Civil Engineering PE Civil Engineering Theory of Structure 5

Question 1

For a cable carrying a uniformly distributed horizontal load w over span L with a central sag d, the horizontal tension H at the supports is:

Accepted Answer

wL²/8d

Answer

For a parabolic cable with UDL, the horizontal component of cable tension is H = wL²/(8d), derived from moment equilibrium at midspan.

Question 2

The upper bound (kinematic) theorem of plasticity states that a load computed by:

Accepted Answer

Assuming a valid mechanism is an upper bound on collapse load

Answer

The kinematic (upper bound) theorem states that a collapse load calculated from any assumed valid mechanism is greater than or equal to the true collapse load.

Question 3

For a beam-column subjected to combined axial load P and moment M, the interaction equation used in design checks the condition that:

Accepted Answer

P/P_n + M/M_n ≤ 1.0

Answer

The linear interaction equation P/P_n + M/M_n ≤ 1.0 ensures combined axial and bending demands remain within the member's capacity.

Question 4

The theorem of three moments assumes that the slope of the elastic curve is continuous at:

Accepted Answer

Each intermediate support

Answer

The three-moment equation enforces compatibility by requiring the slope of the deflection curve to be continuous (equal from both sides) at each intermediate support.

Question 5

Which of the following correctly describes the stiffness of a member with a pin at the far end versus a fixed far end?

Accepted Answer

Far-end pinned stiffness = (3/4) × far-end fixed stiffness

Answer

For a prismatic member, releasing the far-end fixity to a pin reduces the near-end rotational stiffness from 4EI/L to 3EI/L, which is 3/4 of the fixed-far-end value.

Civil Engineering PE Practice Test

Civil Engineering PE Practice Test

Civil Engineering PE Civil Engineering Theory of Structure 5