A multicell bridge cross section given in the Figure is subjected to a torque, T = 25 kNm. Determine the rate of twist of the cross section and the shear flow in the walls. Shear modulus is: G = 78 GPa. Data given in the Figure are the sizes of the midline.
Solve Problem
Rate of twist, ×10-5 Shear flow in the exterior cells, q1[kN/m]=q3[kN/m]= Shear flow in the exterior cells, q2 [kN/m]=Solve
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Steps
Step 1. Cut cells, draw shear flows and summarize them to get torque resultant. where Step 2. Determine the relative displacement at the cuts from the sear flow. The length of the inclined wall is . Cell 1 Cell 2 Cell 3 Step 3. The relative displacement at the cuts must be zero. Write the compatibility condition. Step 4. Determine shear flows from the above condition for unit rate of twist, Ratio of the given torque and the resultant torque arises from unit rate of twist gives the rate of twist arising from the given torque.Step by step
Check shear flows
Check relative displacement
Check compatibility condition
Check shear flows from unit rate of twist
Step 4. Calculate rate of twist and the shear flows from the given torque.
Check result
Results
First cells are cut, we draw shear flows and we summarize them to get torque resultant. where Then we determine the relative displacement at each cut from the shear flow. The length of the inclined wall is . Cell 1 Cell 2 Cell 3 The relative displacement at the cuts must be zero. The compatibility condition is Shear flows can be determined from the above condition for unit rate of twist, Ratio of the given torque and the resultant torque arises from unit rate of twist gives the rate of twist arising from the given torque.Show worked out solution