Structural Stresses -Basics of designing a structure Part-1
Design of a structure comprise of three major design tasks, i.e., Design of members, Design of connections and Design of foundation. Before going into design of structure I will describe what structural stresses are. In this article I will answer questions like, what are stresses in structural members, what is difference between stress and strain, etc. Explanation will be provided in simple language so that the people with limited knowledge can also get benefit from this article. Engineering students and those who want to learn structural engineering will get benefit from this article.
Prior to designing, we need to analyse the structure to determine what internal forces will develop internally. Design of a structure basically is optimal sizing of its constituent members, connections and foundation so that the internally developed stresses are within the safe limit. By doing this we make sure that the entire structure can carry the applied loads and transfer it safely to the mother foundation soil.
Depending on method of design, either we compare the developed stresses with the allowable stresses or compare the internal forces, i.e., moments, forces, etc, with the respective capacity of the constituent elements, connections and foundations. Capacity is actually derived using stresses.
In general, stress is obtained by dividing a force by the area bearing the force. Therefore, unit of stress is force per unit area, for example, N/mm2, pounds per square inch, etc. Prior to explaining how to design a structure, let us see what are the main stresses that we need to check during design of a structure.
Normal stress: Normal stress is caused by a normal force and is obtained by dividing the normal force by the cross section area which is bearing the force. When we say normal force, the force acts in perpendicular to the surface, cross section area in this case. Normal stress is denoted mostly by σ and σ = F/A
Where F is normal force say N is its unit, A is cross section area, say mm2 then normal stress σ has a unit of N/mm2.
Depending on nature of the normal force the normal stress can be a compressive stress or tensile stress. If the normal force is compression then the stress is compressive and it is a tensile if the normal force is tension. They are denoted by σc and σt respectively. Normal stress can either be compressive or tensile in a cross section.
For example, different members of a truss can have compressive or tensile stresses.
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| Types of stresses in a truss |
Bending stress: Bending stress is caused by a bending moment. This stress is also called a flexural stress. Bending stress is obtained by the following way:
σ = M y / I
Where, M is Bending Moment, say Nmm is its unit, I is moment of inertia or second moment of area, say mm4 and y is the distance of extreme fibre of the cross section from its centroid, say mm. Then bending stress σ has a unit of N/mm2.
Bending stress can be compressive and tensile in a cross section. Following figures showing cross section of a beam explain it further:
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| B.M. and Shear force in a beam |
Amount of bending stress in a beam depends on orientation of the beam. Following figure describes how the bending stress is calculated depending on orientation of a beam.
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| Calculation of bending stress |
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| Distribution of bending stress |
Shear stress: Shear stress is caused by shear force. Shear stress is calculated by dividing Shear force by shear area. Since shear force acts in perpendicular to the beam the shear area is cross section area of the beam. Therefore, shear force acts in parallel direction to the plane of cross section.
Shear stress, τ = V/A where, V is shear stress and A is shear area unit is again force per unit area, say N/mm2
Stress due to torsion: Torsion in a structure causes special shear stress. The shear stress caused by torsion is calculated as follows.
τ = T r / J where, T is torsion, say its unit is Nmm, r is radial distance from centre to where torsional stress is required, say mm, J is Polar moment of inertia, say mm4. Distribution of torsional stress is shown in the following figure:
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| Distribution of torsional stress |
Horizontal Shear: Horizontal Shear is special type of shear which acts along the length of a bending member. For example, if there is a bending structure, such as a beam, that is made up of two or more independent layers connected to each other with some connectors or glue then, the horizontal shear develops in between the two layers in the connectors or in the glue. This type of shear is checked mostly in the design of composite bridge decks.
Horizontal shear stress is calculated in the following way:
τ = V A y /(I b)
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| Distribution of Horizontal stress |
Where, V is vertical shear, say unit is N, Ay is the first moment of area about neutral axis of the cross section, say mm3, I is second moment of area or moment of inertia, say mm4 and b is width of cross section, say mm. Thus unit of the horizontal shear stress is N/mm2.
Foundation stress: Here we must not forget about the stresses that develop in the foundation soil due to applied loads. Generally, stresses in the foundation soil is kept less than the allowable stress of the soil. Allowable stress in the soil is called the bearing capacity of foundation. Bearing capacity of foundation is determined using the shear stresses and allowable settlement in the soil.
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| Basics of foundation pressure calculation |
In practice, the foundation stress is also called foundation pressure. Because of the moments in the foundation the distribution of foundation pressure is not constant. The foundation pressure caused by moment needs to be added to normal foundation pressure as shown in the figure above. Distribution of foundation pressure are not always linear as it depends on nature (elasticity) of the foundation soil.
Stresses in connections: Computation of stresses in a connection is slightly complex as compared to the stresses explained above. The calculation depends on type and arrangement of connections. However, calculation of stresses in a connection is carried out based on the basics of stresses shown above.
Stresses in connections of constituent elements of the structure needs to be calculated to compare it with the related allowable values. I will explain in other article how the stresses in the connections are calculated.
In the design process all the maximum stresses developed due to applied loads are kept less than or equal to the related permissible values. Other method of design compares the developed forces with the related capacities
So far, I have explained about the stresses that develops in the structure. Now, let's look at some parameters of the materials that we use in the design.
Young's Modulus: Young's modulus is also known as Elasticity Modulus which is a ratio of stress and strain of a material. This is basically a measurement of resistance of a material against being deformed.
Young's modulus, E = σ/∊ Its unit is same as that of stress, N/mm2 for example.
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| Typical Stress-Strain curve for a ductile steel |
Strain: Strain is a ratio of elongation and unit length, for example. Depending on direction of force application the strain can be normal or shear strain. If force is applied perpendicular to cross section then, it is normal strain. Similarly, if force is applied in parallel direction to the cross section then it's a shear strain.
Strain, ∊= 𝛿/L Where, 𝛿 is change in length, say its unit is mm and L is original length of a member, say mm. Therefore, strain does not have any unit.
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