Calculate the maximum and minimum stress, Mechanical Engineering

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Calculate the maximum and minimum stress:

A cast iron column of 200 mm diameter carries a vertical load of 400 kN, at a distance of 50 mm from the centre. Calculate the maximum & minimum stress developed in the section, along with the diameter passing through the point of loading.

1786_Calculate the maximum and minimum stress.png

(a)

1990_Calculate the maximum and minimum stress1.png

(b) Stress Distribution along the Diagonal

Figure

Solution

Vertical load, P = 400 kN = 400 × 103 N

Diameter of the section, D = 200 mm

Area of the section,  A = (π/4) (200)2  = 31416 mm2

Direct stress, f0 =(P/A) =4 × 105/31416 = 12.732 N/mm2

Eccentricity, e = 40 mm

Bending moment, M = P × e = (400 × 103 ) 40 = 16 × 106  N-mm

Section modulus, z = π D 3/32            = π (200)3 /32= 785.4 × 103 mm3

Bending stress,  f =± Pe / Z =±  16 × 106 /785.4 × 103=± 20.372 N/mm2

 ∴ Resultant stress at the edge, B = f0  + fb  = 12.732 - 20.372

                                                     = 33.104 N/mm2 (compressive)

∴ Resultant stress at the edge, A =  f0  - fb  = 12.732 - 20.372

                                                        =- 7.640 N/mm2 (tensile)

The stress distribution along with the diameter is as illustrated in Figure (b).


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