What Are the Shear Stress and Angle of Twist for a Steel Member Under Torque?

[Dell]

A 3.5 m long steel member with a W310 x 143 cross- section is subjected to 4.5KNm torque. Knowing that G=77GPa, determine (a) the maximum shearing stress along the line a-a, (b) the maximum shearing stress along the line b-b, (c) the angle of twist

http://lh4.ggpht.com/_H4Iz7SmBrbk/Sysfg6WJmLI/AAAAAAAACBI/SsE4jsJMYAE/22.jpg

i know that

$$\tau$$=$$\frac{M*t}{Jeq}$$

while Jeq=$$\frac{1}{3}$$$$\sum$$h_ib_i³

Jeq=1/3*((0.309*0.0229³) +(0.309*0.0229³) + (0.2872*0.014³))

Jeq=2.7365e-6

$$\tau$$=$$\frac{4500*t}{2.7365e-6}$$

a)

$$\tau$$_a-a=$$\frac{4500*0.0229}{2.7365e-6}$$

=3.7657e7
=37.657MPa

b)

$$\tau$$_b-b=$$\frac{4500*0.014}{2.7365e-6}$$

= 2.3022e7
=23.02MPa

(according to my book the correct answers are meant to be 39.7MPa and 24.2MPa)


for the angle

$$\phi$$=M*L/(G*Jeq*$$\eta$$)

$$\eta$$=1.29)

$$\phi$$=$$\frac{4500*3.5}{77e9*2.7365e-6*1.29}$$

=0.0579rad
= 3.3199 degrees,

but again the correct answer is meant to be 4.72 degrees,

what am i doing wrong??

 

[Dell]

i think i need to SOMEHOW find the torque seperately on the flange and web and them somehow solve the problem,, please help someone

 

[Mene]

I would first check my calculations to see if there were any errors made in the process. It is always important to double check calculations to ensure accuracy. I would also make sure that the units are all consistent and that the values used for G and the dimensions of the cross section are correct.

If everything appears to be correct, I would then consider the possibility of rounding errors. It is possible that the values given in the problem were rounded, and therefore the calculated values may differ slightly from the given correct answers.

Another possibility is that the correct answers were obtained using a different method or formula. Sometimes, there may be multiple ways to solve a problem and different methods may yield slightly different results.

If I am still unable to determine the source of the discrepancy, I would seek guidance from a colleague or consult additional resources to ensure that my calculations and approach are correct. It is important to always strive for accuracy and seek out help when needed in scientific research.