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V.42, COLUMNS Appendix 4*2*2 - p*4(November, 1983)If the self-weight of a footbridge column is neglect ed tand the column is considered as a free-standing cantilever witha concentrated mass f corresponding to the footbridge superstructure!at the top* the natural frequency of the column in a directiontransverse to 1?he span of the footbridge may be determined fromthe expressf1 . ( » x 1(f )* . ( , . 4jU£. x 10-3)* (in^ ffi? HEXwhereM » concentrated mass of super st ruct ure (in Kg) fg m acceleration due to gravity ( m 9«81 H*/^2)?E m elastic modulus (in kl/nf ) 9I m second moment of area of column transverse tolongitudinal axis of footbridge (in m 4 ) 9H m column height (in m f measured from soffit ofsuperstructure or bottom of bearing, to top ofpile cap in soft fill or surrounding groundlevel if paved f as appropriate)*where W m unit load of superstructure (in kN/m),sW , m unit dead load of superstructure (in kN/rn),W 1 m unit live load of superstructure (in kN/m) y8JLL m length of superstructure supported by column (in m)93Ibr a noiMiniform free-standing cantilever column fthe following approximate expression may be used t-f.where X « stiffness at top of column (in