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CE 203 Structural Mechanics

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CE 203 Structural Mechanics

Bending moment & Shearing force diagrams

Lecture 23-24

Members that are loaded in a direction perpendicular to their longitudinal axis

Length is more significant than lengths in cross-section

We could have: Simply supported, Cantilevered, Overhanging or Continuous beams

dV/dx = -w(x)

dM/dx = V(x)

No load constant shear & linear moment variation

Uniform load linear shear & quadratic moment variation

Concentrated load causes jump in shear

Concentrated moment causes jump in moment

40 kips

1 kip/ ft

2 kip/ ft

15 ft

15 ft

5 ft

5 ft

10 ft

5 ft

40 kips

1 kip/ ft

2 kip/ ft

15 ft

15 ft

5 ft

5 ft

10 ft

5 ft

27.5 kips

37.5 kips

40 kips

1 kip/ ft

2 kip/ ft

15 ft

15 ft

5 ft

5 ft

10 ft

5 ft

27.5 kips

37.5 kips

12.5 k

10 k

-15 k

-27.5 k

37.5 k.ft

12.5 k

10 k

-50 k.ft

-15 k

-150 k.ft

-100 k.ft

-27.5 k

SFD

BMD