Maral Amini
Department of Civil Engineering
The Pennsylvania State University
MOTIVATION
Low-rise buildings encompass the majority of the residential structures in the United States.
Predominantly, this category of structures is constructed with dimension lumber. Investigations after
natural disasters report that during high intensity wind pressures, low-rise buildings with wood-frame
construction are at immense risks of damage with the first sign of damage initiated from the roofs.
Stochastic modelling is employed to investigate the effect of random variables such as nail withdrawal
capacity, and missing nails on sheathing panels due to miss-practice construction details. Wind
pressures are obtained from a full-scale structure (UNB) test conducted in New Brunswick, Canada. This
study combines analytical and stochastic modelling to develop a comprehensive understanding of wind
and structure interaction. The developed methodology can be used as a tool to evaluate roof sheathing
performance subjected to wind load.
FULL-SCALE EXPERIMENTAL STRUCTURE
Test House Description
External dimensions : 8.6 x 17.2 m
CERS 2010
STOCHASTIC MODEL
Employ probabilistic design to assess the effects
of uncertainties with various possible sources
Use statistical distributions to describe the
uncertain parameters, defined as random input
variables
Required dimensions for defining a roof include
the width, length, slope, rafter spacing, overhang,
nail spacing, and sheathing panel dimensions
Standard sheathing dimensions for residential
construction are 1.2 x 2.4 m
3D Representation of the gable-end
roof for the experimental house
The roof presented in this poster is of a gable
type, which is the most common roof type for lowrise structures in the United States, and it is also
the most vulnerable type in high wind events [1]
Roof characteristics for the experimental
structure at UNB
Gable roof slope 4/12
Roof trusses spaced at 610 mm, covered by
12 mm plywood sheathing panels
4
@
Developing Pressure Distributions
Data collected at UNB is categorized according to the
wind speed and angle of attack. Due to limited number
of pressure taps it is not feasible to go beyond quadratic
surfaces. The generic function for the surface is of the
form:
UNB experimental building:
front, and back elevations
(openings are not shown in
this figure)
m
0m
We assume that number of fasteners present in a roof
to connect the sheathing panels to the top chords of
roof trusses or rafters is a random variable [2]
Location of the pressure taps
30
m
m
RANDOM VARIABLES
Wind speed and direction on a tower 20
m west of the structure
Total of 27 pressure taps, 9 on walls and
18 on the roof
0
15
Data Recorded
@
UNB experimental
building side elevation
Size
17.2 m
8.6 m
4/12
610 mm
610 mm
1
8
Building orientation 23° right of the geometric
north
House Dimensions
Length
Width
Slope
Overhang
Roof framing spacing
Number of stories
Nailing pattern for segment of the
roof: 150 mm on the edges and 300
mm on the intermediate rafters.
Rafters spaced at 610 mm
Material properties are defined as random variables[3].
Using the experimental data, the probability density
functions for load and displacement at proportional
limit are developed. The displacement in the elastic
range is best fitted by a lognormal distribution with the
corresponding load best described by a Weibull
distribution [4]
n
P ( x, y )   0    i X Y
n
n
(1)
i 1
The following surface is fitted by using the least-square
method to compute the θi parameters for 2nd degree
polynomial of the above equation (1)
P( x, y)  42.21 3.05x  26.82y  0.07x  0.78xy  5.38y
2
Nailing schedule for a segment of
the roof. ‘●’ is the representation for
an existing nail, and ‘○’ is the
representation for a missing nail
2
Load deformation curve for 8d nails, d1, d2, f1, and f2
are drawn at random for each nail
The roof is subjected to forcing functions that in this
case were developed from the pressure readings
recorded on the UNB experimental building.
Wind
ANALYTICAL MODEL
Typical distribution for pressure coefficient:
‘θ2’ in equation (1): wind speed of 30 km/h
and 270° angle of attack
2D pressure on windward side of the experimental
roof at UNB. The dots represent the pressure taps
Pressure time histories are fit with probability
density functions (PDF), chi squared test is
performed to measure goodness of the fit
Correlation coefficients for pressure time histories are
obtained for the θi parameters. Correlation coefficient
matrix for wind direction of 20° is shown in this matrix is
symmetric about the diagonal axis. The correlation
coefficients specify the extent to which pressures can
fluctuation along the roof, closer taps experience higher
correlations. Correlation coefficients fall in the range of
[-1, 1]. For instance, at 20° angle of attack, the 4th
parameter in equation (1) is close to zero, stating that
there is no dependency to the x2 term
 1
 0.69

 0.97
C
 0
 0.93

 0.97
0.69 0.97
0.97 
1
0.58 0.66 0.74 0.58 
0.58
1
0.16 0.92 0.99 

0.66 0.16
1
0.07 0.15 
0.74 0.92 0.07
1
0.88 

0.58 0.99 0.15 0.88
1 
0
0.93
REFERENCES
[1] Crandell J. H., Gibson M.T., Laatsch E.M.,
et.al.: Statistically-based evaluation of homes
damaged by hurricanes Andrew and Inki. In:
Symposium by American Society of Civil
Engineers, 519-528, 1993.
[2] Baker E.J.: Beliefs about Hurricane Andrew,
construction, and evacuation. In: In: Symposium
by American Society of Civil Engineers, 31-36,
1993.
[3] ASTM. Standard Practice for Probability
Sampling of Materials. ASTM E 105-04, 2004.
ASTM International, West Conshohocken, PA.
[4] Groom K. M.: Nonlinear finite-element
modelling of intercomponent connections in
light-frame wood structures. MS. Thesis,
Department of Civil Engineering, Oregon State
University, 1992.
The 2D sheathing panels are shown in the right.
Strength of the connection (nail to the sheathing panel)
can be governed by shear or withdrawal capacity of the
nails. However, previous work has shown that the
majority of panels failed due to nail pull out [1], which is
the withdrawal of the nail from the base material (roof )
Constraints are identified at the location of the nails; the
springs (nails) have one degree of freedom (translation)
at the interface of the sheathing panels and a rigid
connection at the interface of the rafters. Shell elements
are used for plywood panels with 6 degrees of freedom
at each end ( 3 translation, 3 rotation)
-0.37
0.203
0.0277
Deflected roof panels (wind
direction 20°, speed 80 km/h).
Monte Carlo simulation is performed for the mentioned
random input variables
An upper displacement
limitation of 2.5 cm is set
for displacement of the
panels. If any point in a
sheathing panel reaches
the limit displacement,
the
entire
roof
is
declared as failed
Sheathing panel peel off
failure for maximum allowable
deflection of 2.5 cm (Δmax),
Δ is the maximum computed
nodal deflection
-6.8
-6.0
-5.1
-4.4
-3.7
-2.8
-2.1
-1.4
-0.63
Failed roof panels (wind direction
20°, speed 210 km/h).
Printing Funded by UPAC