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Wind fragility curves for roof sheathing were developed for single-family building models to investigate the effects of roof shape and roof pitch on the wind performance of roof sheathing. For gable roofs, it was found that more complex roof shapes are more likely to suffer roof sheathing damage when subjected to high winds. The probability of no roof sheathing failure can be up to 36% higher for a simple gable roof than for a complex gable roof. For hip roofs with different configurations, variation in roof shape has minimal effect on roof sheathing fragility. Roof pitch effects were also evaluated for 10 pitch angles, ranging from 14° to 45°. Results suggest that for roof pitches smaller than 27°, the effects of this angle are more substantial on the performance of gable roofs than on hip roofs. For gable roofs, the probability of no roof sheathing failure can be up to 23% higher for a 23° roof pitch than that for an 18° roof pitch. Furthermore, the inclusion of complex roof shapes in a regional hurricane loss model for New Hanover County, North Carolina, accounted for a 44% increase in estimated annual expected losses from roof sheathing damages compared to a scenario in which all roofs are assumed to have rectangular roof shapes. Therefore, to avoid an underestimation of roof damages due to high-wind impact, the inclusion of complex roof geometries in hurricane loss modeling is strongly recommended.
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Effects of Roof Shape and Roof Pitch on Extreme Wind Fragility for Roof Sheathing
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A method is presented addressing quantitative assessment of tunnel roof stability, based on the kinematic approach of limit analysis. Long tunnels with both rectangular (flat-ceiling) and circular cross-sections are considered. The rock is considered to be governed by the Hoek-Brown strength envelope and the normality flow rule, and it is assumed to provide enough ductility at failure, making plasticity theorems applicable. A failing block in the collapse mechanism is separated from the stationary rock by a deformation band with a large gradient of velocity across its width. The shape of the block in the critical mechanism is found from the requirement of the mechanism’s kinematic admissibility and an optimization procedure consistent with respective measures of stability. Both the stability number and the supporting pressure needed for tunnel stability are calculated first. Although less commonly used in rock engineering, a procedure is developed for estimating the factor of safety, defined as the ratio of the rock shear strength determined from the Hoek-Brown criterion to the demand on the strength. Curiously, for flat-ceiling tunnels, such definition of the factor of safety yields results equivalent to the ratio of a dimensionless group dependent on the uniaxial compressive strength and the size of the tunnel to the stability number. Such an equivalency does not hold for tunnels with ceilings of finite curvature. Not surprisingly, all measures of tunnel roof stability are strongly dependent on the Geological Strength Index that describes the quality of the rock.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1061/JSENDH.STENG-11846
