Test No. VS19  Find the stress concentration in a
        filleted notch when torque is applied.
        Definition 
            
            
                
                    
                     
                Figure 1.   
             
            The shaft is fixed at one end and a torque of 0.19625 lbf-in is applied on the other
                end. Shear stress is calculated as 1 psi using the following equation. The units are
                    IPS.
(1)  
                    
                    
                        
                            
                                
                                    
                                        τ 
                                        0 
                                     
                                      
                                    = 
                                      
                                    
                                        
                                            T 
                                            c 
                                         
                                        / 
                                        J 
                                     
                                 
                                MathType@MTEF@5@5@+=
                                    feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                    hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                    4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                    vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                    fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aaS
                                    baaSqaaiaaicdaaeqaaOGaaGPaVlabg2da9iaaykW7daWcgaqaaiaa
                                    dsfacaWGJbaabaGaamOsaaaaaaa@3F6A@  
                             
                         
                     
                Where, 
                    
                        
                                    
                                        
                                            c 
                                            MathType@MTEF@5@5@+=
                                                feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                                hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                                4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                                vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                                fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yaaaa@36DB@
                                             
                                         
                                     
                                  
                        
                                    
                                        
                                            
                                                d 
                                                / 
                                                2 
                                             
                                            MathType@MTEF@5@5@+=
                                                feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                                hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                                4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                                vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                                fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaac+
                                                cacaaIYaaaaa@384B@  
                                         
                                     
                                  
                    
                    
                        
                                    
                                        
                                            J 
                                            MathType@MTEF@5@5@+=
                                                feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                                hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                                4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                                vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                                fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaaaa@36C2@
                                             
                                         
                                     
                                  
                        
                                    
                                        
                                            
                                                
                                                  
                                                  π 
                                                  
                                                  d 
                                                  4 
                                                   
                                                   
                                                  / 
                                                  
                                                  32 
                                                   
                                                 
                                             
                                            MathType@MTEF@5@5@+=
                                                feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                                hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                                4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                                vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                                fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaacq
                                                aHapaCcaWGKbWaaWbaaSqabeaacaaI0aaaaaGcbaGaaG4maiaaikda
                                                aaaaaa@3B1D@  
                                         
                                     
                                  
                    
                 
                    
                        Model Dimensions 
                        D = 2 in 
                        d = 1 in 
                        r = 0.05 in 
                        r/d = 0.05 
                        D/d = 2 
                    
                 
 
         
        Results 
            
                
                    
                        τ   =   K 
                            τ 
                            0 
                         
                     
                    MathType@MTEF@5@5@+=
                        feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                        hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                        4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                        vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                        fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdqNaaG
                        PaVlabg2da9iaaykW7caWGlbGaeqiXdq3aaSbaaSqaaiaaicdaaeqa
                        aaaa@3F4F@
                     
                 
             
             
            
                
                    
                        K   ∼   1.7  
                    MathType@MTEF@5@5@+=
                        feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                        hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                        4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                        vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                        fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiaayk
                        W7cqWI8iIocaaMc8UaaGymaiaac6cacaaI3aaaaa@3D30@
                     
                 
             
             
                 
The following table summarizes the stress results.
                            
                                  
                                Theory1  
                                SimSolid  
                                % Difference 
                             
                         
                            
                                Shear stress 
                                1.72 
                                1.717 
                                ~0.01 
                             
                         
 
 
 
     
1   Page 1030 ,
                Shigley’s Mechanical Engineering Design, Ninth Edition, Richard G Budynass and
                J.Keith Nisbett