(a) Wrie equations for the shear and the bending maorsent for any section of the beam in the interval CD. (10%)

a. The maximum um axial load P that can be applied to the shaft. (15%)

b. The principal stresses es and the maximun shearing stress st a point an the outside surface of midway BC. (10%) 

(b) Draw complete shear and bending moment dingrams for the beam. (15%6)

Prablem 3 (25%) The stress-strain dingram for a bone is shown as the right figure snd can be described by the equstion, where g is in kPa. Determine the modulus of toughness and the a amount of elongation of a 200-mm-long region just before it fractures if failure occurs at σ =6873.52 kPa.

Problem 4 (25%) The bone sbown as the right figure can be modeled as a tube having an inner diameter of 9.5 mm and an outer G (MPa) dianneter of 32 mm. Dotermine the maximum um eiasti tic 16.10 static force P that can be applied to its center. r. Assume 8.75 the bone to be roller supported at its ends. The stress-strain diagran for the bone is shown as the figure below, and is the sanne in tension as in compression.

(b) The solid shaft is subjected to a torque, bending moment, and shear force as shown in Figure 4. Determine the principal stresses acting at points A and B. (16%)

(a) Please draw graphs to show the variation of stress Mohr's circle for a steel bar under axial constant amplitude fatigue loading. The ratio of minimum stress σmin to maximum stress σmax is -0.5. (9%)

3. Determine the deflection of end C of the 150-mm-diameter solid circular shaft (Figure 3). The shaft is made of steel having a modulus elasticity of E = 200 GPa. (25%)

2. As shown in Figure 2, the allowable working stresses for the manufactured wood beam are 10 MPa in bending and 1 MPa in shear. Determine the maximum intensity w0 of the distributed loading that the beam can safely support. (25%)

(b) 下圖1-b所示的組件由橫截面積為400 mm²的鋁管AB組成。一直徑為10 mm 的鋼桿連接到剛性軸環上,並穿過管子。如果對鋼桿施加了80 kN 的拉 伸載荷,試決定鋼桿端 C 的位移。已知鋼桿和鋁管的楊氏係數分別為 Est = 200 GPa, Eal = 70 GPa。(15%)

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