
| 114 |
1/8" |
7/32" |
24.1 |
30% |
.436 |
| 115 |
1/8" |
1/4" |
18.5 |
23% |
.529 |
| 116 |
5/32" |
7/32" |
24.1 |
46% |
.249 |
| 117 |
5/32" |
1/4" |
18.5 |
35% |
.362 |
| 118 |
3/16" |
1/4" |
18.5 |
51% |
.205 |
| 119 |
3/16" |
5/16" |
11.8 |
33% |
.395 |
| 120 |
1/4"" |
5/16" |
11.8 |
58% |
.146 |
| 121 |
1/4" |
3/8" |
8.2 |
40% |
.310 |
| 122 |
1/4" |
7/16" |
6.0 |
30% |
.436 |
| 123 |
1/4" |
1/2" |
4.6 |
23% |
.529 |
| 124 |
3/8" |
1/2" |
4.6 |
51% |
.205 |
| 125 |
3/8" |
9/16" |
3.6 |
40% |
.310 |
| 126 |
3/8" |
5/8" |
3.0 |
33% |
.395 |
| 127 |
7/16" |
5/8" |
3.0 |
44% |
.265 |
| 128 |
1/2" |
11/16" |
2.4 |
48% |
.230 |
| 129 |
9/16" |
3/4" |
2.1 |
51% |
.205 |
| 130 |
5/8" |
13/16" |
1.7 |
54% |
.178 |
| 131 |
3/4" |
1" |
1.2 |
51% |
.205 |
Figure 4: Effective Elastic Modulus, E*, and Poisson's Ratio, v*, vs. Percent Open Area
THIS MATERIAL WAS DEVELOPED FOR THE IPA BY O'DONNELL & ASSOCIATES, INC.