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Evaluate secure axial load:
A small piece of ISA (200 × 100 × 15) angle carries a compressive load, the line of action of which coincides along the intersection of the middle planes of the legs. If the maximum compressive stress is not to exceed 112 N/mm2, what is the secure axial load P? Given A = 4278 mm2, rxx = 64 mm, ryy = 26.4 mm.
Figure
Solution
Area of cross-section A = 4278 mm2
Eccentricity of load with respect of xx-axis = (71.8 - 7.5) = 64.3 mm
Eccentricity of load with respect to yy-axis = 22.2 - 7.5 = 14.7 mm
Maximum compressive stress at any section will be
= (P/ A) + (M xx/ I xx) × y + (M yy/ I yy) × x
or
Here, rxx = 64 mm and ryy = 26.4 mm fmax = 112 N/mm2
∴ 112 = (P/A) (1 + ((64.3 × 71.8 )/(64)2)+ 14.7 × 22.2 /((26.4)2)
= (P/4278) [1 + 1.127 + 0.4684]
∴ P = 184.6 kN.
Use the graphics and the equation to define the term principal stress and principal planes.
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