Prova de Resistência dos Materiais III - P1 ResMat III 20221

P1 ResMat III 20221 Paulo Câmara P1 ResMat III 20221 Paulo Câmara Problem 263 263 A 275 kN tensile load is applied to a test coupon made from 16mm flat steel plate E200 GPa v030 Determine the resulting change a in the 50mm gage length b in the width of portion AB of the test coupon c in the thickness of portion AB d in the crosssectional area of portion AB A 1612 192 mm² 192 10⁶ m² P 275 10³ N σₓ PA 275 10³ 192 10⁶ 143229 10⁶ Pa εₓ σₓE 143229 10⁶ 200 10⁴ 71615 10⁶ εᵧ εᵨ νεₓ 03071615 10⁶ 21484 10⁶ a L 0050 m σᵡ Lεₓ 005071615 10⁶ 3581 10⁶ m 00358 mm b w 0012 m σᵧ wεᵧ 001221484 10⁶ 2578 10⁶ m 000258 mm c t 00016 m σᵨ tεᵨ 0001621484 10⁶ 3437 10⁹ m 00003437 mm d A w₀1εᵧt₀1εₓ εᵧεₓ w₀t₀1 εₓ εᵧ 2w₀t₀εᵧ ΔA A A₀ w₀t₀εₓ εᵧ Neglecting terms K00010001621484 10⁶ 000825 mm² Problem 373 373 The design of a machine element calls for a 40mmouterdiameter shaft to transmit 45 kW a If the speed of rotation is 720 rpm determine the maximum shearing stress in shaft a b If the speed of rotation can be increased 50 to 1080 rpm determine the largest inner diameter of shaft b for which the maximum shearing stress will be the same in each shaft τₓ TcJ 2τ59683πc³ 47494 10⁶ Pa a f 72060 12 Hz P 45 kW 45 10³ W T P2πf 45 10³2π12 59683 Nm c 12 d 20 mm 0020 m b f 108060 18 Hz T 45 10³2π18 39789 Nm τₓ Tc₂J 2Tc₂c₁⁴ c₄ C₁⁴ c₁⁴ 2Tc₂π² C₁⁴ 0020⁴ 2397890020 53333 10⁹ e₁ 1520 10³ m 1520 mm d₂ 2c₁ 304 mm