Statically Indeterminate Shaft - MAXIMUM SHEAR STRESS | Mechanics of Materials

PROBLEM D.48
Determine the absolute maximum shear stress on the shaft. JG is constant.
00:00 Problem Introduction
01:00 Applying the Sections Method
✅ The section method consists of making a cut at a distance x from the bezel C of the shaft and at a distance x from point B where the torque of 600 N.m is applied.
When making the cuts, remember that the reaction at support C is in the opposite direction to the torque applied at B, that is, counterclockwise.
NOTE: when summing the moments for each shaft section, the internal torques BC and AB to be determined act counterclockwise by convention. Note that we are going to obtain the TAB and TBC torques as a function of the TC reaction.
06:40 Applying the Torsional Angle Formula
✅ Using the concept of torsional angle we know that the torsional angle of C with respect to A, that is, the torsional angle of one end of the shaft in relation to the other has to be equal to zero because the shaft is statically indeterminate .
Therefore, it is known that because we have two sections on the axis, the angle of twist that occurs in section CB plus the angle of twist that occurs in section AB is equal to zero. Therefore, by applying the torsional angle formula, we will obtain a third equation whose unknowns to be determined are TAB and TCB. This makes it possible to determine the values ​​of the internal torque acting in the AB and BC region of the axis.
11:20 Calculation of Maximum Shear Stress
✅ Now, as we know the values ​​of the internal torques in each region of the shaft, the highest torque is found in the CB region, thus producing the highest shear stress in the shaft.
Source: Mechanics of Materials 7th Ed. (R.C. Hibbeler)
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