Civil Engineering PE Civil Engineering Theory of Structure 4

Question 1

In plastic analysis, a beam mechanism forms when the number of plastic hinges equals:

Accepted Answer

The degree of static indeterminacy plus one

Answer

For a beam to form a mechanism, the number of plastic hinges must equal the degree of static indeterminacy plus one (n = r + 1).

Question 2

The flexibility coefficient f_ij represents:

Accepted Answer

The displacement at coordinate i due to a unit force at coordinate j

Answer

Flexibility coefficient f_ij is the displacement (or rotation) at coordinate i caused by a unit force (or moment) applied at coordinate j.

Question 3

Castigliano's second theorem states that the partial derivative of total strain energy U with respect to a force P_i equals:

Accepted Answer

The deflection at the point and direction of P_i

Answer

Castigliano's second theorem: δ_i = ∂U/∂P_i, giving the displacement in the direction of force P_i at its point of application.

Question 4

In a continuous beam analyzed by the three-moment equation (Clapeyron's theorem), the equation relates:

Accepted Answer

Moments at three consecutive supports to the applied loads and spans

Answer

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.

Question 5

The shape factor (f = Z/S) for a solid circular cross-section is approximately:

Accepted Answer

1.5

Answer

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.

Civil Engineering PE Practice Test

Civil Engineering PE Practice Test

Civil Engineering PE Civil Engineering Theory of Structure 4