For the two-member truss in Example 14.1, Member 2 has near end 2 (codes 1,2) and far end 1 (codes 5,6). It has L=5, lx=0.6, ly=0.8. What is the value of the k_26 element (row 2, col 6) in the member stiffness matrix k2, before multiplying by AE?
Explanation
This is a quantitative question testing the ability to identify and calculate a specific element of the member global stiffness matrix using the formula from Eq. 14-16, paying attention to the correct signs and terms.
Other questions
In the stiffness method for analyzing trusses, what are the discrete finite elements and nodes typically represented by?
When using the stiffness method, what is the convention for assigning code numbers to the degrees of freedom?
What does the member stiffness matrix, k', represent in the context of a single truss member?
For a truss member with constant AE and length L, what is the correct form of the member stiffness matrix k' in local coordinates?
What is the physical meaning of a member stiffness influence coefficient, k'_ij?
A truss member connects a near node N at (xN, yN) = (2, 3) to a far node F at (xF, yF) = (6, 6). What is the value of the direction cosine lx for this member?
What is the primary function of the displacement transformation matrix, T?
How is the member global stiffness matrix, k, derived from the local stiffness matrix k' and the transformation matrix T?
For a truss member with AE/L = 100, lx = 0.6, and ly = 0.8, what is the value of the element k_NxNx in the 4x4 member global stiffness matrix k?
When assembling the structure stiffness matrix K, what happens if two or more members are connected to the same joint?
In Example 14.1, for Member 1, the near end is node 2 (codes 1, 2) and the far end is node 3 (codes 3, 4). The member has AE and length L=3. Its global stiffness matrix k1 is given as AE times a 4x4 matrix. What is the value of element (3,3) in that 4x4 matrix before it is multiplied by AE?
In Example 14.1, how is the element K11 of the final structure stiffness matrix K calculated?
What is the primary purpose of partitioning the structure stiffness equation Q = KD into the form involving Qk, Qu, Dk, and Du?
After partitioning the structure stiffness equation and assuming the known displacements Dk are zero, what is the equation used to solve for the unknown displacements Du?
How is the force in a specific member, qF, calculated once the global nodal displacements D are known?
In Example 14.3, a two-member truss is subjected to a -2 k load in direction 2. What are the solved values for the displacements D1 and D2?
In Example 14.3, what is the calculated internal force in Member 2?
When analyzing a truss with an inclined roller support, why is a special set of nodal coordinates (x'', y'') used at that support?
For a member connecting a global-coordinate node (N) to a nodal-coordinate node (F) at an inclined support, which equation correctly represents the member's global stiffness matrix k?
In the analysis of trusses with thermal changes, what does the term Q0 in the equation Q = KD + Q0 represent?
A truss member of length L, with coefficient of thermal expansion alpha, and properties AE, is subjected to a temperature increase of deltaT. What is the initial compressive force q0 needed to hold the nodes of the member fixed?
A truss member is fabricated 0.01 m too short before being fitted into a truss. The member has length L = 5 m and properties AE. What is the initial tensile force (qF)0 that must be applied to the member to fit it into the truss?
In a space-truss analysis, how many degrees of freedom are generally considered for each joint (node)?
What is the size of the member global stiffness matrix k for a single space-truss member?
How many direction cosines are needed to define the orientation of a space-truss member in global coordinates?
According to the Procedure for Analysis in Section 14.6, what is a partial check that can be performed after assembling the member and structure stiffness matrices?
For a truss member with AE/L = 200, lx = -0.8, and ly = 0.6, what is the value of the element k_NyNx in the 4x4 member global stiffness matrix k?
In the final step of the stiffness method, after finding unknown displacements Du and reactions Qu, what equation is used to find the internal member forces, including the effects of fabrication errors?
Why is the stiffness method generally preferred over the flexibility (force) method for computer analysis?
A truss member in a space frame connects node N at (0,0,0) to node F at (3,4,12). What is the length L of this member?
For the space-truss member in the previous question with length L=13 and connecting (0,0,0) to (3,4,12), what is the direction cosine lz?
What is the relationship between the force transformation matrix and the displacement transformation matrix for a truss member?
In the context of the stiffness method, what does kinematic indeterminacy refer to?
If a statically determinate truss is subjected to a temperature change in one of its members, what is the effect on the support reactions and member forces?
In Example 14.2, a 4-joint, 6-member truss is analyzed. What is the size (order) of the final structure stiffness matrix K?
In Example 14.2, for Member 2, the near end is node 1 (codes 1, 2) and the far end is node 4 (codes 7, 8). The member has AE, L = 10*sqrt(2), lx = 0.707, ly = 0.707. What is the value of the k_17 element (row 1, col 7) in the member stiffness matrix k2, before multiplication by AE?
In Example 14.5, a support settlement of 25 mm downward is applied at joint 1. How is this settlement represented in the initial Dk vector?
What is the primary difference in the stiffness method procedure when a member has a fabrication error versus when a support settles?
In the analysis of the space truss in Section 14.9, the transformation matrix T is a 2x6 matrix. What does it transform?
For the symmetric truss in Example 14.2, consider the final assembled structure stiffness matrix K. Why is the element K13 equal to zero?
What is represented by the submatrix K21 in the partitioned stiffness equation?
In Example 14.7, a member is fabricated 0.01 m too short. What is the value of the initial fixed-end force (qF)0 for this member if AE = 8000 kN and L = 5m?
In Example 14.8, a member is subjected to a temperature increase of 150 F. What is the value of (qN)0, the initial force at the near end, if AE=21750 k and the coefficient of thermal expansion alpha = 6.5(10^-6)/F?
The formulation of the stiffness method requires several matrices to be created and manipulated. Which of the following is NOT a matrix used in the direct formulation of the member global stiffness matrix k?
For a space-truss member with direction cosines lx, ly, and lz, what is the formula for the element k_NxNx in its 6x6 global stiffness matrix?
What is the structure stiffness matrix K?
After solving for the unknown displacements Du, the unknown support reactions Qu are found using the equation Qu = K21*Du (assuming Dk=0). What physical principle does this equation represent?
For the truss member in Example 14.1, Member 1 is horizontal, so ly = 0. What is the value of the k_12 element (force in x-dir due to y-disp) in its global stiffness matrix k1?
The final element of the structure stiffness matrix K for the truss in Example 14.2 is K88. Which member stiffness matrices contribute to this element?