Transcript Slide 1

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
q (N/ m)
Wind pressure on the W.M. :
( Bernoulli’s flow law )
Calculations give a nearly constant wind
force by unit of height : q = 32 kN/m
Load modelling
3 – INTERNAL FORCES
q (N/ m)
The maximal stresses
are in the section x = 0
4 – INTERNAL 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.
4.1 NORMAL STRESSES
5 – SAFETY AND EFFICIENCY
stresses or forces
would induce failure
5.2 TENSION
The structure is made of stone blocks
which can not resist tension stresses.
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 :
( q  Cv 2 )
5.3 - OVERTURNING
Extreme winds could tip the W.M. over.
q (N/ m)
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.