The uniaxial bar shown in figure 2.21 is of uniform cross sectional area \(A\) and length \(L\). It is clamped at the left end and subjected to a concentrated force \(F\) at the right end as shown. In addition, a uniformly distributed load \(b_{x}(x)\) acts along the length of the bar. Use the RayleighRitz method to determine the displacements \(u(x)\), the axial force resultant \(P(x)\), and the support reaction. The Young's modulus of the material of the bar is \(E\). Provide numerical results for the case: \(L=1 \mathrm{~m}, A=100 \mathrm{~mm}^{2}, E=100 \mathrm{GPa}, F=10 \mathrm{kN}\), and \(b_{x}=10 \mathrm{kN} / \mathrm{m}\).

Transcribed Image Text:

bx Figure 2.21 Uniaxial bar subject to distributed and concentrated forces F