Plane truss
The lower-right joint of the three-member plane truss shown in Figure 2 is supported
by a skew roller. The truss members are of a solid circular cross section having diameter
d D 25 mm and elastic modulus E D 50 GPa. The force P D 70 kN is applied to the
unconstrained joint. Number the nodes and elements, and solve for unknown nodal
displacements and reaction forces using:
a) Master-slave method,
b) Penalty element method,
c) Lagrange multiplier method.
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Figure Q5(a) shows a plane truss supported by a horizontal spring at the top node. The...
Figure Q5(a) shows a plane truss supported by a horizontal spring at the top node. The truss members are of a solid circular cross section having a diameter of 20 mm and an elastic modulus (E) of 80 GPa (10° N/m2). The spring has a stiffness constant of k-2000 kN/m. A point load of 15 kN is applied at the top node. The direction of the load is indicated in the figure. The code numbers for elements, nodes, DOFS, and...
Problem 2: The figure below shows a two-member plane truss supported by a linearly elastic spring....
Problem 2: The figure below shows a two-member plane truss supported by a linearly elastic spring. The truss members are of a solid circular cross section having diameter, d = 20mm, and E = 80 GPa. The linear spring has a stiffness constant of 50 N/mm. A load of 15 kN is applied at 3 at an angle of 50 degrees with the horizontal. Find (a) The global displacements of the unconstrained node and (b) compute the reaction forces and...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the c...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the circular truss members is 4 cm. The material used has an elastic modulus E-160GPa 1. Calculate the forces in each truss member. 2. Calculate the horizontal and vertical displacements 1 KN of the truss nodes B and C Calculate the margin of safety. Note: Tension members can fail by stress failure and compression members can fail by stress failure or buckling. 3. 1.732 m 2 KN...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the c...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the circular truss members is 4 cm. The material used has an elastic modulus E-160GPa 1. Calculate the forces in each truss member. 2. Calculate the horizontal and vertical displacements 1 KN of the truss nodes B and C Calculate the margin of safety. Note: Tension members can fail by stress failure and compression members can fail by stress failure or buckling. 3. 1.732 m 2 KN...
A plane structure consists of three truss elements connected to four nodes, as shown below. All t...
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...
1. The members of truss are attached together by pins having 5 cm in diameter and...
1. The members of truss are attached together by pins having 5 cm in diameter and 10 cm in length. The truss is supported by a frictionless pin at one end (joint A) and a roller system at the other joint k). The load Lis equal to 5 kN. The section view of the truss member is below and it is homogeneous all along the truss. Elastic modulus is 200 GPa, shear modulus is 75 GPa for the truss. (a)...
The plane truss shown in Figure is composed of members having a square 15 mm ×...
The plane truss shown in Figure is composed of members having a
square 15 mm × 15 mm cross section and modulus of elasticity
E = 69 GPa.
a. Assemble the global stiffness matrix.
b. Compute the nodal displacements in the global coordinate
system for theloads shown.
c. Compute the axial stress in each element
3 kN 3 5 kN 2 1.5 m 4. 1.5 m
Problem 2: a. For the plane truss shown in Figure 2, determine the nodal displacements, the element forces and stresses, and the support reactions. All elements have E-70 GPa and A-25 cm 100 k...
Problem 2: a. For the plane truss shown in Figure 2, determine the nodal displacements, the element forces and stresses, and the support reactions. All elements have E-70 GPa and A-25 cm 100 kN 50 kN 50 kN 4 4 6 Figure 2. Plane Truss
Problem 2: a. For the plane truss shown in Figure 2, determine the nodal displacements, the element forces and stresses, and the support reactions. All elements have E-70 GPa and A-25 cm 100 kN 50...
The truss is constructed from three aluminum alloy members, each having a cross-sectional area of A...
The truss is constructed from three aluminum alloy members, each
having a cross-sectional area of A = 1350 mm2 and an elastic
modulus of E = 62 GPa. Assume a = 2.8 m, b = 9.0 m, and c = 5.5 m.
If the horizontal displacement of roller B must not exceed 5.0 mm,
calculate the maximum vertical load Pmax that can be supported by
the truss.
Chapter 5, Supplemental Question 008 The truss is constructed from three aluminum alloy...
The truss is constructed from three aluminum alloy members, each having a cross- sectional area of...
The truss is constructed from three aluminum alloy members, each having a cross- sectional area of A = 850 mm2 and an elastic modulus of E = 63 GPa. Assume a = 3.4 m, b = 11.6 m, and c = 5.7 m. If the horizontal displacement of roller B must not exceed 3.6 mm, calculate the maximum vertical load Pmax that can be supported by the truss. Answer: Pmax = KN
Figure Q5(a) shows a plane truss supported by a horizontal spring at the top node. The truss members are of a solid circular cross section having a diameter of 20 mm and an elastic modulus (E) of 80 GPa (10° N/m2). The spring has a stiffness constant of k-2000 kN/m. A point load of 15 kN is applied at the top node. The direction of the load is indicated in the figure. The code numbers for elements, nodes, DOFS, and...
Problem 2: The figure below shows a two-member plane truss supported by a linearly elastic spring. The truss members are of a solid circular cross section having diameter, d = 20mm, and E = 80 GPa. The linear spring has a stiffness constant of 50 N/mm. A load of 15 kN is applied at 3 at an angle of 50 degrees with the horizontal. Find (a) The global displacements of the unconstrained node and (b) compute the reaction forces and...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the circular truss members is 4 cm. The material used has an elastic modulus E-160GPa 1. Calculate the forces in each truss member. 2. Calculate the horizontal and vertical displacements 1 KN of the truss nodes B and C Calculate the margin of safety. Note: Tension members can fail by stress failure and compression members can fail by stress failure or buckling. 3. 1.732 m 2 KN...
Problem 1 Analyze the truss structure (statically determinate) shown below. The diameter of the circular truss members is 4 cm. The material used has an elastic modulus E-160GPa 1. Calculate the forces in each truss member. 2. Calculate the horizontal and vertical displacements 1 KN of the truss nodes B and C Calculate the margin of safety. Note: Tension members can fail by stress failure and compression members can fail by stress failure or buckling. 3. 1.732 m 2 KN...
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...
1. The members of truss are attached together by pins having 5 cm in diameter and 10 cm in length. The truss is supported by a frictionless pin at one end (joint A) and a roller system at the other joint k). The load Lis equal to 5 kN. The section view of the truss member is below and it is homogeneous all along the truss. Elastic modulus is 200 GPa, shear modulus is 75 GPa for the truss. (a)...
The plane truss shown in Figure is composed of members having a
square 15 mm × 15 mm cross section and modulus of elasticity
E = 69 GPa.
a. Assemble the global stiffness matrix.
b. Compute the nodal displacements in the global coordinate
system for theloads shown.
c. Compute the axial stress in each element
3 kN 3 5 kN 2 1.5 m 4. 1.5 m
Problem 2: a. For the plane truss shown in Figure 2, determine the nodal displacements, the element forces and stresses, and the support reactions. All elements have E-70 GPa and A-25 cm 100 kN 50 kN 50 kN 4 4 6 Figure 2. Plane Truss
Problem 2: a. For the plane truss shown in Figure 2, determine the nodal displacements, the element forces and stresses, and the support reactions. All elements have E-70 GPa and A-25 cm 100 kN 50...
The truss is constructed from three aluminum alloy members, each
having a cross-sectional area of A = 1350 mm2 and an elastic
modulus of E = 62 GPa. Assume a = 2.8 m, b = 9.0 m, and c = 5.5 m.
If the horizontal displacement of roller B must not exceed 5.0 mm,
calculate the maximum vertical load Pmax that can be supported by
the truss.
Chapter 5, Supplemental Question 008 The truss is constructed from three aluminum alloy...
The truss is constructed from three aluminum alloy members, each having a cross- sectional area of A = 850 mm2 and an elastic modulus of E = 63 GPa. Assume a = 3.4 m, b = 11.6 m, and c = 5.7 m. If the horizontal displacement of roller B must not exceed 3.6 mm, calculate the maximum vertical load Pmax that can be supported by the truss. Answer: Pmax = KN
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