THE WASHINGTON MONUMENT (1884) The purpose of this study is to show how this structure supports its own weight and wind load, by calculating its efficiency. 1 – Geometrical modelling 2 – Load modelling 3 – Internal forces 4 – Internal stresses 5 – Safety and efficiency
1 – GEOMETRICAL MODELLING 2 – LOAD MODELLING 2.1 – Dead loads unit weight of the stone : 23.6 kN/m3 incorporated machinery : 58 kN /m (stairs + elevator) weight of the cap : 2670 kN 2.2 – Live loads : wind The wind is assumed to act horizontally all along one side
Distribution of the critical wind speed along the height Wind pressure on the W.M. : Load modelling ( Bernoulli’s flow law ) Calculations give a nearly constant wind force by unit of height : q = 32 kN/m
3 – INTERNAL FORCES The maximal stresses are in the section x = 0
4 – INTERNAL STRESSES 4.1 NORMAL STRESSES Cross-section at the base (x=0) 4.1 SHEAR STRESSES If we assume max = 5 av , which is exagerated, we find a low value (105 kN/m2) compared with normal stresses (1790 kN/m2). Shear stresses can be neglected.
5 – SAFETY AND EFFICIENCY 5.2 TENSION The structure is made of stone blocks which can not resist tension stresses. stresses or forces would induce failure safety factor = actual stresses or forces 5.1 CRUSHING Wind force which would cause failure : The maximum compressive stress that the stones used can support is 20000 kN/m2 Wind speed which would cause failure :
5.3 - OVERTURNING Extreme winds could tip the W.M. over. 5.4 - CONCLUSION The W.M is safe but not efficient regarding as well the dead loads than the wind forces. Maximum winds recorded in the region (60 m/s) have almost no influence on the dimension of the structure.