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Question

A composite beam is made of two brass [E=110GPa][E=110 \mathrm{GPa}] bars to two aluminum [E=70GPa][E=70 \mathrm{GPa}] bars, as shown in Figure P8.44. The beam is subjected to a bending moment of 380 N380 \mathrm{~N}-m acting about the zz axis. Using a=5 mm,b=40 mm,c=10 mma=5 \mathrm{~mm}, b=40 \mathrm{~mm}, c=10 \mathrm{~mm}, and d=d= 25 mm25 \mathrm{~mm}, calculate (a) the maximum bending stresses in the aluminum bars. (b) the maximum bending stress in the brass bars.

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Answered 1 year ago
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Given:\bold{Given:}

  • Length of the aluminum bars, LalL_{al} = 40 mm40~\text{mm}
  • Height of the aluminum bars, HalH_{al} = 5 mm5~\text{mm}
  • Length of the brass bars, LbrL_{br} = 10 mm10~\text{mm}
  • Height of the brass bars, HbrH_{br} = 25 mm25~\text{mm}
  • Bending-moment acting about the z-axis of the beam, M=380 NmM = 380~\text{N} \cdot \text{m}
  • Modulus of elasticity of the aluminum bars, E1E_1 = 70 GPa70~\text{GPa}
  • Modulus of elasticity of the brass bars, E2E_2 = 110 GPa110~\text{GPa}

Required:\bold{Required:}

  • Maximum bending stress in the aluminum bars, σmax (al)\sigma_{\text{max (al)}}
  • Maximum bending stress in the brass bars, σmax (br)\sigma_{\text{max (br)}}

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