NCEES Mechanics of Materials 5

Question 1

A beam is made of two materials bonded together (composite beam). The transformed section method converts one material to an equivalent width using:

Accepted Answer

The modular ratio n = E₁/E₂

Answer

The transformed section scales one material's width by the modular ratio n = E₁/E₂ so standard flexure formulas apply.

Question 2

In a biaxial stress state (σ_x and σ_y, no shear), which expression gives the principal stresses?

Accepted Answer

σ₁,₂ = (σx + σy)/2 ± (σx − σy)/2

Answer

With no shear stress, Mohr's circle degenerates and principal stresses are simply σ_x and σ_y directly.

Question 3

A rod is loaded in fatigue. The endurance limit Se is 200 MPa and the mean stress is 100 MPa (Su = 500 MPa). Using the Goodman criterion, the allowable alternating stress amplitude is:

Accepted Answer

160 MPa

Answer

Goodman: σa/Se + σm/Su = 1 → σa/200 + 100/500 = 1 → σa = 200 × 0.8 = 160 MPa.

Question 4

Which boundary condition produces the LOWEST Euler critical buckling load for a column of given L and EI?

Accepted Answer

Fixed-free (flagpole) with K = 2

Answer

P_cr = π²EI/(KL)²; the largest K = 2 (fixed-free) gives the smallest critical load.

Question 5

What does a stress concentration factor K_t represent in design?

Accepted Answer

The ratio of maximum local stress to nominal (average) stress at a geometric discontinuity

Answer

K_t = σ_max/σ_nom; it quantifies the amplification of stress caused by holes, notches, fillets, or other geometric changes.

NCEES Practice Test

NCEES Practice Test

NCEES Mechanics of Materials 5