composite beam transformed homogeneous beam obtained through a transformation factor: n = e1e2e1e2...

Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E 1 E 2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

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Composite Beam

Transformed homogeneous beam obtained through a transformation factor:

n = E1

dF = σ dA = σ dA’

σ dz dy = σ’ n dz dy

σ = n σ’

and

Typical Example of Composite Beam

Page 3: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Typical Example of Composite Beam

Page 4: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Transverse Loading on Prismatic Beams

Page 5: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Sign Convention of Beams

Page 6: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

wdx

Vdx

VVVxw

xwV

MxVMMxxw 2/

xVM

Governing Equations of Beams

Page 7: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Shear and Bending Moment Diagram (I)

Page 8: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Shear and Bending Moment Diagram (II)

Page 9: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Shear and Bending Moment Diagram (III)

Page 10: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Shear and Bending Moment Diagram (IV)

Page 11: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Shear and Bending Moment Diagram (V)

Page 12: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Shear and Bending Moment Diagram (VI)

Page 13: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Shear and Bending Moment Diagram (VII)

Page 14: Composite Beam Transformed homogeneous beam obtained through a transformation factor: n = E1E2E1E2 dF = σ dA = σ dA’ σ dz dy = σ’ n dz dy σ = n σ’ and

Summary of Shear and Bending Moment Diagram

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