Strains in circular bar vary linearly

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Unformatted text preview:   Segment BC: LBC=500mm •  Segment CD: LCD=400mm DETERMINE: (A) MAX. SHEAR STRESS IN SECTIONS BC AND CD (B) ANGLE OF TWIST BETWEEN GEARS B AND D FREE- BODY DIAGRAMS USED TO CALCULATE REACTION TORQUES TBC AND TCD IN SEGMENTS BC AND CD, RESPECTIVELY 2/1/13 M. Mello/Georgia Tech Aerospace 5 PROBLEM WORKED OUT ON BOARD GIVEN: •  TAPERED BAR AB OF CIRCULAR CROSS SECTION •  Twisted by torques (T) applied at the ends •  dA = diameter at right- hand end •  dB = diameter at leP- hand end (dB > dA) DETERMINE: (A) MAX. SHEAR STRESS IN THE BAR (B) DERIVE A FORMULA FOR THE ANGLE OF TWIST IN THE BAR y = r ( x) ✓ 0, dA 2 dx ◆ ✓ dB L, 2 r ( x) = ◆ x ✓ dB d( x) = ✓ dA 2 2 L dB dA L ◆ ◆ x+ dA 2 x + dA radius diameter x 2/1/13 M. Mello/Georgia Tech Aerospace 6 POWER TRANSMISSION ²་  MOST IMPORTANT USE OF CIRCULAR DRIVE SHAFTS IS TO TRANSMIT MECHANICAL POWER FORM ONE DEV ICE OR MACHINE TO ANOTHER. •  SHIP PROPELLER SHAFT •  AUTOMOBILE DRIVE SHAFT •  BICYCLE AXLE ²་  TYPICAL DESIGN PROBLEM: DETERMINE REQUIRED DIAMETER OF CIRCULAR SHAFT TRANSMIT REQUIRED POWER AT SPECIFIED ROTATIONAL SPEED, WITHOUT EXCEEEDING ALLOWABLE STRESSES TORQUE SHOWN IN FIGURES IS REACTION TORQUE EXERTED ON THE SHAFT BY THE DEVICE 2/1/13 M. Mello/Georgia Tech Aerospace 7 TORQUE – POWER RELATIONSHIPS FROM ELEMENTARY PHYSICS Work done by torque of constant magnitude (3- 36) W =T Applied torque Power: rate at which Work is done P= Angle of rotaZon dW d =T dt dt angular speed (ω) in rad/s Recall, ! = 2⇡ f (f = Hz = s- 1) P = 2⇡ f T (3- 40) also, n = # of revoluZons/minute and so, n = 60f and … P= 2/1/13 2⇡ nT 60 (3- 42) M. Mello/Georgia Tech Aerospace P = T ! (3- 36) Power Units: N ewton = 1W att second horsepower = 550f t lb/s 8...
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This note was uploaded on 09/19/2013 for the course CEE 3001 taught by Professor Zhu during the Spring '09 term at Georgia Tech.

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