Problem 2 (20 pts): Consider the following structure consisting of a set of bars. Assume the...
as shown in Fig.2. The lengths of two 2. Three bars form an isosceles right triangle, right angle sides are L, which is 1000 mm. The cross section area of the three bars are 1000 mm2. Young's modulus of bars are E-21x10 N/ mnt Please find the global stiffness matrix of these bar element system. If the numbering of the bar nodes changes, does the global stiffness matrix change? (15 %) y 1 (3) (1) (2) 3 2 Fig.2 Bar...
blem 5 (25 points): Consider the system of bars shown below. Bars AB, CD, and EF are connected d link BED. Determine the horizontal displacement of point F B by a rigid . Bar AB has a cross-sectional area of 0.012 m2, a Young's modulus of 200 GPa, and a length of 0.34 m. . Bar CD has a cross-sectional area of 0.010 m2, a Young's modulus of 200 GPa, and a length of 034 m . Bar EF has...
2. For the pin-jointed truss shown in Figure Q2.1 applied at node 4. The Young's modulus E(GPa) is the same for the three truss vertical downward force P(kN) is a members. The cross sectional area of each of the truss members is indicated below and expressed in terms of a constant A. By using the stiffness method: (a) Compute the reduced stiffness matrix Kg [5 marks [10 marks (b) Calculate the global displacements of node 4 in terms of P,...
Question 3 The structure shown in Figure Q(3) is a two-bar truss with spring support. Both bars have modulus of elasticity and cross-sectional area of E- 210 GPa and A -5.0 x10 m. Bar one has a length of 5 m and bar two a length of 10 m. The spring stiffness is k -2000 kN/m. CVE 4303(F) Page 2 of 4 Determine (a) the stiffness matrix for each of the three elements (15 marks) (b) the normal stresses in...
Problem 3. (3 points). Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that the bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 3 are fixed. Element 1 has Young's Modulus of 300 Pa, length of 1 m and cross-sectional area of m. Element 2 has Young's Modulus of 200...
The pin-connected structure shown in Fig. 5 consists of a rigid bar ABCD and two 1,500-mm-long bars. Bar (1) is steel [E=200 GPa] with a cross-sectional area of A1 = 510 mm2. Bar (2) is an aluminium alloy [E-70 GPa] with a cross-sectional area of A2 1,300 mm2. All bars are unstressed before the load P is applied. If a concentrated load of P 200 kN acts on the structure at D determine: (a) the normal stresses in both bars...
Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that the bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 3 are fixed Element 1 has Young's Modulus of 300 Pa, length of 1 m and cross-sectional area of 1 m2. Element 2 has Young's Modulus of 200 Pa, length of 2...
A plane structure consists of three truss elements connected to four nodes, as shown below. All trusses have cross sectional area A -7.104 m2 and elastic modulus E = 210 GPa. The length of each truss element is L = 1 m. A point force, P -5 kN, is acting on node 4 L/2 3.1 Calculate the displacements at the nodes 3.2 Calculate the reaction forces 3.3 Calculate the stress in each bar A plane structure consists of three truss...
Chapter 5, Problem 35P Bookmark Show all steps ON Problem The pin-connected structure shown in Figure P5.35/36 consists of a rigid beam ABCD and two supporting bars. Bar (1) is a bronze alloy [E105 GPa] with a cross-sectional area of A1 290 mm2. Bar (2) is an aluminum alloy [E70 GPa] with a cross-sectional area of A2 650 mm2. If a load of P 30 kN is applied at B, determine (a) the normal stresses in both bars (1) and...
The plane truss is subjected to a load as shown in Figure 4. Take E = 200 GPa and cross sectional areas of members 1, 2 and 3 as 150, 250 and 200 mm2 respectively a) Assemble the upper triangular part of the global stiffness matrix for the truss b) Determine the horizontal and vertical displacements at node 4 c) Calculate the forces in each member of the truss. (25 marks) 20 kN 3 60° 4 1.5m 2 2 20m...