Homework Answers
Static indeterminacy of the given structure = 3m + r - 3j (where m=no. of members, r = no. of reactions, j= no. of joints)
SI = (3 x 3) + 5 - (3 x 4) = 2
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Prob. 4 Identify the order of the indeterminacy of the following plane frame, and form the...
For the structure shown, write the static equilibrium equation of the structure in matrix form 2...
For the structure shown, write the static equilibrium equation of the structure in matrix form 2 in terms of EI. Clearly identify your DOF's and their order in the matrix equations. You can neglect axial deformations E 200 GPa, I 300(10)6 mm1 A 101 12 kN/m 2 m 10) mm for each member 4 m 2 m
Problem 3 Analyze the frame structure subjected to the following support movements: a beam-end settlement at...
Problem 3 Analyze the frame structure subjected to the following support movements: a beam-end settlement at Node #4; . a column base rotation at (Node #1). All members have a constant bending stiffness El and are considered as axially rigid. a) Determine the degree of kinematic indeterminacy (DKI) and show the independent DOFs. b) Assemble the structure stiffness matrix Kg. c) Assemble the structure fixed-end force vector Po. Then solve for nodal displacement vector Us based on the equations of...
1. The number of equilibrium equations available in 2D is 6. 2. The Method of Sections...
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5. The following structure represents the two-dimensional model of a bent in a bridge. The distributed...
5. The following structure represents the two-dimensional model of a bent in a bridge. The distributed dead and live loads on the bent are 35 kN/m and 25 kN/m, respectively. The bent at points A and B is resting on square foundations which transfer the axial loads in columns AE and BD to the underlying soil. In order to design the foundations, we need to know the value of reaction forces. First, calculate the degree of indeterminacy of this structure....
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26.23 The moment distribution method in structural analysis can be treated as: Displacement method Force method Flexibility method First order approximate method 26.24 The method of moment distribution in structural analysis is: An approximate one An interative method An exact one None of the above 26.25 The strain energy method in structural analysis is based on the minimization of the energy with respect to: Strains Force Stress Displacement 26.26 The minimization of potential energy in structural analysis results in: Equilibrium...
The frame ABCD (Figure 2) is subject to the distributed loadw The supports do not move...
The frame ABCD (Figure 2) is subject to the distributed loadw The supports do not move 5.2 kN/mas shown. The dimensions are H-4 m and L 20 m EI is constant in each span. Learning Goal: To use the slope-deflection equations to analyze the moments in a frame with no sidesway. The slope-deflection equations for a frame member are given below, where N signifies the near end, F means the far end Part A - Write the slope-deflection equations ,...
What is the reaction Ax to the nearest 0.01 kN for the following frame? El are...
What is the reaction Ax to the nearest 0.01 kN for the following frame? El are constant and the same for all members. Consider only bending energy. W = 67 kN/m w -5 m-+ 10 m ---5 m 5 m А B 422 CHAPTER 10 ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES BY THE FORCE METHOD 10.5 Force Method of Analysis: Frames The force method is very useful for solving problems involving statically indeterminate frames that have a single story and unusual...
1) Consider a pendulum of constant length L to which a bob of mass m is attached. The Q6. pendulum moves only in a two-dimensional plane (see figure below). The polar frame of reference attached to t...
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3. (40 pts) Analyze the following statically determinate frame by hand and clearly draw the shear...
3. (40 pts) Analyze the following statically determinate frame by hand and clearly draw the shear force, axial force, and bending moment diagrams indicating relevant (maximum and minimum) values for each of the following load cases: a) Uniform dead load (q) applied on the beam must add beam self-weight (concrete) to this value b) Uniform live load (qu) applied on the beam. c) Horizontal wind force (H H=12kip 12 x 20 gp-1.4 kip/ft -2.0 kip/ft 14 ft 12" x 12...
Q.2: Taking A, B, C and D as the nodes for the grillage frame (AB and...
Q.2: Taking A, B, C and D as the nodes for the grillage frame (AB and BC are parallel to Y axis and BD is parallel to X axis) shown below, evaluate the nodal load vector {P) and the stiffness matrix [K] of the structure taking same elastic modulus (E = 100GPa) and Poisson's ratio (v = 0.25) for all members. The members are having same rectangular cross-section (a = 200mm, b = 250 mm). Solve the governing equation [K]{X}={P}...
For the structure shown, write the static equilibrium equation of the structure in matrix form 2 in terms of EI. Clearly identify your DOF's and their order in the matrix equations. You can neglect axial deformations E 200 GPa, I 300(10)6 mm1 A 101 12 kN/m 2 m 10) mm for each member 4 m 2 m
Problem 3 Analyze the frame structure subjected to the following support movements: a beam-end settlement at Node #4; . a column base rotation at (Node #1). All members have a constant bending stiffness El and are considered as axially rigid. a) Determine the degree of kinematic indeterminacy (DKI) and show the independent DOFs. b) Assemble the structure stiffness matrix Kg. c) Assemble the structure fixed-end force vector Po. Then solve for nodal displacement vector Us based on the equations of...
1. The number of equilibrium equations available in 2D is 6. 2. The Method of Sections results in a 2D rigid body equilibrium problem. 3. Indeterminate trusses can only be solved by Method of Joints, not Sections. 4. By definition, truss members must be pin connected & carry only axial load. 5. Shear Force is the first derivative of Bending Moment. 6. Distributed Load is the integral of Shear Force. 7. The maximum Bending Moment is always at the center...
5. The following structure represents the two-dimensional model of a bent in a bridge. The distributed dead and live loads on the bent are 35 kN/m and 25 kN/m, respectively. The bent at points A and B is resting on square foundations which transfer the axial loads in columns AE and BD to the underlying soil. In order to design the foundations, we need to know the value of reaction forces. First, calculate the degree of indeterminacy of this structure....
The frame ABCD (Figure 2) is subject to the distributed loadw The supports do not move 5.2 kN/mas shown. The dimensions are H-4 m and L 20 m EI is constant in each span. Learning Goal: To use the slope-deflection equations to analyze the moments in a frame with no sidesway. The slope-deflection equations for a frame member are given below, where N signifies the near end, F means the far end Part A - Write the slope-deflection equations ,...
What is the reaction Ax to the nearest 0.01 kN for the following frame? El are constant and the same for all members. Consider only bending energy. W = 67 kN/m w -5 m-+ 10 m ---5 m 5 m А B 422 CHAPTER 10 ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES BY THE FORCE METHOD 10.5 Force Method of Analysis: Frames The force method is very useful for solving problems involving statically indeterminate frames that have a single story and unusual...
1) Consider a pendulum of constant length L to which a bob of mass m is attached. The Q6. pendulum moves only in a two-dimensional plane (see figure below). The polar frame of reference attached to the bob is defined by er,ce where er is the unit vector orientecd away from the origin and e completes the direct orthonormal basis. The pendulum makes an angle 0(t) between the radial direction and the vertical direction e(t) The position vector beinge ind...
3. (40 pts) Analyze the following statically determinate frame by hand and clearly draw the shear force, axial force, and bending moment diagrams indicating relevant (maximum and minimum) values for each of the following load cases: a) Uniform dead load (q) applied on the beam must add beam self-weight (concrete) to this value b) Uniform live load (qu) applied on the beam. c) Horizontal wind force (H H=12kip 12 x 20 gp-1.4 kip/ft -2.0 kip/ft 14 ft 12" x 12...
Q.2: Taking A, B, C and D as the nodes for the grillage frame (AB and BC are parallel to Y axis and BD is parallel to X axis) shown below, evaluate the nodal load vector {P) and the stiffness matrix [K] of the structure taking same elastic modulus (E = 100GPa) and Poisson's ratio (v = 0.25) for all members. The members are having same rectangular cross-section (a = 200mm, b = 250 mm). Solve the governing equation [K]{X}={P}...
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