Multiple random-error effect analysis of cable length and tension of cable-strut tensile structure

Cable-strut tensile structure is composed of tensile cables and compressive struts; its prestressed forming state is obviously influenced by cable length and tension force, so the key control objects of construction are active forces of tensioned cables, lengths of passively tensioned cables, and outer node coordinates. Error effect analysis is required to obtain rational control indexes. The method of multiple random-error effect analysis including errors of the above three control objects is proposed and described in the text: (1) outer node coordinate errors along the linked cables are regarded as additional length errors of outer linked cables; (2) random cable length errors and tension errors based on probability distribution are introduced into error analysis cases by modifying initial strains of cables; and (3) for avoiding the interaction between passive cable length errors and active cable tension errors, elastic modulus of active cables is modified to small values. According to the statistics of measured cable lengths, cable length errors may not be complied with normal distribution. Therefore, the M-shaped probability distribution is proposed, and derivations of probability density function, cumulative distribution function, and its inverse function are carried out, by which calculated random cable length error distribution is comparatively consistent with measured errors. Taking Yueqing Stadium, a wheel-spoke cable truss with crescent shape, as an example, multiple error analysis including passive cable length errors of M-shaped probability distribution, outer node coordinate errors, and active tension errors of normal distribution is carried out. Some useful conclusions and construction control indexes are obtained.