Three solid cylindrical rods are welded together to form the compound axial member shown in the figure. The compound axial member is attached to a fixed support at A. Each rod has an elastic modulus of E= 37 GPa. Use the following values for the rod lengths and areas: L₁ = 1350 mm, L₂ = 1580 mm, L3 = 1260 mm, A₁ = 240 mm², A₂ = 150 mm², and A3 = 75 mm². What magnitude of external load P is needed to displace end D a distance of up = 80 mm to the right? A L₁ (1) + B L2 L3 (3) D
(a) Find the relationship between δ1, the elongation of rod (1), and the internal tensile force, F1, in rod (1). Assume δ1 is a positive value in units of mm and F1F1 is a positive value in units of kN. So, the answer you enter for the ratio (δ1/F1) must be in units of (mm/kN).
(b) Similar to the previous step, find the relationship between δ2, the elongation of rod (2), and the internal tensile force, F2, in rod (2). Assume δ2 is a positive value in units of mm and F2 is a positive value in units of kN. So, the answer you enter for the ratio (δ2/F2) must be in units of (mm/kN).
(c) Similar to the previous step, find the relationship between δ3, the elongation of rod (2), and the internal tensile force, F3, in rod (2). Assume δ3 is a positive value in units of mm and F3 is a positive value in units of kN. So, the answer you enter for the ratio (δ3/F3) must be in units of (mm/kN).
(d) What magnitude of external load P is needed to displace end D a distance of uD=80 mm to the right? in kN
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