SS-V: 1160 Stress Concentration in a Groove Shaft

Test No. VS17 Find the stress concentration in a grooved shaft.

Definition



Figure 1.
The shaft is fixed on one end. A bending moment of 98125 N-mm is applied on the other end. Bending stress is calculated as 1 MPa using the equation below.(1)
σ0 = Mc/l MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4WdmaaBaaaleaacaqGWaaabeaakiaaykW7caqG9aGaaGPaVlaab2eacaqGJbGaae4laiaabYgaaaa@3F52@
Where,
c MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4yaaaa@36D9@
d/2
l MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiBaaaa@36E2@
πd4/64
The units are SI.
The model parameters are:
Parameters
Value
r
25 mm
D
150 mm
d
100 mm
r/d
0.25
D/d
1.5

Results

The following table summarizes the stress results.
  Theory1 SimSolid % Difference
σy MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4WdmaaBaaaleaacaqG5baabeaaaaa@3864@ Bending Stress [MPa] 1.5 1.5 NIL
1
Page 1030 , Shigley’s Mechanical Engineering Design, Ninth Edition, Richard G Budynass and J. Keith Nisbett