A 1 INCH THICK A36 STEEL AXIALLY LOADED MEMBER IS SHOWN IN T

A 1 INCH THICK A-36 STEEL AXIALLY LOADED MEMBER IS SHOWN IN THE FOLLOWING FIGURE: SOLVE FOR THE STRESS CONCENTRATION FACTORS K_1 THRU K_4. IF THE ALLOWABLE TENSILE STRESS IS 12,000 psi, WHAT IS THE MAXIMUM MAGNITUDE OF THE LOAD P THAT CAN BE APPLIED TO THE MEMBER?

Solution

From tha charts of theoritical stress concentration factors for a plate of finite width with a circular hole and a Rectangular filleted bar under axial load, we get

Stress concentration factor K1 with r/d= 0.5 and D/d=2 is <1.76, the chart includes data till r/d=0.3

Stress concentration factor K2 with d/w=1/4=0.25 is 2.42.

Stress concentration factor K3 with d/w=0.5 is 2.16.

Stress concentration factor K4 with r/d=(1/3)/(10/3)=0.1 and D/d=4/(10/3)=1.2 is 1.8.

(Symbols have their usual meanings)

Given thickness of the member t=1 inch

For 1,

Nominal stress= P/dh = P/2*1= P/2

Hence maximum stress in the vicinity of the hole < K1*P/2 = 1.76*P/2=0.88P

For 2,

Nominal stress= P/(w-d)t = P/(4-1)*1= P/3

Hence maximum stress in the vicinity of the hole= K2*P/3 = 2.42*(P/3) = 0.81*P

For 3,

Nominal stress= P/(w-d)t = P/(4-2)*1= P/2

Hence maximum stress in the vicinity of the hole= K3*P/2 = 2.16*(P/2) = 1.08*P

For 4,

Nominal stress= P/dh = P/(10/3)*1= 0.3*P

Whe have seen that the maximum stress appears for 3.

Maximum stress shall not exceed the allowable tensile stress i.e 12000 psi

Hence 1.08*P=12000

P=12000/1.08=11111.11 lb