Beam Design Under Multi-Axial Loading | Stress Analysis Tutorial

Описание: In this video, we solve Question 4 from the mechanics of materials exam — an L-shaped machine component (ABD) subjected to multi-axial loading.
We step through the complete stress analysis at point H, including bending and shear in two orthogonal planes.

🔍 Topics Covered

1️⃣ Internal force components on the cross-section through H
2️⃣ Calculation of normal and shear stresses at point H
3️⃣ Determination of principal stresses and maximum shear stress
4️⃣ Application of the Maximum Shear Stress (Tresca) Criterion to check yielding
5️⃣ Discussion of results and failure interpretation for a ductile material (σᵧ = 200 MPa)

📘 Learning Outcomes

By the end of this video, you’ll understand how to:

Build a 3-D stress state for a beam under combined bending and shear

Visualize and interpret the stress components on an element

Compute principal stresses analytically

Apply the Tresca yield criterion for design safety assessment

⚙️ Given Data

Beam cross-section: 20 mm × 40 mm

Forces: 2.5 kN, 3 kN, 0.5 kN

Material yield strength: 200 MPa

Point H located at y = 20 mm, z = 40 mm

📐 Key Concepts

Bending about multiple axes, shear stress distribution, principal stress transformation, and the Maximum Shear Stress Theory (Tresca) for ductile materials.

💡 Perfect for:

Mechanical & Civil Engineering students

Exam preparation for Mechanics of Structures / Strength of Materials

Anyone wanting a clear, step-by-step explanation of multi-axial beam stress analysis

🧠 Chapters
0:00 Introduction
0:35 Problem setup & geometry
2:10 Internal forces at section H
5:45 Normal and shear stress calculations
9:15 Principal stresses and Mohr’s circle concept
11:00 Tresca criterion & failure check
13:00 Final summary and design implications

📎 Keywords: beam design | multi-axial stress | bending and shear | principal stress | maximum shear stress theory | Tresca criterion | yielding | mechanics of materials | engineering design | Mohr’s circle