An existing simply supported reinforced concrete beam has a span of 6 meters. The beam has a rectangular cross-section with width $b = 300$ mm and effective depth $d = 450$ mm. The existing tension reinforcement consists of 3 bars of 20 mm diameter ($A_s = 942 \text{ mm}^2$). The concrete compressive strength is $f'_c = 28$ MPa, and steel yield strength is $f_y = 414$ MPa.

Due to a change in occupancy, the factored design moment $M_u$ is increased to 250 kN·m. The existing nominal flexural capacity is determined to be $\phi M_n = 185$ kN·m.

To provide the required additional capacity, CFRP strips will be bonded to the tension face (bottom) of the beam. The CFRP has an ultimate tensile strength $f_{fu} = 2800$ MPa, an elastic modulus $E_f = 165$ GPa, and a design rupture strain $\epsilon_{fu} = 0.017$. A single strip of CFRP with width $w_f = 150$ mm and thickness $t_f = 1.2$ mm is proposed. Verify if this strip provides sufficient nominal moment capacity (ignore strength reduction factors for this basic calculation).

A research team is developing "smart concrete" for a highway bridge deck. They incorporate a 0.5% (by weight of cement) dosage of multi-walled carbon nanotubes (MWCNTs) dispersed ultrasonically into the mix water.

The objectives are twofold:

A new dual-carriageway highway is being constructed over a saturated, highly compressible clay subgrade with a California Bearing Ratio (CBR) of less than 2%. The original design called for excavating 1.5 meters of the weak clay and replacing it with imported crushed stone to form a stable foundation.

To reduce costs and environmental impact, the engineer proposes a geosynthetic-reinforced design. A layer of woven geotextile will be laid directly over the weak clay, followed by a stiff, biaxial geogrid, and then only 0.5 meters of crushed stone base course.