ENGR 220 Section 6.1~6.2 BENDING. Internal Forces.
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Transcript of ENGR 220 Section 6.1~6.2 BENDING. Internal Forces.
ENGR 220Section 6.1~6.2
BENDING
Internal Forces
Method of Sections
Internal Forces in 2-D
Shear and Moment Diagrams
• For beams we can calculate the shear and moment diagrams as a function of position along the beam.
• Internal normal force will not be considered in that most loadings are vertical on a beam and were are primarily concerned about shear and bending failures.
Graphical Method for Shear and Bending Moment Diagrams
Vdx
dM
xwdx
dV
)(
Sign Convention
• Shear ~ positive direction is denoted by an internal force that causes a clockwise rotation on which it acts.
• Moment ~ positive direction is denoted by and internal moment that causes a compression or pushing on the upper part of the member
Graph the internal forces shear force and bending moment along the axis of the beam.
Problem 7-11
-30
-20
-10
0
10
20
30
40
50
60
70
0 5 10 15
Position along the beam
Sh
ear
Fo
rce
(kip
) o
r B
end
ing
Mo
men
t (k
ip f
t)
Shear Force
Bending Moment
7-87: Draw the shear and loading diagrams
Problem 7-87
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
0 2 4 6 8 10 12
Position on Beam
Sh
ear
(kip
) o
r M
om
ent
(kip
*ft)
ShearBending Moment