CE 203 Structural Mechanics
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CE 203 Structural Mechanics. Bending moment & Shearing force diagrams Lecture 23-24. What is a beam. Members that are loaded in a direction perpendicular to their longitudinal axis Length is more significant than lengths in cross-section

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CE 203 Structural Mechanics

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Ce 203 structural mechanics

CE 203 Structural Mechanics

Bending moment & Shearing force diagrams

Lecture 23-24


What is a beam

What is a beam

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


Find the internal forces at c

Find the internal forces at C.


Make section at c indicate internal forces

Make section at C & Indicate internal forces


Sign convention

Sign Convention


Draw shear bending moment diagrams

Draw shear & bending moment diagrams


Draw shear bending moment diagrams1

Draw shear & bending moment diagrams


Load shear moment relations

Load-shear-moment relations

dV/dx = -w(x)

dM/dx = V(x)


Notes

Notes

No load constant shear & linear moment variation

Uniform load linear shear & quadratic moment variation


Notes1

Notes

Concentrated load causes jump in shear

Concentrated moment causes jump in moment


Draw shear force and bending moment diagrams

40 kips

1 kip/ ft

2 kip/ ft

15 ft

15 ft

5 ft

5 ft

10 ft

5 ft

Draw shear force and bending moment diagrams


Reactions

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

Reactions


Ce 203 structural mechanics

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


Ce 203 structural mechanics

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


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