Solve Shear Stress Qn: Mx,My,Mz, Mc,I,J, VQ,It

[Solidsam]

Homework Statement

Homework Equations

Mx=200Nm

My=300Nm

Mz=600Nm


Normal stress caused by bending moment at A = Mc/I = (300*0.02)/((pi*0.02^4)/4)= 47.7MPa. This answer is correct.




Shear stress by Torsional Moment=Tc/J

Polar moment of inertia J=(pi/2)*c^4

So I did (600*0.02)/((pi*0.02^4)/2)= 47.7MPa Is this correct?

&

VQ/It=1000*((4*0.02)/3*pi)*((pi*0.02^2))/(1.257*10^-7*0.04)=10.47 MPa Is this correct?

One of the stress calculations is wrong beacuse when added that should equal 48.8 MPa

So what I'm I doing wrong?

 

[PhanthomJay]

it appears you calculated Q incorrectly, ormade a math error, one or the other. The Q of a semicircle about its base is 2r^3/3

 

[Solidsam]

it appears you calculated Q incorrectly, ormade a math error, one or the other. The Q of a semicircle about its base is 2r^3/3

Is Q not =y bar prime * A prime = 4r/3pi * (pi*r^2)/2 ?

 

[PhanthomJay]

Is Q not =y bar prime * A prime = 4r/3pi * (pi*r^2)/2 ?

certainly, which simplifies to 2r^3/3. So you have made a math error...you
forgot to divide by 2 when determing area of semicircle...and some other calculation error..try again and you should get the correct shear stress as 1.06 MPa

 

[DeeNos]

I would first like to commend you for attempting to solve this problem and showing your calculations. It is always important to check our work and make sure our calculations are accurate. In this case, there are a few things that could be causing the discrepancy in your final answer of 48.8 MPa.

Firstly, it is important to note that the units for shear stress are different from those for normal stress. While normal stress is measured in MPa (megapascals), shear stress is measured in N/m^2 (newtons per square meter). This means that your final answers for shear stress should have different units than your final answer for normal stress.

Secondly, I would recommend double checking your calculations for the polar moment of inertia (J) and the second moment of area (I). These values are crucial in determining the shear stress and can greatly affect the final answer if calculated incorrectly.

Lastly, I would suggest reviewing the equations and making sure you are using the correct values for each variable. It is easy to mix up values or use the wrong formula, so it is always a good idea to double check.

I hope this helps you in solving the shear stress problem. Keep up the good work and always double check your calculations to ensure accuracy.