Corrective Measure. The flange and web of the side-rail extrusion were increased in thickness from 1. 2 to 1. 4 mm(0.046 to 0.057 in. ) This increased the safety factor from 1. 2 to 1.56. After this change, no further failures were reported. Note that this example is presented for illustrative purposes only, and this safety factor may not be appropriate in other applications Amount of Distortion. When designing structures using limit analysis, the designer does not al ways consider the amount of distortion that will be encountered. a rough illustration of the distortion that resulted from overloading of small cantilever beams is given in Fig. 4. Known loads were applied to rectangular-section beams of low-carbon steel and of stainless steel, and the permanent deflection at the loading point was measured. Maximum fiber stresses were calculated from the applied load and original specimen dimensions 2.50 Type 302 stainless steel, quarter hard Tensile strength, 135, 000 pal 200 1.75 |50 lolO steel(annealed) ield strength, 26, 000 psi ensile strength, 32 000 pal 1.0o 0.75 Distortion ratio Fig. 4 Relation of distortion ratio to stress ratio for two steel cantilever beams of rectangular cross section. Distortion ratio is permanent deflection, measured at a distance from the support ten times the beam thickness, divided by beam thickness. Stress ratio is maximum stress, calculated from applied load and original beam dimensions, divided by yield strength. This type of test provides a simplistic but useful concept of distortion by showing how much distortion occurs at strains beyond the yield point. As shown in Fig. 4, the beam of low-carbon steel, which strain hardens only slightly, exhibited no distortion when the calculated maximum fiber stress was equal to the yield strength(at a stress ratio of 1.00).However this beam collapsed at a load equivalent to a fiber stress just above the tensile strength, as shown in Fig 4 where the lower curve became essentially horizontal. This collapse load agrees with the limit-analysis collapse load of 1.5 times the load at yield. The beam made of stainless steel, which strain hardens at a rather high rate, showed no distortion at fiber stresses up to 1. 47 times the yield strength. When the calculated stress equaled the tensile strength(at a stress ratio of 1.59), distortion was 0.7 times the beam thickness, and the beam supported a calculated stress of 1.5 times the tensile strength without collapse It should be noted that the preceding example is intended simply to illustrate the differences in deformation behavior between two different materials. As a practical matter, one would not substitute stainless steel for low-carbon steel to increase load capacity. One would use a heavier section, or perhaps, a higher-strength alloy When loads increase gradually, distortion is gradual, and design can be based on knowledge of the amount of distortion that can be tolerated. Thus, simple bench tests of full-size or scaled-down models can often be used in estimating the loads required to produce various amounts of distortion Effect of Impact/Very High Strain Rates. When rapid or impulse loads are applied, as in impact, shock loading, or high- frequency vibration, the amount of distortion that can occur without fracture is considerably less predictable. The crystallographic processes involved in deformation and fracture are influenced by strain rate as well as temperature. For most structural materials, measured values of strength are higher under impulse loading, and values of ductility are lower, than the values measured under static loading. Tensile and yield strengths as much as 20% higher than the slow-tension test values have been measured under very high rates of loading. Strain-rate sensitivity data have been compiled for many Thefileisdownloadedfromwww.bzfxw.comCorrective Measure. The flange and web of the side-rail extrusion were increased in thickness from 1.2 to 1.4 mm (0.046 to 0.057 in.). This increased the safety factor from 1.2 to 1.56. After this change, no further failures were reported. Note that this example is presented for illustrative purposes only, and this safety factor may not be appropriate in other applications. Amount of Distortion. When designing structures using limit analysis, the designer does not always consider the amount of distortion that will be encountered. A rough illustration of the distortion that resulted from overloading of small cantilever beams is given in Fig. 4. Known loads were applied to rectangular-section beams of low-carbon steel and of stainless steel, and the permanent deflection at the loading point was measured. Maximum fiber stresses were calculated from the applied load and original specimen dimensions. Fig. 4 Relation of distortion ratio to stress ratio for two steel cantilever beams of rectangular cross section. Distortion ratio is permanent deflection, measured at a distance from the support ten times the beam thickness, divided by beam thickness. Stress ratio is maximum stress, calculated from applied load and original beam dimensions, divided by yield strength. This type of test provides a simplistic but useful concept of distortion by showing how much distortion occurs at strains beyond the yield point. As shown in Fig. 4, the beam of low-carbon steel, which strain hardens only slightly, exhibited no distortion when the calculated maximum fiber stress was equal to the yield strength (at a stress ratio of 1.00). However, this beam collapsed at a load equivalent to a fiber stress just above the tensile strength, as shown in Fig. 4 where the lower curve became essentially horizontal. This collapse load agrees with the limit-analysis collapse load of 1.5 times the load at yield. The beam made of stainless steel, which strain hardens at a rather high rate, showed no distortion at fiber stresses up to 1.47 times the yield strength. When the calculated stress equaled the tensile strength (at a stress ratio of 1.59), distortion was 0.7 times the beam thickness, and the beam supported a calculated stress of 1.5 times the tensile strength without collapse. It should be noted that the preceding example is intended simply to illustrate the differences in deformation behavior between two different materials. As a practical matter, one would not substitute stainless steel for low-carbon steel to increase load capacity. One would use a heavier section, or perhaps, a higher-strength alloy. When loads increase gradually, distortion is gradual, and design can be based on knowledge of the amount of distortion that can be tolerated. Thus, simple bench tests of full-size or scaled-down models can often be used in estimating the loads required to produce various amounts of distortion. Effect of Impact/Very High Strain Rates. When rapid or impulse loads are applied, as in impact, shock loading, or high￾frequency vibration, the amount of distortion that can occur without fracture is considerably less predictable. The crystallographic processes involved in deformation and fracture are influenced by strain rate as well as temperature. For most structural materials, measured values of strength are higher under impulse loading, and values of ductility are lower, than the values measured under static loading. Tensile and yield strengths as much as 20% higher than the slow-tension￾test values have been measured under very high rates of loading. Strain-rate sensitivity data have been compiled for many The file is downloaded from www.bzfxw.com