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Structural Mechanics 4 Shear Force, Bending Moment and Deflection of Beams

Structural Mechanics 4 Shear Force, Bending Moment and Deflection of Beams. 20 kN. R A. R B. 3.00m. 2.00m. Sum of moments about R A = 0. 20 x (2.00) - R B x (2.00 +3.00) = 0 R B x (5.00) = 20 x (2.00) R B = 20 x (2.00) / (5.00)

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Structural Mechanics 4 Shear Force, Bending Moment and Deflection of Beams

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  1. Structural Mechanics 4Shear Force, Bending Moment and Deflection of Beams 20 kN RA RB 3.00m 2.00m

  2. Sum of moments about RA = 0 • 20 x (2.00) - RB x (2.00 +3.00) = 0 • RB x (5.00) = 20 x (2.00) • RB = 20 x (2.00) / (5.00) • RB = 8.00 kN

  3. Sum of moments about RB = 0 • RA x (2.00 +3.00) - 20 x (3.00) = 0 • RA x (5.00) = 20 x (3.00) • RA = 20 x (3.00) / (5.00) • RA = 12.00 kN

  4. CHECK VERTICAL FORCES • UPWARD REACTION = RB + RA = 8 + 12 = 20 kN • DOWNWARD FORCE = 20 kN • So likely that calculations are correct!

  5. SHEAR FORCE DIAGRAM Space diagram SHEAR FORCE DIAGRAM 20 kN 8kN 12kN 12kN 0 -8kN

  6. BENDING MOMENT DIAGRAM • Space diagram 20 kN 12kN 8kN 24kNm 0kNm 12kN X 2m = 24 kNm 8kN X 3m = 24 kNm

  7. Deflection 20 kN Max deflection at Max BM 12kN 8kN 24kNm SFD + 12kN 0 0kNm BMD

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