It is crucial to understand the stress build-up in the various engineering construction materials, which contribute significantly to the internal material property for the construction and overall stability of the structures being erected. This understanding allows engineers to predict potential failure points and design more robust and reliable infrastructures.
Tension Stress
Defination
Tension stress is the internal resistance developed in a material when it is subjected to two equal and opposite pulling forces acting along the same axis, causing the material to elongate or stretch.
Tensile stress occurs when a material is subjected to two equal and opposite forces that pull it apart along the same straight line.
- The forces act along the same axis but in opposite directions, causing elongation of the material.
- Tensile stress is normal stress because the forces are perpendicular (normal) to the cross-section of the material.
Formula
Mathematically Tension Stress is:
\( \sigma_t=\frac {F_t}A \)
here:
- \(F_{t}\) = applied tensile force
- \(A\) = cross-sectional area
Practical Applications
There are several practical applications of Tension Stress insStructures as illustrated below.
- Cables in Suspension Bridges– Golden Gate Bridge, where the main cables hold the deck, experiencing pure tensile stress.
- Tension Members in Trusses– Roof Trusses, Transmission Towers
- Reinforcement Bars in Concrete Beams– As Concrete is weak in tension, steel rebars are used to resist tension forces.
- Bolts and Fasteners in Joints– Bolts experience tensile stress when holding two plates together under axial loads.
- Tension Rods in Tension Structures– Used in stadium roofs, cable-stayed bridges, and lightweight structures.
Also, Read: Comprehensive Guide to Tension Members in Steel Structure 101
Compression Stress
Defination
Compression stress is the internal resistance developed in a material when it is subjected to two equal and opposite pushing forces acting along the same axis, causing the material to shorten or compress.
- Acts perpendicular to the cross-sectional area.
- Causes decrease in length and increase in cross-section (in some cases).
- Common in columns, concrete structures, and machine components.
Formula
The mathematical formula for compression Stress is:
\( \sigma_s=\frac{F_c}A \)
where:
- \(F_{c}\) = applied compression force
- \(A\) = cross-sectional area
Practical Applications
- Columns in Buildings – Vertical columns in buildings bear the weight of floors and roofs, experiencing high compressive forces.
- Brick or Masonry Walls – The weight of floors and roofs applies compressive stress on the walls.
- Gravity & Arch Dams –Water pressure pushes against the dam, generating compressive stress along the face of the structure.
- Bridge Piers – Support bridge decks and withstand heavy compression.
- Railway Tracks and Sleepers– The weight of trains compresses the sleepers and ballast beneath them.
- Engine Pistons – Pistons in engines experience compression stress as they push against the fuel- air mixture during the power stroke.
- Shoe Soles When Walking – The weight of your body compresses the sole of your shoe as you step.
Also, Read: Compressive Strength of Concrete
Shear Stress
Defination
Shear stress is a measure of the internal resistance of a material to sliding or deformation along a plane parallel to the direction of the applied force. It is defined as the force per unit area acting tangentially to the surface of a material.
Formula
Mathematically, shear stress (\( \tau \)) is expressed as
\( \tau=\frac{F_s}A \)
where:
- \( F \) is the tangential force applied,
- \( A \) is the area over which the force is distributed.
Practical Applications
- Earthquake Resistance – Shear stress is a critical factor in designing buildings and structures to withstand seismic forces.
- Soil Stability – Shear stress is a key factor in analyzing the stability of slopes, embankments, and retaining walls. Excessive shear stress can lead to landslides or soil failure.
- Foundation Design – Shear stress must be considered when designing foundations to ensure they can resist lateral forces.
Bearing Stress
Defination
Bearing stress is the contact pressure between two bodies when one presses against another, commonly occurring in bolted, riveted, or pinned connections. It is the localized compressive stress that develops at the surface of contact.
Formula
Mathematically, shear stress (\( \sigma_s \)) is expressed as
\( \sigma_b=\frac F{A_b} \)
Where:
- σb\sigma_bσb = Bearing stress (N/m² or Pa)
- FFF = Applied force (N)
- AbA_bAb = Bearing area (m²) (usually the projected area of the contact surface)
For a bolt in a plate, the bearing area is calculated as:
\( A_b=d\times t \)
where:
- d = Diameter of the bolt (m)
- t = Thickness of the plate (m)
Bending Stress
Defination
Bending stress is the internal stress induced in a material when it is subjected to a bending moment, causing it to bend. It results in
- Tensile stress on one side (elongation).
- Compressive stress on the opposite side (shortening).
Formula
Formula for Bending Stress (Flexural Formula
\( \sigma_b=\frac{My}I \)
Where:
- \( \sigma_b\) = Bending stress (N/m² or Pa)
- M = Bending moment (Nm)
- y = Distance from the neutral axis (m)
- I = Moment of inertia of the section (m⁴)
Torsional Stress
Defination
Torsional stress is the stress induced in a material when it is subjected to a twisting force (torque) around its longitudinal axis. This stress causes shear deformation within the material and is common in shafts, beams, and helical springs.
Formula
\( \tau=\frac{rT}J \)
Where:
- \( \tau \) = Torsional shear stress (N/m² or Pa)
- T = Applied torque (Nm)
- r = Distance from the center (m)
- J = Polar moment of inertia (m⁴)
For a solid circular shaft:
\( J=\frac{\mathrm{πd}^4}{32} \)
For a hollow circular shaft:
\( J=\frac{\mathrm\pi\left(\mathrm d_0^4-\mathrm d_{\mathrm i}^4\right)}{32} \)
where \(d_o\) and \(d_i\) are the outer and inner diameters, respectively.
Also, Read:
FAQs:
Q: What is the unit of measurement for stress?
Answer: The unit of measurement for stress is the pascal (Pa), which is defined as one newton per square meter (N/m²).
Q: What are the types of longitudinal stress?
Answer: Longitudinal stress refers to the stress that acts along the length of a structural member. It can be categorized into two main types:
1. Tensile Stress – When a force is applied along the length of an object, causing it to elongate, the stress induced is called tensile stress. This occurs in members subjected to pulling forces, such as cables in suspension bridges or steel rods in tension.
2. Compressive Stress – When a force is applied along the length of an object, causing it to shorten, the stress induced is called compressive stress. This is common in columns, beams under axial loads, and other compression members.
Q: What is the mathematical representation of stress?
Answer: Mathematically, stress is represented as:
\( Stress=\frac{Resisting\;Force}{Cross\;Section\;Area} \)
\( \sigma=\frac FA \)
References:
- Bansal, Dr. R.K. (2009). Strength of Materials. Laxmi Publication (P) Ltd.
- Wikipedia contributors. (2024, December 13). Stress (mechanics). Wikipedia. https://en.wikipedia.org/wiki/Stress_(mechanics)
- Wikipedia contributors. (2025, January 31). Shear stress. Wikipedia. https://en.wikipedia.org/wiki/Shear_stress
