Displacement Method of Analysis: Slope-Deflection Equations

In the displacement method of analysis, what is the term for the unknown displacements at specified points (nodes) on a structure?

What is the sign convention for moments and angular displacements used in the slope-deflection equations presented in the chapter?

In the general slope-deflection equation, what does the term ψ (psi) represent?

Under which specific condition is the modified slope-deflection equation `MN = 3Ek(θN - ψ) + (FEM)N` applicable?

A frame is considered to have no sidesway if it is symmetric with respect to what?

What additional type of equation is required for the analysis of frames with sidesway that is not typically needed for frames without sidesway?

In Example 11.1, a continuous beam is analyzed. For span BC, which has a length of 6 m and a triangular load peaking at 6 kN/m, what is the value of the fixed-end moment (FEM) at support B, (FEM)BC?

In Example 11.2, a beam span BC has its end C on a roller, making it a pin-supported end span. The span is 8 ft long and has a 12 k load applied 4 ft from B. What is the value of the fixed-end moment at B, (FEM)BC?

In Example 11.3, support B of the 4 m long span AB settles by 80 mm. What is the value of the cord rotation ψAB?

For the symmetric frame in Example 11.5, which is subjected to a parabolic load of 24 kN/m on the 8 m long beam BC, what is the value of (FEM)BC?

In Example 11.7, a frame with columns AB (length 12) and DC (length 18) experiences sidesway. How is the cord rotation of column AB (ψAB) related to the cord rotation of column DC (ψDC)?

What is the final calculated value of the unknown rotation θB in Example 11.1, given that MBA + MBC = 0, where MBA = (EI/2)θB and MBC = (2EI/3)θB - 7.2?

In the analysis of the frame with sidesway in Example 11.8, what is the relationship between the unknown angular displacement θB and the unknown cord rotation ψ?

For the beam in Example 11.4 with support C pushed downward 0.1 ft, what is the cord rotation for span CD (ψCD), which is 15 ft long?

What does the general slope-deflection equation `MN = 2Ek(2θN + θF - 3ψ) + (FEM)N` relate?

In the context of the slope-deflection method, a beam is kinematically indeterminate to the fourth degree. How many degrees of freedom does it have?

What is the final calculated moment MAB in Example 11.2, after solving for the unknown rotation θB = -144.0/EI and substituting it into the equation MAB = 0.08333EIθB - 96?

In the frame analysis of Example 11.6, the far ends at D and E are pinned. Which slope-deflection equation is used for members CD and CE?

What physical principle is used to derive the general slope-deflection equation by considering the effects of displacements and loads separately and then adding them?

What does a negative value for a final calculated moment, such as MBC = -3.09 kN·m in Example 11.1, indicate about its direction on the beam?

For the frame in Example 11.10 with a sloping member AB, how are the linear displacements Δ2 and Δ3 related to Δ1?

In the derivation of the slope-deflection equation, when a moment MAB is applied to cause a rotation θA at the fixed-pinned end A, what is the resulting carry-over moment MBA at the fixed end B?

Why must the moment at the roller or pin support be zero in a pin-supported end span?

In the two-story frame analysis in Example 11.9, why are two separate cord rotations, ψ1 and ψ2, considered?

A prismatic beam member AB has a length L and constant EI. If it is subjected to a relative linear displacement Δ such that both ends are fixed against rotation, what is the induced moment MAB?

In the Procedure for Analysis for beams (Section 11.3), after solving for the unknown joint displacements, what is the next step?

What is the member stiffness, k, for a span in the slope-deflection equations?

In Example 11.5, the moment equilibrium equation at joint C is MCB + MCD = 0. Given MCB = 0.5EIθC + 0.25EIθB + 80 and MCD = 0.333EIθC, what is the resulting equation in terms of the unknown rotations?

What is the primary difference between the displacement method (like slope-deflection) and the force method of analysis?

In Example 11.8, a frame sways such that the cord rotation is ψ = Δ/4. There are no external loads on the spans, so all FEMs are zero. What is the slope-deflection equation for the moment MAB?

For the frame in Example 11.7, the shear in column AB is VA = -(MAB + MBA)/12. Why is this relationship used?

In Example 11.6, what is the member stiffness kCE for member CE, which has I = 650 in^4 and L = 12 ft?

What are the three degrees of freedom for the frame shown in Figure 11-1c, assuming axial deformation is neglected?

In Example 11.4, what are the final solved values for the unknown rotations θB and θC?

According to the procedure for analysis, if a calculated joint displacement is negative, what does this signify?

What is the final moment MDC for the frame in Example 11.5, given that the unknown rotation is EIθC = -137.1 and the governing equation is MDC = 0.1667EIθC?

Why are there no Fixed-End Moments (FEMs) for the members in Example 11.7?

In the derivation of member end moments, if a beam rotates by θB at end B while end A is held fixed, what is the reaction moment MAB at the fixed wall A?

In Example 11.9, the frame has two stories. How many force equilibrium equations are needed to solve for the sidesway displacements?

What is the final moment MCE in Example 11.6, given that EIuC = 5.113(10^-4) and the equation is MCE = 32725.7uC - 54?

The slope-deflection equation relates the internal end moments to the angular displacements θ and the span's cord rotation ψ. In which units must these angles be measured?

In the analysis of the frame with sidesway in Example 11.8, the equation for the moment MDC is `MDC = 3E(I/4)(0 - ψ) + 0`. What does the zero term for θN signify?

What is the physical meaning of a Fixed-End Moment (FEM)?

In Example 11.2, what is the final calculated moment for the fixed support at A, MAB?

Why does the slope-deflection method generally require less work than the force method for highly indeterminate structures?

In the horizontal force equilibrium equation for the frame in Example 11.7, `40 - VA - VD = 0`, what does the term `40` represent?

In Example 11.3, what is the final calculated moment at the fixed support A, MAB, given the equation MAB = 2(200(10^9))(1.25(10^-6))[θB - 3(0.02)] and the solved value of θB = 0.054 rad?

What does it mean if the term ψ (psi) is equal to zero in the slope-deflection equations for a frame?

For the frame in Example 11.6 with a 6 k point load on span BC (length 16 ft), what is the fixed-end moment (FEM) at C, (FEM)CB?

When analyzing a frame with sidesway, which of the following is considered an unknown in the slope-deflection equations along with the joint rotations?