Buckling, failure

Internal-pressure design rules and formulas are given for cylindrical and spherical shells and for ellipsoidal, torispherical (often called ASME heads), hemispherical, and conical heads. The formulas given assume membrane-stress failure, although the rules for heads include consideration for buckling failure in the transition area from cylinder to head (knuckle area). 

The failure mechanisms of interest in reinforced masonry wall elements include flexural, transverse shear, in-plane shear and in some cases, combined axial compression and flexure. Buckling failure modes of compression elements and connection failures are to be avoided. 

Fig. 3.19. Scanning electron microphotograph of buckling failure near the loading nose of a carbon fiber-epoxy matrix short beam shear specimen. After Whitney and Browning (1985).

The term buckling refers to an unstable state. The force causing the instability is called the critical force. The stress that causes buckling failure is always less than that required for a direct compressive failure. 

Since the margin on the stress is obviously very large, it is not this failure mode which is the most relevant, but the buckling failure mode. 

Creep buckling failure occurs when, after a period of time, the creep process results in an unstable combination of the loading and geometry of a part so that the critical buckling limit is exceeded and failure ensues. 

Now consider what happens if an arch forms across a silo s cylinder section, and material below it is withdrawn. Not only is the restraining effect of the bulk solid lost, but the full weight of the silo contents above the arch are transferred to the now unsupported region of the silo walls. Buckling failure is likely when this occurs. 

Bhattacharya (2006) discusses the deterministic approach to determine the factor of safety of pile foundations against the buckling instability failure. Bhattacharya and Goda (2013) developed a probabilistic procedure for determining the occurrence of a buckling failure of existing piled foundations due to a scenario earthquake. 

The applicability of the elastic critical load, as in Eq. 4, to pile buckling failure is an important factor. Experiments show that the actual failure load of a slender column is much lower than that predicted by Eq. 4. Rankine (1866) recognized that the actual failure involves an interaction between elastic and plastic modes of failure. Lateral loads and inevitable geometrical imperfection lead to creatifMi of bending moments in addition to axial loads. Bending moments have to be accompanied by stress resultants that diminish the cross-sectimial area available for carrying the axial load thus the actual failure load is likely to be less than the elastic critical load,... 

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