HOW FAILURE UNDER STRESS OCCURS IN TIMBER. A431 
to the strain, and on reaching the fracture value EK no further increase of stress 
takes place in the extreme fibres, any further increment of Joad being met by the 
adjacent internal fibres becoming stressed in turn beyond the elastic limit to the fracture 
point. Since the total stress area across the section remains zero, there must follow a 
deviation of the neutral axis towards the tension side, and an increase of the compression 
area to keep pace with the tension area, and EC,N,T., represents the new diagram. 
From period 2 to 4, with increase of load, the extreme tension fibres are being 
stretched plastically till they reach fracture point D with a stress diagram EC,N,D. 
Then, as on the compression side, the stress is transmitted to the internal fibres by 
cohesion until they too reach their fracture point, and this further stage would be 
represented by EC,N.D. The limits that can be set to this process are (a) when the 
tension and compression stress areas assume the rectangular form, and are equal 
to each other, the ordinates in each case being equal to the ultimate breaking stresses 
of the material in direct tension and compression respectively, and (b) when the cohesion 
between adjacent fibres measured from the neutral axis outwards is not sufficient to 
withstand the shear induced by the resisting moment of the beam, which is at a 
maximum along the neutral axis of the beam. 
The first alternative occurs only when the induced shear has not risen to the shear 
fracture value of the material, before the compression and tension stress areas assume ap- 
proximately the rectangular form ; the second, when the induced shear reaches the value 
of the shearing strength, even though the maximum compressive and tensile strengths 
may not be reached. 
Maximum Fipre StREss. 
Let EC;N.T,D represent the stress diagram at instant of fracture. 
AO, =C,O¢ = elastic limit in compression = K, ultimate compressive stress. 
cup = lh M tension =K, . tensile es 
0,0, = fibres still being stressed elastically. 
O,O,y = tension fibres stressed plastically. 
O,O¢ = compression fibres stressed plastically. 
BD and AK are assumed to be parabolic curves. 
Tension area OyN;BD = compression area O.N,AE. 
The number of fibres which are stressed elastically may be reckoned so small that 
AB may be assumed to coincide with the final neutral axis, N,. 
Let b = breadth of beam and d=depth; then 
Tension area = b x OpN, {elastic stress + $(fracture stress — elastic stress)} 
=b x O,N,{K, fracture stress + 8 x (1 —K,) fracture stress} 
=b.OyN,. Z Se ultimate tensile or fibre stress = b. ON,. : eae t. 
