Although it has been several years now since my graduation in the civil engineering, I still want to share what I’ve learned from the civil engineering subject of what we called “reinforced concrete design” where the working stress design was one of the topics.
It was fun during those times, especially when it came to design subjects like reinforced concrete, steel design, timber design and much more but one of my favorites was reinforced concrete design.
Now, here let me discuss working stress design and its parameters.
Working Stress Design evolved around 1900. It introduced Young’s Modulus, where it referred to the ratio between modulus of elasticity of steel and concrete. Although it is a conservative method of design. It was used by many civil engineers during that time and it has had much influence on the contemporary structural design.
It is also based on the elastic theory in which the materials, concrete, and steel are assumed to be stressed well below their elastic limit under the design loads.
Here are the parameters of working stress design.
1. Stress-Strain Diagram
This is a diagram showing the stress and strain relationships and the elastic limit where the young’s modulus applies and is called the “elastic region” occurs. The yield point, ultimate tensile stress, and the point of fracture are also indicated.
Stress (δ) is the applied load Force (F) per unit area in meters or millimeters (m/mm).
Formula: δ = F/A
Strain is the change in material length Delta-L (∆L) per original length Lo.
Formula: ε = ∆L/Lo
Modulus of elasticity is the change in stress(∆δ) over the change in change in strain (∆Ԑ).
Formula: Є = (∆δ/∆Ԑ) is called “Young’s Modulus”
0 – 1 is the line of elastic region modulus where it also called a proportional limit.
Point 2 is the point of yield stress. Where the elastic happens to the material when the force is loaded. It is commonly assumed by the structural engineers that yield stress has the value of the strain of 0.002.
Point 3 is the ultimate yield stress where the necking happens at its maximum stress.
Point 4 is the point where the material is continuously loaded and It breaks and is called a point of fracture.
Read Also: Design Methods: Working Stress Design and Ultimate Stress Design and Limit State
2. Allowable Stresses
The allowable stress is to be considered in order to know if, in the output of the design, the stress relating to concrete and steel are safe to go beyond the limit. In brief, it is the maximum stress that can be allowed on concrete and steel. Below are the limits.
2.1 Allowable stress for Concrete = 0.45 ƒ’c where ƒ’c is the specified compressive stress of concrete.
2.2 Allowable stress for steel = 0.60 ƒy where ƒy is the yield stress of steel
3. Factor of Safety
It is important to identify the factor of safety of material stress or strength, in order to determine its maximum capacity, and whether it still can resist the stress beyond expected load.
3.1 Concrete = ƒ’c/(0.45 ƒ’c) = 2.22
3.2 Steel = ƒy/(0.60 ƒy) = 1.67
Here are the important parameters for the design.
ƒ’c = 28th day specified compressive strength in Mpa or psi.
ƒc = Compressive strength in Mpa or psi.
ƒs = Stress of steel in Mpa.
Ԑs = Strain of steel
Ԑc = Strain of concrete
Єs = Modulus of elasticity of steel (200, 000 mpa or 29, 000, 00 psi)
Єc = Modulus of elasticity of concrete, 4700 Square root of ƒ’c
n = Modulus ration usually rounded whole number but not less than 6.0
n = Єs/ Єc
γc= Unit weight of concrete 24 KN/m³
5. Water-Cement Ratio
It has a great effect on the strength of concrete if the water cement ratio is not properly identified. The proper determination of water-cement ratio can be done by a series of concrete trial mixes.
Here is the graph of the effect of water-cement ratio on 28 days compressive, flexural and tensile strength.
6. Concrete and Steel Stress-Strain Curve
The stress-strain of the two materials are best shown so that it will give a raw projection or the tentative conditions of a concrete element. See the figure below.
m = ƒs/ Ԑs = Єs, stress of steel over strain of steel
Єc= ƒc/ Ԑc, Modulus of elasticity of concrete is stress of concrete over strain of concrete
Ԑs= ƒs/ Єs
Ԑc= ƒc/ Єc
Read Also: Why Civil Engineering is the Best Course Ever?
7. Analysis of beam by WSD assumptions
There is an analysis of the beam below:
a. Plane section before bending remains plane after bending.
b. Stress is proportional to strain
c. The tensile strength of concrete is negligible and tensile force are carried completely by steel.
d. The concrete and steel bond together perfectly so that no slip occurs.
It is important to figure out the section of the beam in order to project the distances of the depth of beam, the clear cover, the total height of the beam and the diameter of the steel bar.
9. Uncracked concrete stage
When the tensile stresses at the bottom of the beam are less than the Modulus of rupture. The formula is:
ƒr= 0.62 squaroot of ƒ’c
The above are the important parameters to consider by a civil engineer in designing concrete structural element especially beams. In the next article, I am going to show you samples of calculation using working stress design method.
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