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)  
                    
                    
                        
                            
                                
                                    σ 
                                    0 
                                 
                                  =   Mc/l  
                            MathType@MTEF@5@5@+=
                                feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4WdmaaBa
                                aaleaacaqGWaaabeaakiaaykW7caqG9aGaaGPaVlaab2eacaqGJbGa
                                ae4laiaabYgaaaa@3F52@
                             
                         
                     
                     
                Where,
                    
                        
                                    
                                        
                                            c 
                                            MathType@MTEF@5@5@+=
                                                feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                                hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                                4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                                vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                                fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4yaaaa@36D9@
                                             
                                         
                                     
                                  
                        d/2 
                    
                    
                        
                                    
                                        
                                            l 
                                            MathType@MTEF@5@5@+=
                                                feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                                hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                                4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                                vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                                fr=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 
                             
                         
                            
                                
                                            
                                                
                                                  
                                                  
                                                  σ 
                                                  y 
                                                   
                                                   
                                                  MathType@MTEF@5@5@+=
                                                  feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                                  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                                  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                                  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                                  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4WdmaaBa
                                                  aaleaacaqG5baabeaaaaa@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