Beams and Frames Having Nonprismatic Members

According to the text, what is a primary reason for designing girders to be nonprismatic, such as having a variable moment of inertia?

For a nonprismatic member, what does the Stiffness Factor (K) represent?

What does the Carry-Over Factor (COF) represent for a nonprismatic member in moment distribution analysis?

What relationship between stiffness factors (KA, KB) and carry-over factors (CAB, CBA) for a nonprismatic beam is derived from the Maxwell-Betti reciprocal theorem?

How is the absolute stiffness factor, KA, for a nonprismatic member determined from the tabulated stiffness factor, kAB, and other member properties?

For a nonprismatic beam with its far end B being pin supported, what is the formula for the modified absolute stiffness factor K'A at the near end A?

What is the modified absolute stiffness factor K'A for a symmetric nonprismatic beam subjected to symmetric loading?

For a symmetric nonprismatic beam subjected to antisymmetric loading, what is the formula for its modified absolute stiffness factor K'A?

What is the generalized slope-deflection equation for the moment MN at the near end (N) of a nonprismatic member?

In the generalized slope-deflection equation for nonprismatic members, what does the term ψ represent?

A nonprismatic beam has an absolute stiffness factor at end A of KA = 0.171E. The carry-over factors are CAB = 0.619 and CBA = 0.619. If the far end of span BA is pinned, what is the modified stiffness factor K'BA?

A nonprismatic beam with parabolic haunches has a length L of 10 units. Its tabulated stiffness factors are kBC = 13.12 and kCB = 15.47. The moment of inertia at the minimum section is IC, and the modulus of elasticity is E. What is the absolute stiffness factor KBC if the term E*IC is equal to 7.5 units?

For a nonprismatic member with a pinned far end, the fixed-end moment due to a relative joint translation Δ is given by the formula (FEM)'AB = -K'A * (Δ/L) * (1 - CAB * CBA). For a prismatic member, what does this formula simplify to, given KA = 4EI/L and CAB = CBA = 0.5?

What are the common forms of nonprismatic structural members mentioned in the chapter?

For a prismatic beam, KA = 4EI/L and CAB = 0.5. If this beam is symmetric and under symmetric loading, what is its modified stiffness factor K'A?

A nonprismatic member with parabolic haunches is subjected to a uniform load. For the given geometry (aA = aB = 0.2, rA = rB = 1.0), the tabulated coefficient for the fixed-end moment at end A, MAB, is -0.0956. If the uniform load w is 2 k/ft and the span L is 25 ft, what is the value of (FEM)AB?

For a nonprismatic member with parabolic haunches under a concentrated load, the geometry is defined by b = 0.3 (ratio of load distance from end A to span L). The tabulated coefficient for the fixed-end moment at end B, MBA, is 0.0759. If a concentrated load P of 30 k is applied on a span L of 10 ft, what is (FEM)CB, where C is the far end?

When analyzing a symmetric nonprismatic beam with antisymmetric loading, what happens to the stiffness factor compared to the standard fixed-end case?

In the generalized slope-deflection equation MN = KN(θN + CNF * θF - ψ(1 + CNF)) + (FEM)N, how are the fixed-end moments (FEM)N defined in terms of sign convention?

What does the analysis of nonprismatic members in Chapter 13 have in common with the analysis of prismatic members in Chapter 12?

A nonprismatic member has an absolute stiffness KA = 100 units and a carry-over factor CAB = 0.6. If it is a symmetric beam with symmetric loading, what is its modified stiffness K'A?

A nonprismatic member is part of a symmetric beam with antisymmetric loading. Its absolute stiffness KA is 200 k-ft/rad and its carry-over factor from A to B, CAB, is 0.7. What is the modified absolute stiffness factor K'A for this member?

What is the fixed-end moment at end A, (FEM)AB, for a nonprismatic member with absolute stiffness KA = 300 k-ft/rad and carry-over factor CAB = 0.5, if it undergoes a relative joint translation Δ of 0.02 ft over a length L of 20 ft?

A nonprismatic beam with a pinned far end has an absolute stiffness KA = 500 units, and carry-over factors CAB = 0.6 and CBA = 0.7. The member has a length L of 25 units. What is the fixed-end moment at the near end A, (FEM)'AB, if the far end settles by an amount Δ = 0.1 units?

If a nonprismatic member has an absolute stiffness KA = 800 k-in/rad, a carry-over factor CAB = 0.65, and is subjected to a clockwise rotation at the near end A of θA = 0.01 rad and a clockwise rotation at the far end B of θB = 0.02 rad, what is the moment MAB due to these rotations only (ignore settlement and FEMs)?

The nomenclature in the provided tables for nonprismatic members defines rA and rB as ratios for rectangular cross-sectional areas. How are these ratios calculated?

A nonprismatic member with parabolic haunches has a haunch at end A with a depth of hA = 4 ft and a haunch at end B with a depth hB = 5 ft. The minimum section depth is hC = 2 ft. What are the values of the haunch ratios rA and rB?

How does the moment distribution method for nonprismatic members simplify the analysis compared to solving a system of slope-deflection equations?

For a prismatic beam with K = 4EI/L and C = 0.5, what is the modified stiffness for a pinned far end using the general formula K'A = KA(1 - CAB * CBA)?

If a nonprismatic member has an absolute stiffness factor KB = 1.031E and a carry-over factor CCB = 0.664, and its far end is pinned, what is its modified stiffness factor K'CB? Assume CBC = 0.781.

What is the primary information source suggested in the chapter for finding the properties (FEM, K, COF) of common nonprismatic shapes without performing complex derivations?

A nonprismatic beam has a length of 10 ft. It is part of a symmetric frame and is subjected to symmetric loading. Its absolute stiffness KA is 50 k-ft/rad and its carry-over factor CAB is 0.8. What is the modified stiffness K'A used for the analysis?

In the nomenclature for nonprismatic members, what does 'b' represent?

What is the key difference in the application of the stiffness method to frames with nonprismatic members compared to beams with nonprismatic members?

A nonprismatic member with an absolute stiffness of KA = 400 k-in/rad and a carry-over factor CAB = 0.75 experiences a clockwise rotation at the near end of θA = 0.002 rad, while the far end is fixed (θB = 0). What is the moment induced at the far end, MB?

If you are using the moment distribution method to analyze a beam with a nonprismatic end span that is pinned at the far support, which of the following simplifications is recommended in the chapter?

A symmetric nonprismatic beam with a length of 20 m is loaded symmetrically. The absolute stiffness factor KA is determined to be 10,000 kN-m/rad and the carry-over factor CAB is 0.6. What modified stiffness factor K'A should be used if you analyze only half of the beam?

In the generalized slope-deflection equation for a nonprismatic member, what does the term CN represent?

For a nonprismatic member, what is the effect of a positive (clockwise) chord rotation ψ on the end moments, according to the generalized slope-deflection equation?

Which method of analysis, moment distribution or slope-deflection, is described in the chapter as being more efficient for many cases when analyzing nonprismatic members, especially for manual calculations?

A nonprismatic beam with absolute stiffness KA = 600 units and carry-over factors CAB = CBA = 0.7 has its far end pinned. What is its modified stiffness factor K'A?

In the context of the provided tables for nonprismatic members, what does the parameter 'aA' signify?

If a nonprismatic member has a haunch at end A that is 5 ft long and the total span length is 20 ft, what is the value of the parameter 'aA'?

For a prismatic beam, the carry-over factor is always +0.5. For a nonprismatic beam, can the carry-over factor be greater than 0.5?

If a nonprismatic member is subjected to a clockwise rotation θN at the near end and a counter-clockwise rotation θF at the far end of the same magnitude (θF = -θN), which loading condition does this correspond to?

How does the generalized slope-deflection equation in Chapter 13 reduce to the standard equation for prismatic members?

If a concentrated load P is applied at the midspan of a symmetric nonprismatic beam, what simplification can be made in the analysis?

A nonprismatic member with parabolic haunches has parameters aA=0.2, rA=1.0 and aB=1.0, rB=1.0. For these values, the tabulated stiffness factor kAB is 6.41 and the carry-over factor CAB is 0.619. If E*IC/L is 1000, what is the absolute stiffness KA?

Consider a nonprismatic member with its far end B pinned. The absolute stiffness at the near end is KA and the carry-over factors are CAB and CBA. For the special case of a prismatic member, where KA=4EI/L and CAB=CBA=0.5, the modified stiffness K'A is 3EI/L. How does K'A relate to KA for this prismatic case?

Why is it necessary to determine properties like fixed-end moments, stiffness factors, and carry-over factors for nonprismatic members before analysis?