Figure < 1 of 1 Consider, for instance, a bar of initial length L and cross-sectional...
Learning Goal:To understand the meaning of Young's modulus and to perform some real-life calculations related to the stretching of steel.Hooke's law states that for springs and other "elastic" objectsF=K(delta x)where F is the magnitude of the stretching force, delta x is the corresponding elongation of the spring from equilibrium, and k is a constant that depends on the geometry and the material of the spring. If the deformations are small enough, most materials, in fact, behave like springs: Their deformation...
Question 1 (10 marks) Consider the bar element shown in Figure 1. Cross sectional area A = 200 mm and Young's modulus E = 200 x 107 kPa. If u = 3 mm and u2 = 2 mm, determine: (a) the displacement at point P, (b) the strain, (c) the stress, and (d) the strain energy in the element. U] U2 x = 400 mm xi = 200 mm x2 = 700 mm Figure 1 EAL 2 Note: the strain...
3. 2090] Consider a uniform bar of Young's modulus E, cross-sectional area A, moment of inertia density p, length L, with an attached end mass, m, connected to a rigid wall via a linear spring of spring constant, k, see Figure. Let the longitudinal vibration of the bar be Wa.f). (a) [4] Write down the boundary conditions. m E, p Boundary condition at x 0 Boundary condition at x L (b) [81 Derive the equation for the natural frequency (c)...
5) Consider a bar shown below. Cross-sectional area Ae = 1.2 in., and Young's modulus E = 35 x 106 psi. If ui = 0.02 in, and u2 = 0.025 in., considering linear interpolation, determine the following: (a) the displacement at point P; (b) the strain & and stress o; and (c) the element stiffness matrix. u2 2 x = 20 in. x = 15 in. X = 23 in.
1. Consider a bar under tension. The bar has length L, rectangular cross-section of sides b and h, Young's modulus E, density p, and applied tensile force P. a) If all parameters are fixed except for h, find the value of h that minimizes the mass of the bar under stress, elongation, and stiffness constraints. Assume safety factors oo, Os, and Ok and failure values o*, 8*, and k* b) Also find the minimum mass of the bar m under...
5. EVALUATION I. Create a stress-strain diagram for the measured values in table 1 and identify the mechanical properties of the material. (4 marks) II. Identify the following and label them in the graph. (12 marks) • Young's modulus Yield strength Elongation Ultimate tensile strength THEORETICAL BACKGROUND Equations: Cross-sectional Area (A) Modulus of Elasticity (E) Tensile Strength (ST) Percent Elongation (%EL) d? E = Sy Ey Sr Pu А %EL Extension at fracture Gauge Length Where: A: Cross- Sectional Area...
A brass rod with a length of 1.50 m and a cross-sectional area of 2.50 cm2 is fastened end to end to a nickel rod with length L and cross-sectional area 0.880 cm2 . The compound rod is subjected to equal and opposite pulls of magnitude 3.46×104 N at its ends. a.Find the length L of the nickel rod if the elongations of the two rods are equal. b.What is the stress in the brass rod? c.What is the stress...
Write down which one of the following statements is false: (A) for a wire of a certain substance and certain cross-sectional area, the spring constant is inversely proportional to natural length (B) Young's modulus is the gradient of stress as a function of strain (C) uids do not have a bulk modulus (D) spring constant is the gradient of load as a function of deformation (E) some substances do not obey Hooke's Law at all
Consider a steel guitar string of initial length 2.00m and cross-sectional area A = 0.500mm^2. The Young s modulus of the steel is 2.0 times 10^11 N/m^2. How far would such a string stretch under a tension of 1500 N?
Problem 1 Consider the bar shown below with a cross-sectional area A, 1.2 m2, and Young's modulus E-200 X 109 Pa. Ifq,-0.02 m and q,-0.025 m determine the following (by hand calculation) (a) the displacement at point P., (b) the strain E and stress σ (e) the element stiffness matrix, and (d) the strain energy in the element 91 *p 20 m x,-15 m x,-23 m Problem 2. Consider a finite element with shape functions N1) and N2(Š) used to...