For the beam in figure 1, find the value and location of the largest tensile and compressive stresses. There may be more than one candidate location for each of these. 3.2 kN/m 2 1.9 kN.m Im A 3m 2m Figure 1 Figure 2 The cross section shown in Figure 2 is 125x75x8 UA the cross section and material properties are shown below; (Note that in the tables, the horizontal and vertical coordinate n and p, and are right and up respectively. Table 26 Unequal Angles - x-axis and y-axis - Dimensions and Properties Designation Nominal Mass Actual Radii Thickness per Thickness About x-axis About y-axis Torsion Tan Designation Constant Alpha Gross Coordinate metre Area of of Centroid Cross Leg-size Root Toe (b,-t) (b,-t) Section b, x b, t r 5, t A Рап y Z V₁ mm mm mm ka/m mm mm mm mm² mm mm 10 mm mm 10 mm mm 125 x 75 x 12 UA 17.7 12.0 10 UA 14.2 9.5 8 UA 11.8 7.8 8.0 5.0 9.42 5.25 2260 8.0 5.0 12.2 6.89 1810 8.0 5.0 15.0 8.62 1500 43.3 18.4 42.3 17.5 3.20 41.5 16.8 2.68 3.91 83.2 83.8 84.2 59.7 31.8 Z Y₁ Z S r 10-mm³ mm 10 mm 10mm³ 47.0 65.5 34.6 113 81.4 41.6 38.2 59.3 53.9 33.9 94.4 65.8 58.9 45.5 33.3 80.4 54.6 V x, Z 2日 X mm 10 mm mm 0.585 19.9 42.0 0.476 19.2 42.2 0.399 18.6 10 mm³ mm 29.3 414 24.9 41.6 21.5 Z 10-mm³ mm 10 mm² 10mm 14.1 31.9 18.4 29.7 11.4 30.7 15.5 24.1 16.2 9.55 29.9 13.3 20.1 16.3 S r J mm 10 mm 16.1 110 0.356 125 x 75 x 12 UA 56.2 0.360 31.7 0.363 10 UA 8 UA Form Factor Table 27 Unequal Angles - x-axis and y-axis - Properties for Assessing Section Capacity Designation Yield Stress About x-axis About y-axis Yield Stress Form Factor About x-axis About y-axis Designation Load A Load C Load B Load D Load A f k₁ Z Z Z Z f k Z Load C Z Load B Z Load D Z mm mm mm MPa 10mm 10 mm 10'mm³ 10 mm MPa 10 mm 10 mm 10/mm³ 10-mm³ 300PLUS AS/NZS 3679.1-350 125 x 75 x 12 UA 300 1.00 68.6 70.5 20.6 21.2 340 1,00 67.6 70.5 20.3 21.2 125 x 75 x 12 UA 10 UA 320 1.00 51.6 572 15.5 17.2 360 1.00 50.6 57.2 15.2 17.2 10 UA 8 UA 320 0.964 39.8 46.0 119 14.3 360 0.931 38.8 44.7 11.6 14.3 8 UA Table 28 Unequal Angles - n-axis and p-axis - Dimensions and Properties Designation About n-axis About p-axis Product of 2nd Moment of Area Designation P Z P. Z S Z n₂ 6 mm mm mm 10 mm mm 10°mm³ mm 10 mm 10 mm mm 10 mm mm 10°mm³ mm 10'mm³ 10 mm mm 10 mm² 125 x 75 x 12 UA 3.54 43.3 818 81.7 43.3 77.3 39.6 0.958 18.4 52.0 56.6 16.9 31.4 20.6 -105 125 x 75 x 12 UA 10 UA 2.88 42.3 68.2 827 34.9 62.5 39.9 0.789 17.5 45.2 575 13.7 25.1 20.9 -0.867 10 UA 8 UA 2.41 415 58.1 83.5 28.9 52.0 40.1 0.664 16.8 39.6 58.2 114 20.7 21.0 -0.731 8 UA Value (MPa) Does this stress exceed the yield stress of the member? Location on beam (draw sketch) Location on Cross section (draw sketch) Largest tensile stress Largest compressive stress

For the beam in figure 1, find the value and location of the largest tensile and compressive stresses. There may be more than one candidate location for each of these. 3.2 kN/m 2 1.9 kN.m Im A 3m 2m Figure 1 Figure 2 The cross section shown in Figure 2 is 125x75x8 UA the cross section and material properties are shown below; (Note that in the tables, the horizontal and vertical coordinate n and p, and are right and up respectively. Table 26 Unequal Angles - x-axis and y-axis - Dimensions and Properties Designation Nominal Mass Actual Radii Thickness per Thickness About x-axis About y-axis Torsion Tan Designation Constant Alpha Gross Coordinate metre Area of of Centroid Cross Leg-size Root Toe (b,-t) (b,-t) Section b, x b, t r 5, t A Рап y Z V₁ mm mm mm ka/m mm mm mm mm² mm mm 10 mm mm 10 mm mm 125 x 75 x 12 UA 17.7 12.0 10 UA 14.2 9.5 8 UA 11.8 7.8 8.0 5.0 9.42 5.25 2260 8.0 5.0 12.2 6.89 1810 8.0 5.0 15.0 8.62 1500 43.3 18.4 42.3 17.5 3.20 41.5 16.8 2.68 3.91 83.2 83.8 84.2 59.7 31.8 Z Y₁ Z S r 10-mm³ mm 10 mm 10mm³ 47.0 65.5 34.6 113 81.4 41.6 38.2 59.3 53.9 33.9 94.4 65.8 58.9 45.5 33.3 80.4 54.6 V x, Z 2日 X mm 10 mm mm 0.585 19.9 42.0 0.476 19.2 42.2 0.399 18.6 10 mm³ mm 29.3 414 24.9 41.6 21.5 Z 10-mm³ mm 10 mm² 10mm 14.1 31.9 18.4 29.7 11.4 30.7 15.5 24.1 16.2 9.55 29.9 13.3 20.1 16.3 S r J mm 10 mm 16.1 110 0.356 125 x 75 x 12 UA 56.2 0.360 31.7 0.363 10 UA 8 UA Form Factor Table 27 Unequal Angles - x-axis and y-axis - Properties for Assessing Section Capacity Designation Yield Stress About x-axis About y-axis Yield Stress Form Factor About x-axis About y-axis Designation Load A Load C Load B Load D Load A f k₁ Z Z Z Z f k Z Load C Z Load B Z Load D Z mm mm mm MPa 10mm 10 mm 10'mm³ 10 mm MPa 10 mm 10 mm 10/mm³ 10-mm³ 300PLUS AS/NZS 3679.1-350 125 x 75 x 12 UA 300 1.00 68.6 70.5 20.6 21.2 340 1,00 67.6 70.5 20.3 21.2 125 x 75 x 12 UA 10 UA 320 1.00 51.6 572 15.5 17.2 360 1.00 50.6 57.2 15.2 17.2 10 UA 8 UA 320 0.964 39.8 46.0 119 14.3 360 0.931 38.8 44.7 11.6 14.3 8 UA Table 28 Unequal Angles - n-axis and p-axis - Dimensions and Properties Designation About n-axis About p-axis Product of 2nd Moment of Area Designation P Z P. Z S Z n₂ 6 mm mm mm 10 mm mm 10°mm³ mm 10 mm 10 mm mm 10 mm mm 10°mm³ mm 10'mm³ 10 mm mm 10 mm² 125 x 75 x 12 UA 3.54 43.3 818 81.7 43.3 77.3 39.6 0.958 18.4 52.0 56.6 16.9 31.4 20.6 -105 125 x 75 x 12 UA 10 UA 2.88 42.3 68.2 827 34.9 62.5 39.9 0.789 17.5 45.2 575 13.7 25.1 20.9 -0.867 10 UA 8 UA 2.41 415 58.1 83.5 28.9 52.0 40.1 0.664 16.8 39.6 58.2 114 20.7 21.0 -0.731 8 UA Value (MPa) Does this stress exceed the yield stress of the member? Location on beam (draw sketch) Location on Cross section (draw sketch) Largest tensile stress Largest compressive stress

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.2.19P: At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with...

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