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Chapter 7: Internal forces in Frames and Beams
In Chapter 6, we considered internal forces in trusses. We saw that all the members are 2-force members that carry only tension or compression. In this chapter, we will consider internal forces in Frames and Beams. Recall that these structures have atleast one multi-force member. Multi shear - force members can carry additional types ofand bending moment in addition to tension/compression internal forces. such as For example, consider the cantilever beam shown with an end load. We can find the external forces using the FBD of the entire beam.
However we may also want to find out the internal forces (and moments) at different points of the beam. This will help us decide if the beam can support the applied load or not. To do this, we imagine two (or more) sub-parts of the beam as shown.
Tuesday, November 17, 2009 10:53 PM
Read example 7. Exercise 7.17 & 7.18 Radius of pulleys = 200 mm Find the internal forces (& moments) at J & K.
7.5 Shear and Bending Moment Diagrams Recall the cantilever beam from the previous section.
Using the FBD of individual parts of the beam we found:
Axial force Shear force diagram N(x)diagram V(x) Bending moment diagram M(x)
If we plot these INTERNAL forces and moments along the length of the beam, the resulting diagrams are called
N(x) x
N
V(x) x
P
M(x) x
Exercise 7. Plot the Shear force and Bending moment diagrams.
Friday, November 20, 2009 9:20 AM
7.6 Load vs. Shear vs. Bending moment
Drawing Shear force and Bending moment diagrams for a beam can be simplified by using relationships between Load vs. Shear and Shear vs. Bending Moment.
These relationships can be derived simply from statics as follows.
Consider a small ∆x length of any beam carrying a distributed load.
− =− ∫ D =− (area underloadcurve)
C
x
D C x
V V wdx
− = ∫ D = ( areaundershearcurve)
C
x
D C x
M M Vdx
Read examples 7.4, 7.5, 7.6 and 7.7.
Sunday, November 22, 2009 8:09 PM
Exercise 7. Write the expressions of Shear and Bending Moments. Draw the diagrams. Verify the relationships between Load vs. Shear and Shear vs. Bending Moment. Find the location of the maximum Bending Moment.
Monday, November 23, 200911:59 AM
