# Working Stress Design

Situation
A concrete beam with cross section in Figure CO4-2B is simply supported over a span of 4 m. The cracking moment of the beam is 75 kN·m.

1.   Find the maximum uniform load that the beam can carry without causing the concrete to crack, in kN/m.

 A.   35.2 C.   33.3 B.   37.5 D.   41.8

2.   Find the modulus of rapture of the concrete used in the beam.

 A.   4.12 MPa C.   3.77 MPa B.   3.25 MPa D.   3.54 MPa

3.   If the hallow portion is replaced with a square section of side 300 mm, what is the cracking moment of the new section in kN·m?

 A.   71.51 C.   78.69 B.   76.58 D.   81.11

## Working Stress Design of Reinforced Concrete

Working Stress Design is called Alternate Design Method by NSCP (National Structural Code of the Philippines) and ACI (American Concrete Institute, ACI).

Code Reference
NSCP 2010 - Section 424: Alternate Design Method
ACI 318 - Appendix A: Alternate Design Method

Notation

fc = allowable compressive stress of concrete
fs = allowable tesnile stress of steel reinforcement
f'c = specified compressive strength of concrete
fy = specified yield strength of steel reinforcement
Ec = modulus of elasticity of concrete
Es = modulus of elasticity of steel
n = modular ratio
M = design moment
d = distance from extreme concrete fiber to centroid of steel reinforcement
kd = distance from the neutral axis to the extreme fiber of concrete
jd = distance between compressive force C and tensile force T
ρ = ratio of the area of steel to the effective area of concrete
As = area of steel reinforcement