5.7 Bending of a Narrow Cantilever Beam Subjected to End Load
147
Boundary conditions
At
y = ±h, σ y = 0
At
y = ±h, τ xy = 0
Hence,
0 = −b 2 ±
d 4
2
h
2
or
d 4 = −2
b 2
h 2
Now consider an elemental strip of thickness ‘dy’ at a distance ‘y’ above centroidal
axis as shown in Fig. 5.9b.
Therefore,
+h
−h τ xy · b dy = −P (−ve sign denote load acting downwards).
i.e.,
−P =
+h
−h
−b 2 −
d 4
2
y
2
· 1 · dy
But
d 4 = −2
b 2
h 2
Hence,
147
Boundary conditions
At
y = ±h, σ y = 0
At
y = ±h, τ xy = 0
Hence,
0 = −b 2 ±
d 4
2
h
2
or
d 4 = −2
b 2
h 2
Now consider an elemental strip of thickness ‘dy’ at a distance ‘y’ above centroidal
axis as shown in Fig. 5.9b.
Therefore,
+h
−h τ xy · b dy = −P (−ve sign denote load acting downwards).
i.e.,
−P =
+h
−h
−b 2 −
d 4
2
y
2
· 1 · dy
But
d 4 = −2
b 2
h 2
Hence,