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E= Modulus of elasticity A= Cross-sectional area I= Cross-section moment of inertia

M= Moment due to external loading M'= Moment due to unit loading Δ= Deformation

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Q: unit load D 1 , D 3 : Support responses M'(2): 2 DN torque value L: Element length

M' 1-2 (x): 1-2 Torque function M 2-3 (x): 2- 3 Torque function ΣM1,dn: Total torque relative to 1 DN.
ΣD: Total balance

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Step 2: Finding the Moment Function Based on the Given Load

 

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q: Distributed load D 1 , D 3 : Support responses M(2): 2 DN torque value L: Element length

M(x): Torque function ΣM 1,dn : Total torque with respect to 1 DN.
ΣD: Total balance

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body--uriencoded--$$ \normalsize ΣM_%7B1,dn%7D =0 $$

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body--uriencoded--$$ \normalsize EI = 62.208 tf.m%5e2 %7D $$

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body--uriencoded--$$ \normalsize Δ = 6.666/EI = 6.666/62.208 = 0.107 m %7D $$

Deformation of node 2 = 0.107m