SHEAR STRESS – PERFORMANCE TASK
1. Individual Task
A. Case Study Analysis (Two Scenarios)
Scenario 1: Bolt Failure in a Machine Frame
A steel bolt (diameter = 10 mm) connects two steel plates in a machine frame. The plates are
pulled in opposite directions by a force of 5,000 N.
Shear stress formula:
𝐹
𝐴
𝜋𝑑2 𝜋(0.01)2
𝐴=
=
= 7.85 × 10−5 m2
4
4
5000
𝜏=
= 63.7 MPa
7.85 × 10−5
𝜏=
Scenario 2: Door Hinge Supporting a Door
A door weighs 200 N and is supported by two hinges.
Each hinge carries 100 N.
Pin diameter = 5 mm
𝜋(0.005)2
= 1.96 × 10−5 m2
4
100
𝜏=
= 5.1 MPa
1.96 × 10−5
𝐴=
B. Everyday Object Investigation
Example: Scissors
SHEAR FORCE
At the pivot screw, the two blades try to slide past each other.
The screw experiences shear stress because the cutting force tries to push one blade sideways
relative to the other.
2. Simulation / Tool Use (Virtual Lab)
A simple shaft was modeled in a free online beam simulator and loaded with torque.
Observation:

Maximum shear stress occurs at the outer surface

Zero shear at the center
This confirms the torsion equation:
𝜏=
𝑇𝑟
𝐽
Where shear stress increases as radius increases.
3. Shear Stress Distribution
Shape
Stress Distribution
Rectangular beam
Non-uniform; max at
center
Circular shaft
Zero at center, max at
surface
Thin-walled tube
Nearly uniform
Conclusion:
Non-uniform stress causes weak points and cracking. Circular shafts resist shear better.
4. Discussion Prompt
Why is shear stress analysis critical for safe mechanical design?
Shear stress causes components to slide, snap, or fracture. Without analyzing shear, bolts, pins,
and joints can suddenly fail even when normal stresses are low. Machines, bridges, and tools
rely on shear-loaded parts, so incorrect design can lead to collapse, accidents, or death.
5. Ethics & Sustainability Reflection
Neglecting shear stress analysis can lead to mechanical failures such as broken bolts, collapsing
structures, or malfunctioning machines. These failures can injure people, destroy property, and
release harmful materials into the environment. For example, if a machine joint breaks, oil or
chemicals may leak, causing pollution. Engineers have an ethical duty to protect human life and
the environment. Proper shear stress analysis reduces waste, prevents accidents, and ensures
sustainable use of materials.
6. Mini-Project: Simple Bolted Joint Design
Design:
Two steel plates joined by a 12-mm steel bolt
Applied force = 8,000 N
𝜋(0.012)2
𝐴=
= 1.13 × 10−4 m2
4
8000
𝜏=
= 70.8 MPa
1.13 × 10−4
Mild steel shear strength ≈ 250 MPa
Safety Factor
𝑆𝐹 =
250
= 3.5
70.8
Conclusion:
The bolt is safe.
Material Choice:
Steel was chosen because it has high shear strength, low cost, and is recyclable.
7. Peer Review (Sample)
Reviewer Comment:
“The bolt size is adequate, but corrosion protection should be added. The safety factor is
acceptable, but environmental exposure may weaken the joint.”
8. Wrap-Up Summary
This project showed how shear stress affects bolts, hinges, and shafts. Calculations, sketches,
and simulation proved that shear is a major cause of failure. Proper design prevents accidents,
protects the environment, and ensures long-term performance.