Civil Engineering Theory of Structure Flashcards
7 cards from real Civil Engineering PE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Civil Engineering Theory of Structure flashcards as text
In plastic analysis, a beam mechanism forms when the number of plastic hinges equals:
Answer: The degree of static indeterminacy plus one
For a beam to form a mechanism, the number of plastic hinges must equal the degree of static indeterminacy plus one (n = r + 1).
The flexibility coefficient f_ij represents:
Answer: The displacement at coordinate i due to a unit force at coordinate j
Flexibility coefficient f_ij is the displacement (or rotation) at coordinate i caused by a unit force (or moment) applied at coordinate j.
Castigliano's second theorem states that the partial derivative of total strain energy U with respect to a force P_i equals:
Answer: The deflection at the point and direction of P_i
Castigliano's second theorem: δ_i = ∂U/∂P_i, giving the displacement in the direction of force P_i at its point of application.
In a continuous beam analyzed by the three-moment equation (Clapeyron's theorem), the equation relates:
Answer: Moments at three consecutive supports to the applied loads and spans
The three-moment equation (Clapeyron's) relates the bending moments at three consecutive supports M_A, M_B, M_C in terms of span lengths, loads, and EI values.
The shape factor (f = Z/S) for a solid circular cross-section is approximately:
Answer: 1.5
For a solid circular section, the shape factor f = Z/S = (4r³/3)/(πr³/4) = 16/(3π) ≈ 1.70; however the most commonly cited rounded value is 1.70, making 1.7 correct.
An arch is efficient for carrying loads primarily because:
Answer: It converts vertical loads into axial compression with minimal bending
A properly shaped arch converts applied vertical loads into predominantly axial compression along its axis, minimizing bending and using material efficiently.
The distribution factor (DF) at a joint in the moment distribution method for member AB is:
Answer: K_AB / ΣK at the joint
The distribution factor for member AB at a joint equals the relative stiffness of that member divided by the sum of stiffnesses of all members meeting at the joint.