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Internal loadings in structure member

The internal loads can at a specific point, be determined using the method of section. The internal loads for a coplanar member are normal or axial force N, shear force V, the bending moment M. once the internal loads determined, the magnitude of internal stress for the given cross-section can be determined.





To determine the internal loads at a specified location. An imaginary cut should be made at the required location. Then the cut member will be isolated. And the free body diagram should be drawn, all external loading and reaction should be kept for the member. You can indicate the internal loading at the location of the cut as N, V and M as shown in figure 1. the external reaction at support should be determined before cutting the member


Figure 1


A sign convention should be adopted to determine whether the internal force is negative or positive. figure 2 showing the most used sign convention. If the normal force is trying to elongate the member, it is considered as a positive normal force, as shown in figure no:2. The positive shear force will try to rotate member clockwise. The positive bending moment will tend to rotate the segment up. 


Figure 2



Determine the internal shear and moment acting at a section passing through point C in the beam shown in Figure no:3

Figure 3

The resultant of triangle loading=0.5*18*3=27 K. the center is located at (2/3) of the base=12 ft from point A.

Figure 4


ΣMa=0
18*VB-27*12=0
VB=18 K

ΣFy=0

-27+18+VA=0
VA=9K

now we can make the cut at point C

the distributed load intensity at point C from the triangle similarity 

w=(3/18)*6=1 k/ft

ΣMc=0

-9*6+3*2+Mc=0
Mc=48 k-ft

ΣFy=0

9-3-Vc=0
Vc=-6K

ΣFx=0

Nc=0
Figure 5


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