विकृति ऊर्जा विधि का उपयोग करते हुए, O पर लंबवत विक्षेपण निम्न में से क्या है? (प्रत्यास्थता मापांक E = 2 × 105 N/mm2 लें, तार का अनुप्रस्थ काट क्षेत्र, A = 100 mm2)।F8 Ram S 20-3-2021 Swati D7

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  1. 2.12 mm
  2. 21.2 mm
  3. 1.50 mm
  4. 15.0 mm

Answer (Detailed Solution Below)

Option 1 : 2.12 mm
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संकल्पना:

ट्रस में भंडारित विकृति ऊर्जा,

U = UOA + UOB

U=P12L2AE+P22L2AE

O पर विक्षेपण होगा, Δ=UP

गणना:

F8 Ram S 20-3-2021 Swati D8

 O पर 

ΣFx = 0, FOA = FOB..............(i)

ΣFy = 0, FOA × cosθ + FOB × cosθ = P ..........(ii)

2FOA × cosθ = P

यहाँ, cosθ = 3/4.24 और P = 10 kN

FOA=P2cosθ=P2×34.24=0.7067P

ट्रस में भंडारित विकृति ऊर्जा,

U = UOA + UOB

U=FOA2L2AE+FOB2L2AE=2FOA2L2AE=FOA2LAE

⇒ U=(0.7067P)2LAE=0.5P2LAE

O पर विक्षेपण होगा, Δ=UP

Δ=0.5×2PLAE=PLAE

Δ=10×103×4.24×103100×2×105=2.12 mm

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