# WSD Method

## Example 01: Total Compression Force at the Section of Concrete Beam

**Problem**

A rectangular reinforced concrete beam with width of 250 mm and effective depth of 500 mm is subjected to 150 kN·m bending moment. The beam is reinforced with 4 – 25 mm ø bars. Use alternate design method and modular ratio *n* = 9.

- What is the maximum stress of concrete?
- What is the maximum stress of steel?
- What is the total compressive force in concrete?

## Example 01: Required Steel Area of Reinforced Concrete Beam

**Problem**

A rectangular concrete beam is reinforced in tension only. The width is 300 mm and the effective depth is 600 mm. The beam carries a moment of 80 kN·m which causes a stress of 5 MPa in the extreme compression fiber of concrete. Use *n* = 9.

1. What is the distance of the neutral axis from the top of the beam?

2. Calculate the required area for steel reinforcement.

3. Find the stress developed in the steel.

## 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**

_{c}= allowable compressive stress of concrete

f

_{s}= allowable tesnile stress of steel reinforcement

f'

_{c}= specified compressive strength of concrete

f

_{y}= specified yield strength of steel reinforcement

E

_{c}= modulus of elasticity of concrete

E

_{s}= 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

A

_{s}= area of steel reinforcement