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

The degree of static indeterminacy

Answer

The number of spans

Answer

The number of applied loads

Question 2

The flexibility coefficient f_ij represents:

Accepted Answer

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

Answer

The stiffness at coordinate i due to unit force at j

Answer

The force at i required to produce unit displacement at j

Answer

The moment at i due to unit rotation at 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

The stress at the point of application

Answer

The strain energy density

Answer

The reaction force at the support

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

Reactions at three consecutive supports

Answer

Deflections at midspan of adjacent bays

Answer

Shear forces at three consecutive sections

Question 5

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

Accepted Answer

1.5

Answer

1.0

Answer

1.7

Answer

2.0

Question 6

An arch is efficient for carrying loads primarily because:

Accepted Answer

It converts vertical loads into axial compression with minimal bending

Answer

It develops large bending moments at the crown

Answer

It is inherently statically indeterminate

Answer

It relies on tensile strength of the material

Question 7

The distribution factor (DF) at a joint in the moment distribution method for member AB is:

Accepted Answer

K_AB / ΣK at the joint

Answer

ΣK / K_AB

Answer

K_AB × L_AB

Answer

1 / K_AB