Mohr’s Circle kya hota hai? 2D aur 3D Stress Analysis ka Asaan Tarika in Hindi

Mohr’s Circle kya hota hai? 2D aur 3D Stress Analysis ka Asaan Tarika

Mohr's Circle ek graphical representation hoti hai jise stress analysis ke liye use kiya jata hai. Yeh 2D ya 3D stress components ko visualize karne ka ek efficient tarika hai, jisse structure ya material par padne wale internal stresses ko samjha ja sakta hai.

Mohr's Circle kya hoti hai?

Mohr’s Circle ek graphical tool hai jise 2D stress system ke principal stresses aur maximum shear stress nikalne ke liye use kiya jata hai. Yeh ek circle ke form mein hota hai jo x-axis par normal stress aur y-axis par shear stress ko plot karta hai.

2D Stress Analysis

2D stress analysis mein sirf normal (σ) aur shear stress (τ) in 2 directions consider ki jati hai. Isme following steps shamil hote hain:

Stress components: σx, σy, aur τxy ki values nikalna
Centre of Circle: C = (σx + σy)/2
Radius: R = sqrt[((σx - σy)/2)² + τxy²]
Principal Stresses: σ₁ and σ₂ = C ± R

3D Stress Analysis

3D stress analysis thoda complex hota hai jisme 3 principal stresses (σ₁, σ₂, σ₃) consider ki jati hain. Iske liye teen Mohr’s Circles banti hain:

σ₁ - σ₂ circle
σ₂ - σ₃ circle
σ₁ - σ₃ circle

Is graphical method ke madhyam se hum material failure, yield criteria jaise Von Mises stress ya Tresca theory ke according analysis kar sakte hain.

Mohr's Circle ke Advantages

Mohr’s Circle ka use bahut se advantages provide karta hai:

Visual understanding of stress states
Principal stresses ka asaan calculation
Maximum shear stress easily mil jata hai
Complex stress systems ko simplify karta hai

Conclusion

Mohr’s Circle ek powerful visualization tool hai jo ki stress analysis ko graphical format mein samjha kar, design aur safety analysis mein engineers ke liye help karta hai. Iska use mechanics of materials, strength of materials, aur structural analysis mein hota hai.