Challenge 2

Dead Load (DL) = 100 kN

Superimposed Dead Load (SDL) = 50 kN

Live Load (LL) = 200 kN

Wind Load (WL) = ±150 kN

Earthquake Load (EL) = ±200 kN

Total Dead Load (DL + SDL) = 100 + 50 = 150 kN

Case 1: DL + SDL + LL

= 150 + 200 = 350 kN

Case 2: DL + SDL + LL + WL

= 150 + 200 ± 150 = 500 kN (max), 200 kN (min)

Case 3: DL + SDL + LL + EL

= 150 + 200 ± 200 = 550 kN (max), 150 kN (min)

Design Loads per WSM:

Max: 550 kN

Min: 150 kN

Load Combination Formula Calculation

1 1.5 (DL + LL) 1.5 × (150 + 200) = 525 kN

2 1.2 (DL + LL + WL) 1.2 × (150 + 200 ±150) = 1.2 × (500 or 200) = 600 kN (max), 240 kN (min)

3 1.5 (DL + WL) 1.5 × (150 ±150) = 1.5 × (300 or 0) = 450 kN (max), 0 kN (min)

4 0.9 DL ± 1.5 WL 0.9 × 150 ± 1.5 × 150 = 135 ± 225 = 360 kN (max), -90 kN (min)

5 1.2 (DL + LL + EL) 1.2 × (150 + 200 ±200) = 1.2 × (550 or 150) = 660 kN (max), 180 kN (min)

6 1.5 (DL + EL) 1.5 × (150 ±200) = 1.5 × (350 or -50) = 525 kN (max), -75 kN (min)

7 0.9 DL ± 1.5 EL 0.9 × 150 ± 1.5 × 200 = 135 ± 300 = 435 kN (max), -165 kN (min)

Design Load per LSM:

Maximum: 660 kN

Minimum (considering uplift or reversal): -165 kN

Ans2)

Slab depth 150mm

Bar size 8mm

spacing 125mm

clear cover 20mm

Fy 415Mpa

Fck 30Mpa

Effective depth =150-20-(8/2)=126mm

Steel Area in strip Ast=(1000/125)x (3.14/4)x8x8)=402.123mm^2

Neutal depth xu=(0.87*415*402.123)/(0.36*30*1000)=13.443mm

Moment of resistance Mr=0.87fyast(d-(1.015fy ast/1000 fck)

=0.87*415*402.123(126-(1.015*415*402.123/1000*30)

Mr=17.47 Knm

P=(100/d)(3.14/4)xdxd=(100/126)(0.785*8*8/125)=0.3189

pt lim=41.38*(xumax/d)xfck/fy

pt lim=41.38*0.4791*30/415=1.433

p<pt lim hence the section is under reinforced section.

Design load=990KN

Mr=17.47 Knm,the section is the under reinforced section