In the column analogy technique, the cross-sectional area of the analogous column for an El flexural rigidity fixed beam of span L is specified as__________________?
Show answer Hide answer
Answer: A. L/EI
Explanation
The column analogy technique creates a mathematical analogy between real beam elastic weight and a fictitious column cross-section. For a prismatic fixed-end beam of span length L and flexural rigidity EI, the analogous column width and area are derived. Integrating the elastic weight over the span results in a cross-sectional area equal to span length divided by flexural rigidity. Column analogy is a classical force method used to determine fixed-end moments and stiffness properties of curved or variable beams. The cross-sectional area of the analogous column represents the integral of one over EI along the entire span. Moments of inertia of the analogous column correspond directly to carry-over factors and stiffness coefficients.
Dividing by two EI underestimates the analogous column cross-section area derived from direct integral calculations. Dividing by three EI or four EI introduces incorrect scaling factors that fail to match fixed-end beam elastic weight integration. others_placeholder_fix
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Structural analysis via the displacement method treats which entities as fundamental unknowns__________________?
Show answer Hide answer
Answer: A. displacements
The displacement method of structural analysis formulates equilibrium equations expressed purely in terms of unknown joint displacements. By solving for these unknown translations and rotations first, internal member for...
Q2. The cumulative distribution factor for all members meeting at any joint during moment distribution always equals__________________?
Show answer Hide answer
Answer: C. 1
The sum of distribution factors for all members meeting at any rigid joint in moment distribution must always equal 1. Moment distribution principles dictate that any unbalanced moment applied to a joint is shared among...
Q3. A pin-jointed plane frame characterized by (m + r) > 2j is classified as________________?
Show answer Hide answer
Answer: B. stable and statically indeterminate
A pin-jointed plane frame with member and reaction counts exceeding twice the number of joints has extra constraints. These extra members provide redundancy beyond the minimum required for basic geometric stability. Cons...
Q4. Superposition principles are valid under what conditions___________________?
Show answer Hide answer
Answer: A. deflections are linear functions of applied forces
The principle of superposition requires that structural deflections are strictly linear functions of applied loads. Linearity ensures that the combined effect of multiple loads equals the exact sum of their individual ef...
Q5. A rigid-jointed space frame meeting the condition (6m + r) < 6j is categorized as_______________?
Show answer Hide answer
Answer: A. unstable
A rigid-jointed space frame satisfying the condition (6m + r) < 6j lacks sufficient restraints and members for equilibrium, making it unstable. Space frames require six independent equilibrium equations per joint to prev...
Q6. Slope deflection formulations assume deformations originate due to________________?
Show answer Hide answer
Answer: A. only (i)
Slope-deflection equations are formulated by considering structural deformations resulting exclusively from internal bending moments. Shear and axial deformations are assumed negligible compared to flexural rotations in...