Stress Concentration

Example: Suppose the allowable stress for the beam shown below is 90 MPa where

H = 80 mm and h = 40 mm. Find the maximum allowable bending moment when the radius, r,

of the fillet welding the two parts of the composite beam together is 8 mm and the thickness, t,

of the composite beam is 8 mm.

Strategy: Calculate the average bending stress in the shaft using Mc/I for the smaller section

of the beam. Then use the chart for bending of a composite beam connected by fillet welds to

find the stress concentration factor, K.

The stress concentration factor, K, depends on the ratio of the depth of the larger section, H,

to the depth of the smaller section, h, as well as the ratio of r, of the fillet weld to the depth, h,

of the smaller section. So these values need to be determined.

Finally apply K = σmax / σave.

For the data: D/d = H/h = 2 and r/d = r/h = 8/40 = 0.2

So from the chart, the stress concentration factor, K, is 1.5

Now for the smaller section, σave = Mc/I where c = h/2 = 20 mm

and I = (1/12) t h³ = (1/12) (8)(40)³ mm⁴

σave = Mc/I = M(20)/[(1/12)(8)(40)³] = 3M/6400 N/mm²

Note: 1 MPa = 1 N/mm²

Then 1.5 = σmax / σave = 90/[3M/6400)] , 3M = (90)(6400)/1.5 = 384,000

So M = 128,000 N mm = 128 Nm (result)

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