10 D.A. Nethercot and J.S. Hensman
STEP 1
Define frame geometry
STEP 2
Define load types and magnitude
(1) Gravity
(2) wind
NOTE: This flow chart is not a design procedure.
It should be used only as a 'first check', to
determine if the wind-moment method outlined
in this document is a suitable design method for
the frame in question.
STEP 3
Design composite beams as
simply supported with a capacity
of 0.9Mp
STEP 4
Estimate required column
sections
I.

I
,
I
I
The frame design is likely to be controlled
by SLS sway. However, a suitable frame
design may still be achieved using the
wind-moment method.
Consider increasing the member sizes.
l

moment in the beam should be assumed. For horizontal loading, frame analysis should be by the
"portal method".
Composite beams should be Class 1 designed for 90% of their plastic moment of resistance at mid-
span. This provision has been introduced so as to ensure that adequate rotation capacity is present
in the composite connections to develop the required span moment. Previous studies, Li, Choo
and Nethercot, (1995), Nethercot, Li and Choo, (1995), have shown both that the available rotation
capacity of composite connections is limited and that the non-linear relationship between beam span
design moment and the amount of moment redistribution necessary to achieve this substantially
reduces the rotational demands on the connections.
Columns, which are assumed to be of bare steel, should be designed by the usual interaction
formula approach. Effective lengths for in-plane and out of plane checks should be taken as 1.5L
and 1.0L respectively. Column end moments should allow for both the end restraint moment due
to partial fixity when considering gravity loading and the moments calculated due to horizontal
loading.
Connections must be designed for both maximum hogging and minimum sagging loads in
recognition of the fact that wind loading can reverse.
The parametric study indicated deflections under serviceability loading to be of the order of 30%
greater than those calculated assuming rigid joints due to the greater overall flexibility of the frames
with semi-rigid connections. Rather than permit the use of any method for the determination of
sway deflections, a development of that proposed by
Wood and Roberts, (1975), that employed a simple graphical technique is proposed. In this way the
common drift limit of h/300 recommended by BS5950: Part 1 and EC3 may be achieved. In
addition to considering the behaviour of the complete frame, it is important to check each individual
story. The first story is likely to be the most critical, typically accounting for the percentage of total
frame sway indicated in Table 3.
CONCLUSIONS
Based on the findings of a careful numerical study that employed a synthesis of the best currently
available scientific evidence, proposals for the application of the Wind Moment Method to the
design of a restricted range of unbraced composite frames have been made. In application, these
closely follow the established procedure of the SCI Design Guide for bare steel frames. The

Hensman, J S and Nethercot, D A, (2000b) "Numerical studies of composite sway frames:
Generation of Data to Validate Wind Moment Method of design",
to be published.
Kavianpour, K (1990),
Design and analysis of unbraced steel frames,
PhD thesis, University of
Warwick.
Li, T Q, Choo, B S and Nethercot, D A (1995), Determination of Rotation Capacity Requirements
for Steel and Composite Beams,
Journal of Constructional Steel Research,
Vol. 32, pp. 303-332.
Li, T Q, Nethercot, D A and Choo, B S (1993), Moment curvature relations for steel and composite
beams,
Steel Structures, Journal of Singapore Structural Steel Society,
Volume 4, No. 1, pp 35-51.
Nethercot, D A, Li, T Q and Choo, B S (1995), Required Rotations and Moment-Redistribution for
Composite Frames and Continuous Beams,
Journal of Constructional Steel Research,
Vol. 35. No.
2, pp. 121-164.
Reading, S J (1989), Kavianpour, K (1990), Anderson, D, Reading S, J and Kavianpour, K (1991)
Investigation of the wind connection method,
MSc thesis, University of Warwick,
Wood, R H and Roberts, E H (1975), A graphical method of predicting sidesway in multistorey
buildings,
Proceedings Institution of Civil Engineers,
Part 2, Vol. 59, pp 353-272.
Ye Mei-Xin, Nethercot, D A and Li, T Q (1996), Non-linear finite element analysis of composite
frames,
Proceedings Institution of Civil Engineers, Structures and Buildings,

~ National Key Projects on Basic Research and Applied Research: Applied Research on Safety and Durability of Major Construction
Projects
13
14 Z Y. Shen
In the paper, a cumulative damage model for steel framed structures under seismic actions is
established. The performance of the structures subjected to a major shock and successive aftershocks
of an earthquake can be analyzed and the extent of damage including the damage cumulation of the
structures after each shock can be calculated. Shaking table tests were conducted by the author in the
State Key Laboratory for Disaster Reduction in Civil Engineering of Tongji University for verifying
the theoretical analysis.
CUMUALTIVE DAMAGE MECHANICS MODEL OF STEEL UNDER CYCLIC LOADING
A cumulative damage mechanics model of steel under cyclic loading was established by the author,
Shen and Dong (1997). The model can be expressed as follows.
Damage index D is calculated by
" ~ C - 6g
D = (l-ill e'-eg +fl~ (11
C
-
6g
.= 6=" -
6g
where N is the number of half cycles which cause plastic strain, fl is the weight value, 6 p is the
P is the plastic strain during the ith half cycle, 6 p is the ultimate plastic strain of the material and 6.
largest plastic strain during all halfcycles.
The effects of damage on elastic modulus, yield strength and strain hardening coefficient are
E o
= (1-4D)E
tro = (1 - ~2D)tr,
(2)
where D is the damage index, D = 0 means no damage and D = 1 means complete failure of the

TABLE 1
MATERIAL PARAMETERS FOR DAMAGE
MECHANIC MODEL OF STEEL Q235
0.0081 0.227 0.119 Eqn. 5 0.000073 1.44 0.041
- 0.014-016 t,m i+ 1 l:l'm I - I
(5)
PRECISE HYSTERESIS MODEL OF STEEL MEMBERS WITH DAMAGE CUMULATION
EFFECTS
Shen and Lu have developed a powerful integration method to calculate the behavior of steel members,
Shen and Lu (1983). The method can analyze strength problems and stability problems as well, taking
into account the effects of initial geometrical and physical imperfections including residual stresses of
the steel member and can give the complete load-deflection relationship of the member including both
the ascending and descending branches.
16
Z Y. Shen
Since the basic required input of the integration method is the stress-strain relationship of material, the
method can be used to obtain the hysteresis model of steel members with damage cumulation effects,
if we take the cumulative damage mechanics model of steel under cyclic loading as the input of the
method.
Two experiments conducted by the author, Li et al. (1999), were calculated for verifying the proposed
method. The material properties and the sectional dimension of the H section columns are shown in
Table 2. or, and 6, denote yield stress and yield strain, respectively, crb and 6,, are ultimate stress
and ultimate strain, respectively, b and h are the width and height of the section and t, and
tf are
the thickness of the web and the flange, respectively.
TABLE 2
MATERIAL PROPERTIES AND SECTIONAL DIMENSION
OF H-SECTION COLUMNS
E crs crb 6~ 6= h b
tf

] (for ~os., <(p < ~Op.,) (6)
J
(for q) > ~Op, n )
where D is called equivalent damage index of the cross-section to be substituted for the actual
damage,
.~ IDidA~
D - (7)
A
is the area of the ith subsection, D, is the damage index of the ith subsection. ~o is the yield
function for the spatial member. ~os, . and ~Op,, denote the value of initial yield and the perfect yield
during the nth loading, respectively, and k is the strain hardening coefficient. The yield function for
the spatial member has been developed by many authors, Chen and Austra (1976), Duan and Chen
(1990), Kitipomchai et al. (1991 ).
When damage and plastic yield occur at both ends of the spatial member, the elasto-plastic tangent
stiffness matrix can be expressed by the following equation
18
Z Y.
Shen
[KpD]
= [Ke]-[K,][G][E][L][E]r[G]r[K,]
(8)
where
[Ke]
is the elastic stiffness matrix of the spatial member element, [G],[E] and [L] can be
obtained from the reference, Li et al. (1999)
The same experiments mentioned in the above section can be used for verifying the simplified
hysteresis model for spatial members with damage cumulation effects. Figure 4 shows the comparison
of the test results and the calculated results using the simplified hysteresis model, in which the test
results are shown by solid lines and the calculated results by the dashed lines.
Figure 4: Comparison of tested results and calculated results

5
77
2400
Figure 5 Sketch of the frame model.
TABLE 3
MATERIAL PROPERTIES
E(MPa) o- s (MPa) o- b (MPa) 6s 6= ~' 6
2.03x 105 228.44 369.51 0.00113 0.204 64.76% 34.45%
TABLE 4
SECTIONAL DIMENSION OF H-SECTION BEAMS AND COLUMNS
b(mm) h(mm) tw (mm) t y (mm)
Beams 100 150 5 5
Columns 100 120 5 5
The material properties and the sectional dimension of the H-section members are shown in Table 3