Question

2 a) How to find neutral axis of a beam and explain its importance?
b) A cantilever beam of cross-section 90 mm. width 120 mm deep carries a UDL of 12 KN/m. over the entire length and a concentrated load of 15 KN at the right end. Find the bending stress in the beam, when the length of beam is 10 m.

Answer 1

(a) neutral axis

The neutral axis is the axis about which bending occurs in a beam or a composite section. As a key parameter, the neutral axis position (NAP) is so important that it is needed in most theories of structural design. Moreover, the neutral axis position serves as a potential indicator of the structure's safety condition.

You can use the principle of superposition to find the neutral axis, a uniform stress distribution due to compression load =P/A, P = axial compression load, plus the bending stresses created by the bending moment = M.c/I, where M is the bending moment, c is the centroidal axis of the cross-section, and I is the second moment of area of the section. Adding the two stresses will locate the neutral axis

(b)

The largest bending moment is ∣$M_max$ ∣= 15000 lb · ft acting just to the left of section B. From the tables in Appendix B, we find that the section modulus of a $W14×30 (P520)$ section is$S = 42.0 in^3$ Therefore, the maximum bending stress in the beam is

$\sigma_ {max}= \frac {M_ {max} }{S} =\frac {15000\times 12 } {42}$

$=4290psi$

diagram for sfd and bmd: