Problem_09_09

# Problem_09_09 - Problem 9.9 Given Curved beam is built up...

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Problem 9.9 Given: Curved beam is built up by welding together rectangular and elliptical cross section curved beams. The center of curvature is located 20 mm from B. The curved beam is subjected to a positive bending moment M x . Find: the the stress at B and C in terms of M x . Solution: For the ellipse b 1 7.5 mm := h 1 15 mm := A 1 π h 1 b 1 353.429 mm 2 = := R 1 50 mm := A m1 2 π b 1 h 1 R 1 R 1 2 h 1 2 7.235 mm = := For the rectangle b 2 30 mm := a 2 20 mm := c 2 35 mm := A 2 b 2 c 2 a 2 () 450 mm 2 = := R 2 a 2 c 2 + 2 27.5 mm = := A m2 b 2 ln c 2 a 2 16.788 mm = := Total section AA 1 A 2 + 803.429 mm 2 = := A m A m1 A m2 + 24.024 mm = := R R 1 A 1 R 2 A 2 + A 37.398 mm = := N' 0 := Let M x 1N m := At point B r2 0 m m := σ θθ N' A M x Ar A m () Ar RA m A () + 0.212 MPa = := or σ θθ 0.212 M x = MPa At point C r6 5 m m := σ θθ N' A M x Ar A m () Ar RA m

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Problem_09_09 - Problem 9.9 Given Curved beam is built up...

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