Wiryanto-makalah-scaffolding

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. Fig. 1. Ring-lock modular scaffolding system. DAM

analyzing the stability in structural steel design. The influence is General Information
mostly determined by the structural geometric condition as a
whole (global), which is why when determining the nominal com- DAM is a new computer-based method for structural steel design
pressive strengths using DAM, the effect of K value should be (AISC 2005, 2010, 2016). This method was developed to accurately
omitted with K = 1 (AISC 2016). calculate the influence of structural loading at the analysis stage and
to remove the requirement to calculate the effective length factor,
The basic principle of structural steel design using the LRFD is K, of the column. This is possible because the stability issue has
to ensure that the required strengths (Ru) of the elements due to the been accommodated at the structural analytical stage. This method
loading on the structural system cannot be greater than the available can be used for all types of structure in which their elements will be
strengths (f Rn) of the cross section of the structural element under designed as a beam-column. As for the older design method, ELM,
review. The general design requirement is Ru ≤ f Rn. its use is limited to where it is valid only for a structural system,
which meets the criterion requiring the ratio of maximum second-
Using the LRFD and DAM principles, the structural computer order drift to maximum first-order drift to be less than 1.5. If the ra-
analysis will deliver the information on the required strengths tio exceeds this criterion, then the steel design will be determined
(Ru), and the cross-sectional design results in information on the by DAM (AISC 2005).
available strengths (f Rn). To find the ultimate strengths or maxi-
mum Ru, the incremental loading procedure is required. At each Stability Parameters in Steel Structures
loading stage, the result is compared with condition Ru % f Rn to
see if the failure has taken place. When Ru < f Rn, the load can be The parameters influencing the behavior of element stability are
increased, and when Ru > f Rn, the load given at this stage is too (1) geometric nonlinearities, (2) spread of plasticity, and (3)
great and should be reduced. The ultimate load occurs when the member limit states. These three issues influence the deformation
Ru % f Rn condition is met. The analysis strategy and design at of the structures being loaded (AISC 2005).
each loading stage is basically identical to the structural steel
design strategy. The first parameter is geometric nonlinearities. In slender
structures, deformation resulting from loading cannot be ignored.
The structural modeling for numerical analysis using DAM is Therefore, second-order analysis is needed in which the struc-
relatively simple and just uses the Line element [one-dimensional tural equilibrium is calculated against the geometric condition on
(1D) finite-element analysis formulation] or the commonly called deformation. The factors evaluated include the influence of
Frame element (CSI 2011). This is different from the FEM based second-order effect, known as P-D and P-d . When the influence
on commercial computer programs, such as ABAQUS, ANSYS, of geometric nonlinearities is significant, the parameters of initial
and other similar programs, which can even model the structural geometric imperfections, in the form of member out-of-straight-
geometry realistically. Such programs, in addition to providing the ness, frame out-of-plumbness, and resulting from material and
Line element, also provide a Solid element for three-dimensional fabrication tolerances, become crucial.
(3D) modeling. A more detailed modeling geometry influences
the accuracy of the numerical analysis results. Therefore, it is rea- The second parameter is spreading of plasticity. From the fabri-
sonable to question whether the simple modeling using DAM has cation of steel profiles, residual stresses are left in the steel profile as
represented the real conditions of the structure being evaluated. a result of the cooling process and restraint. This reduces the ele-
Thus, the concern of numerical analysis using DAM is to obtain a ment resistance in case of stability loss.
structural model configuration, which can represent the real
structure. When DAM is not representative, it means that the The third parameter is member limit states. The available
analysis result is inaccurate or not correlated with the real strengths of a structural element are determined by one or more
condition. of its limit state conditions, such as material yielding, local buck-
ling, global buckling in the forms of flexural buckling, torsional
A simple strategy for getting an accurate numerical modeling to buckling, or torsional-flexural buckling, depending on the cross
represent the real structure is to calibrate it against the experimental section conditions. The procedure to calculate the available
test results, i.e., the test is required for accurate results from the nu- strengths of members and connections will be done in accordance
merical analysis. with the provisions of AISC (2010), as applicable, with no further
consideration of overall structure stability.

Computer Software Specification for the DAM

DAM requires a program capable of second-order elastic analyses.
In general, commercial structural analysis programs have this facil-
ity. Nevertheless, there is no guarantee that the outcome will be the
same from all of the programs. The accuracy programmed in the
software will have some influence on the design output. To avoid
any doubt, the computer program used should be tested by launch-
ing the analysis benchmark problems prepared by AISC (2010).
The SAP2000 computer program (CSI 2011) has been tested by
Dewobroto (2016) and has met the intended criteria.

Consideration of Initial Imperfections

Initial imperfection results in destabilizing effects. DAM deals with
it by explicitly modeling the geometry, which contains the initial

© ASCE 04018028-2 Pract. Period. Struct. Des. Constr.

Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. imperfection, or giving a notional load or equivalent lateral load of cross section element. Furthermore, the outcome will be even more
the working load percentage. different if the second-order effect on the structure under review
becomes more and more significant. The difference from the old
Direct modeling is performed by placing additional nodal points method is caused by not explicitly accounting for initial out-of-
on the Line element. The node coordinates can be taken from the plumbness and member-stiffness reduction due to the spread of
material and fabrication tolerance. The pattern is chosen to give the plasticity in the analysis.
greatest destabilizing effect; either the occurring deflection pattern
due to loading or buckling pattern can be chosen. ELM is calibrated to give a resultant axial strength, Pu, consist-
ent with the actual response, but it underestimates the actual internal
Notional load constitutes the lateral load at nodal points based moments under the factored loads. The “actual response” curve has
on the percentage of vertical load working at that nodal point larger moments due to the combined effects of distributed yielding
level. The notional load is added together with other lateral loads, and geometric imperfections, which are not included in the second-
for all combinations, except for certain cases explained in Section order elastic analysis.
2.2b(4) of AISC (2010). The amount of notional load is Ni =
0.002Yi. The factor 0.002 % 1/500 represents the nominal out-of- A major advantage of DAM is that it captures the internal forces in
plumbness value for the story and is in line with the AISC Code of the structure more accurately, particularly for the cases in which there
Standard Practice. When the structure has a greater value, a rear- are high gravity loads and low lateral loads. This advantage comes at
rangement is then needed. the expense of applying notional lateral loads to the structure and
reducing the frame stiffness as part of the input for the analysis.
Adjustments to Stiffness
DAM and Experimental Loading Test
Partial yielding due to residual stress in the steel cross section (hot
rolled or welded) produces stiffness reductions when given a load DAM is considered simpler than FEM; hence, it is chosen as an al-
close to the limit state conditions, and it gives a destabilizing effect, ternative numerical method to predict the ultimate strengths of a
such as geometric imperfection. DAM deals with partial yielding steel scaffolding system. The advantage of DAM is that it can do
by reducing the structural stiffness. The value is found by calibrat- the stability analysis of a structure by calculating the P-D effects.
ing it against the experimental test result, namely EI* = 0.8t bEI and This effect has a significant influence on sway portal buildings
EA* = 0.8EA. This stiffness reduction factor applies only to the cal- (sway frames). For truss structure (nonsway frames), the influence
culation of the ultimate strength condition and the stability of steel of P-D is relatively insignificant; hence, it can be ignored. Such an
structure; it is not used to calculate the drift, deflection, vibration, or assumption happens because the design usually uses the old
vibration periods. method (ELM), which has not taken imperfection into considera-
tion. Meanwhile, DAM has taken imperfection into account as a
Notional Load to Represent the Inelastic Condition standard procedure because the performance of steel scaffolding
is significantly influenced by imperfection and other matters
Giving a notional load can also be used to represent the reduction of related to its stability. For this reason, DAM is deemed appropri-
flexural rigidity, t b, resulting from the inelastic condition due to ate. Consequently, steel scaffolding should be modeled as a por-
cross-sectional residual stress. This strategy is suitable to simplify the tal structure, and the amount of each of its connection system
calculation of DAM in any member with a large compression force of rigidities needs to be predicted carefully.
aPr > 0.5Py, where the value of t b < 1.0. If this strategy is used, then
t b = 1.0, and an additional notional load is given by Ni = 0.001 Yi. The structural modeling process, which considers the influence
of rigidity between secondary elements, such as bracing and the
The load is given simultaneously with the previous notional connection system, produces varied outcomes. Therefore, the nu-
load, which represents the previous initial geometric imperfection, merical simulation with DAM can produce something accountable,
and because it has the nature of enlarging, the final notional load but calibration needs to be performed first. In this way, the modeling
would be Ni = 0.003Yi and t b = 1.0 for all loading combinations. strategy closest to the real condition can be chosen. The experimen-
tal loading test of steel scaffoldings serves as the calibrator. Hence,
Available Strengths of Structures the structural modeling in the numerical simulation gives an out-
come that correlates with the experimental test result, which can
By using DAM for structural stability analysis to calculate the nom- then be used to evaluate similar steel scaffolding parametrically.
inal cross-sectional strengths of the structure, a regular procedure
can be used, such as the one used in ELM, i.e., in the AISC code Experimental Loading Test: One-Story Scaffoldings
(AISC 2005, 2010, 2016), applying Chapters E to I for the nominal
strength of the cross section and Chapters J to K for the nominal General Information
strength of the connection, but by taking K = 1 in the member slen-
derness KL/r. An experimental loading test is a simple and fast method to find the
maximum strengths of a structure, yet it is a costly and risky choice;
Accuracy of DAM (New) against ELM (Old) therefore, it is only used for the smallest configuration, i.e., one-
story steel scaffoldings. Despite its limited amount, its existence is
DAM and ELM use the same column strength equations of Section extremely important for calibrating numerical modeling analysis
E3 of the AISC code (AISC 2005). Therefore, if DAM is used to an- using DAM. It is understandable given that each (1) amount of rigid-
alyze the structural system of a truss, which only receives an axial ity of structural elements and (2) notional load location (representing
force, the result would not be different or is equally accurate. For imperfection) will influence stability. As a result, the final outcome
slender columns, the calculation of the effective length KL is critical can vary, making it hard to determine which model can be deemed
to achieve an accurate solution when using ELM. as the most suitable (accurate) with real structural conditions.

The different design outcomes begin when the loaded steel struc-
ture creates an axial force and a simultaneous flexural moment to its

© ASCE 04018028-3 Pract. Period. Struct. Des. Constr.

Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. Steel Scaffolding Loading Test structural strengths (rigidity) is deemed to have taken place. The
final condition of structural collapse can be seen in Fig. 3.
An experimental loading test is conducted at the Laboratory
of Structure and Construction Research Institute for Human One reason steel scaffolding collapses is because of the buckling
Settlements, Ministry of Public Works, Cileunyi, Bandung, deformations in the columns. The horizontal and diagonal pipe
Indonesia. The loading test with tubular columns with a 58-mm
diameter yielded a capacity of Pmax = 47.29 t. Because the setup Fig. 3. Damage of tested scaffolding.
consists of four columns, the ultimate capacity of each column is
116 kN (11.82 t) corresponding to the maximum load recorded
during the test. The load on the structure in the test is recorded
with the load cell on the scaffolding column support, and the re-
spective horizontal displacement is observed with a transducer
set in between the ends of the column in which the displacement
is not prevented by bracing. This is based on the assumption that
its collapse takes the form of column flexural buckling.

The configuration of the steel scaffolding loading test and testing
atmosphere can be seen in Fig. 2.

Structural Collapse Behavior

In addition to information on the maximum load, which causes the
steel scaffolding to collapse, the behavior is observed when the
scaffolding collapses. The loading is produced using a hydraulic
jack (Fig. 2), which can automatically stop when a significant dis-
placement change occurs. This is a condition in which a loss of the

© ASCE Fig. 2. Frame and loading arrangements. Pract. Period. Struct. Des. Constr.
04018028-4

Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. elements, which serve as bracing, remain intact and show no dam-
age. The connections between elements are still set well, with no
sign of damage. Hence, the damage is of the local type, appearing
only in the columns.

The part of the columns connected to the bracing element tends
to remain intact. This shows that its connection system is rigid
enough to “hold” the columns, even though its rigidity is not the
same when compared with the continuous connection system.
Although the weakest parts in the scaffolding are the pipe columns
loaded vertically, the structural modeling for the analyses using
DAM becomes easier, especially when using the notional loads for
simulating the imperfection effects. Thus, it is best to have the
notional loads in the parts of columns that are free from lateral
restraint.

Calibrated Numerical Simulation: One-Story Scaffoldings Fig. 4. Node and element numbering for a one-story model.

General Information Table 1. Specification components of the structural model

The numerical analysis of structural collapse can generally be per- Element number Component Dimension Note
formed using a FEM-based nonlinear inelastic computer program,
such as ABAQUS, ANSYS, ADINA, and so forth. Using these pro- 1–4 and 13–16 Column f 58 mm t = 3.25 mm Steel pipe
grams, the structural geometry can then be modeled realistically 5, 17 Top column f 58 mm t = 3.25 mm Reduced
using the 3D solid element. Nevertheless, the implementation pro- stiffness
cess is relatively laborious for practical daily design efforts. As an 8–10 Bracing f 48 mm t = 3.25 mm Steel pipe
alternative, the elastic second-order analysis with SAP2000 (CSI 6, 7, 11, 12 Steel plate
2011) and DAM are used. Connection 4 Â 100 mm

To obtain an accurate analytical result, the computer output of by modifying the flexural stiffness in the upper part of the col-
numerical analysis using DAM will be compared with the experi- umn. Whether or not this modeling assumption is appropriate
mental test result. At this stage, the numerical modeling made can depends on the calibration results against the experimental test
be rearranged in such a way that the results can be considered as data.
representing the real conditions; this is called the calibration stage.
To do so, the facility of the SAP2000 program, namely the Display- To find the determining imperfection conditions, the notional
Show Plot Function (F12), can be used to record the output of inter- load (Ni) location is varied, as shown in Fig. 5. The variations are
nal forces and deformation (P-D) for each stage of the loads given. denoted as Case 1 through Case 4.
Moreover, the data can be shown in the form of a curve, making it
easier to do proper comparisons. From the P-D curve, the load just Stability Analysis Using the DAM
before the collapse ensues can be detected due to large deformation
at the observation point. The internal forces then become the To calculate the influence of the residual stress, the elastic modulus
required strengths (Ru). The next stage is the evaluation of the avail- is reduced to 80%. A notional load of Ni = 0.003·Yi is placed
able cross-sectional strengths (f Rn). The maximum load is obtained according to locations shown in Fig. 5. The notional load varia-
when the criterion Ru % f Rn, is met. tions will be evaluated based on the experimental test result data.
Afterward, a second-order elastic analysis using the SAP2000
Modeling the One-Story Scaffoldings program is made, and using the Display-Show Plot Function the
amount of incremental load and displacement at Nodal Point 7
The modeling of the steel scaffolding connection (Fig. 1) is consid- can be recorded. The results are presented in a P-D curve, as seen
ered as semirigid. For convenience, it is deemed to be a plate whose in Fig. 6.
size is found by trial and error to suit the experimental test results.
From a two-dimensional (2D) perspective, a structural modeling is The notional load variations influence the analytical results. The
a plane frame. The perpendicular direction is considered as confined experimental loading test indicates that scaffolding columns experi-
from horizontal deformations. The direction is chosen because the ence some buckling, and the numerical simulation with notional
geometry of the scaffolding is symmetrical; thus, only one side loads in Case 3 shows no buckling. Therefore, the valid model
needs to be reviewed. includes Cases 1, 2, and 4 only, showing how the buckling occurs
after the load exceeds 100 kN. The buckling in these cases is consid-
In reference to the details of the experimental test plan and ered to take place when a small incremental load causes a large
results, a structural model as a plane frame is made with a notation
of the nodal point and member element numbering as shown in
Fig. 4, in which the data for the structural elements are tabulated as
shown in Table 1.

The top end of the column is connected to the hydraulic jack
as a point of loading; thus, it is modeled as being fixed in the rota-
tion but free in the translation of any direction. However, the
flexural stiffness of the column at its upper part is somewhat
questionable; hence, it is considered as a special element member

© ASCE 04018028-5 Pract. Period. Struct. Des. Constr.

Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028

Fig. 5. Different notional load (Ni) positions in the one-story model: (a) Case 1; (b) Case 2; (c) Case 3; and (d) Case 4.

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. Fig. 6. Load-displacement curve due to Ni placement for the one-story model.

lateral deformation, changing the P-D curve to be practically This is where the importance of the experimental test result data
horizontal. lies. The calibration is performed by comparing the P-D curve of
the experimental loading test results versus the P-D curve of the nu-
After the buckling, the P-D curve line tends to be horizontal; merical simulation. Thereafter, a trial-and-error procedure is con-
thus, it is concluded that the elastic second-order analysis computer ducted until a model structure is found in which the results are
program still works well. The load can be increased further, yet the deemed to represent the experimental ones accurately.
result seems irrational or odd; hence, when it happens, the incre-
mental load is ceased manually. The additional loading after buck- The trial-and-error procedure shows that the P-D curve of the
ling is deemed as meaningless. numerical simulation results is influenced by the flexural stiffness
of the end part of the column (f 58-mm pipe) of Elements 5 and 17
When learning the behavior of buckling resulting from Cases 1, (Fig. 4). To adjust this flexural stiffness, the second moment of area
2, and 4, Cases 2 and 4 are similar; thus, only Cases 1 and 2 will be of f 58-mm pipe is multiplied by factors 1.0, 1.25, and 0.75. The
compared. The behavior of buckling caused by Case 1 is preceded results are, respectively, notated as Cases 2, 2A, and 2B in Fig. 7.
by a large deformation. Meanwhile, Case 2 has a collapse from a Correspondingly, TR-3 through TR-13 are the lateral displacements
sudden failure, which is similar to the collapse of the column during measured in the columns of the scaffolding.
the experimental loading test. Therefore, the notional load configu-
ration, which is deemed as right, is Case 2, and it will be used Three numerical models were made based on Case 2. Out of
further. these three, the Case 2A model (end column of 125% of the intact
cross section) gives a P-D curve that is closest to the experimental
Comparisons of Simulation Results and one and implies that the Case 2A model can be taken as the cali-
Real Conditions brated one. The model will be developed using parametric princi-
ples for the next ultimate load capacity analysis of two-story steel
For the behavior of collapse resulting from Case 2 numerical simu- scaffoldings.
lation (Fig. 6) to be correlated with the real conditions (experimen-
tal results), the modeling configuration should then be calibrated. It is proven that when a good calibration is performed, the struc-
tural analysis to find the maximum load for the scaffolding can also
be performed using DAM (AISC 2010). Most important is that the

© ASCE 04018028-6 Pract. Period. Struct. Des. Constr.

Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. Fig. 7. Load-displacement curves, experimental versus numerical.

Table 2. Results of the stability analysis of one-story scaffoldings (Case 2A)

Step UX 7 (mm) RZ 1 (kN) P 14 (kN) M33 14 (kN·m) Note

37 1.10080 110.74471 −111.07195 −0.18151 Check 3
−114.06932 −0.26949 Check 2
38 1.94281 113.71173 −117.06472 −0.43269 Check 1
−120.03893 −1.39921 Buckle
39 3.52047 116.65575

40 12.93401 119.35227

Note: Several steps are deliberately deleted.

Fig. 8. Deformation changes at each step approaching instability (Case 2A).

numerical modeling correlates with the real conditions using cali- Nevertheless, no review has been made in relation to the material
bration in which the P-D curve from the model is adjusted against strengths (material boundary conditions). Hence, the available
that of the experimental test for the same structure. strengths (f Rn) will be evaluated using the provisions of the LRFD
(AISC 2010). The smallest loading quantity, which fulfills both
Evaluation of Column Strengths conditions, is considered as the maximum load of structure.

The P-D curve shows the behavior of the structure, which has Furthermore, some loading stages that cause buckling of Case
accommodated the stability element (geometric boundary condi- 2A output in Element 14 (as a column; Fig. 4), which are considered
tion); thus, it can be used to predict the load, which causes buckling. as maximum, will be shown as seen in Table 2.

To understand the collapse behavior, it would be helpful to
see the deformation for each of these steps (Fig. 8). The stable

© ASCE 04018028-7 Pract. Period. Struct. Des. Constr.

Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028

Table 3. Column interaction check for a one-story model

Check Step Pu (kN) Mu (kN·m) Pu=f Pn R ¼ Pu þ 8 Mu Note
f Pn 9 f Mn
−0.43269 1.004 Not OK
1 39 −117.06472 −0.26949 0.979 Not check Not OK
2 38 −114.06932 −0.18151 0.953 1.053
3 37 −111.07195 1.002 OK

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. Fig. 10. Different notional load (Ni) positions in the two-story model:
(a) Case 5; (b) Case 6; and (c) Case 7.

If the loading condition at Step 39 is deemed as the final condi-

tion before instability (buckle), then the amount of the load based

on the stability or geometry boundary condition is Pu = 117 kN
(Table 2). The material boundary condition will be evaluated as fol-

lows. The smallest load is the determining one. The material bound-

ary condition is evaluated based on the nominal strengths of the

structural cross section of the ELEMENT #14 (see Figure 4) as

follows.

Check the available strength of Element 14 using pipe f 58 mm
(L = 1.5 m) (Fig. 4), Fy = 371 MPa (yield strength from mill certifi-
cate), E = 200,000 MPa (modulus elasticity of steel), D = 58 mm

(outside diameter of pipe), t = 3.25 mm (wall thickness), Ag =
559 mm2 (cross-sectional area), rmin = 19.4 mm (radius gyration),
and Zx = 9753.5 mm3 (plastic-section modulus).

To calculate the compressive strength, first check the local buck-

ling criteria according to Table B4.1a (AISC 2010). The section is a

nonslender element because D/t = 17.85 less than 0.11 E/Fy = 59.3.
The nominal strength, Pn, will be determined based on the limit
state of flexural buckling following the provisions of E3 (AISC

2010)

qffiffiffiffiffiffiffiffiffiffi

Fig. 9. Node and element numbering for a two-story model. ðKL=rmin ¼ 77:3Þ 4:71 E=Fy ¼ 109:4 then Fe

change in the geometric form of the scaffolding is seen in Steps ¼ ðp 2EÞ=ðKL=rminÞ2 ¼ 330 MPa
37–39 and unstable from Step 40 forward. Under such condi-
tions, the structural instability or buckle is assumed to occur. Fy
The structure experiencing the buckle cannot be used; thus, the
loading condition in Step 40 does not need to be examined fur- Fcr ¼ 0:658Fe Á Fy ¼ 231:7 MPa therefore Pn ¼ FcrAg
ther because it cannot be used. Therefore, it is necessary to
review the maximum load before buckling, i.e., Steps 37–39. ¼ 129:5 kN
The check is started from Step 39 and if it fails to fulfill the load
bearing condition, then Step 38 with a smaller load is examined. To calculate the flexural strength, check the local buckling crite-
If the condition Pu % f Pn is met, then the ultimate limit load is ria according to Table B41b (AISC 2010). The steel pipe is a com-
obtained. pact section because D/t = 17.85 less than 0.07 E/Fy = 38. The nomi-
nal flexural strength, Mn, will be determined based on the limit state
of yielding according to F8–1 (AISC 2010), therefore, Mn =
Fy·Zx = 3.618 kN·m.

© ASCE 04018028-8 Pract. Period. Struct. Des. Constr.

Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. Fig. 11. Load-displacement curve due to Ni placement in the two-story model.

Table 4. Results of the stability analysis of two-story scaffoldings forward the flexural moments. Further, following the calibration
(Case 7) result, the flexural stiffness at the upper ends of the column modules
should be increased to be 125% of full cross sections, i.e., Elements
Step UX 7 (mm) RZ 1 (kN) P 2 (kN) M33 2 (kN·m) Note 5, 10, 29, and 34 (Fig. 9). The model structure and its nodal and ele-
ment numbering are now as shown in Fig. 9.
30 3.960 90.18136 −90.14139 −0.458 Check 3
The assumption of notional load placement, to represent imper-
31 7.465 91.99879 −91.96898 −0.815 Check-2 fection, is given according to the deflection prediction when experi-
encing buckling or according to mode shape. There are three
32 15.416 93.47612 −93.46949 −1.623 Check-1 notional load placement configurations classified as load Cases 5–7.
From these three, the smallest incremental load that causes the
33 28.467 95.04253 −95.07358 −2.956 Buckle instability condition is selected. The configuration is shown in
Fig. 10.
Note: Several steps are deliberately deleted.
Stability Analysis Using the DAM
The interaction of flexure and compression in doubly symmetric
members (pipe) will be limited by Eqs. H1–1 (AISC 2010) as seen Similarly with the strategy presented previously with the numerical
in Table 3. analysis based on the form of the loaded structure, the analytical
results will be treated as the P-D diagram of a representative point
The numerical analysis result indicates that the capacity of the in the column in which buckling is predicted to occur. For this rea-
steel scaffolding is determined by the nominal strength of cross sec- son, Nodal Point 7 is chosen for lateral displacement and Nodal
tion that fulfills the criterion Pu % f Pn. Thus, the ultimate load Point 1 for reaction force.
capacity of the column of one-story steel scaffoldings is Pu = 111
kN (from Step 37). As shown in Fig. 11, Case 7 gives a shape for the curve that best
matches the sudden buckling behavior as well as the smallest load
Note that the maximum load of the experimental load test is 116 without the preceding initial deformation.

kN (11.82 t). Evaluation of Column Strengths

Numerical Simulations of the Two-Story Scaffoldings Representative loading stages of Case 7 that precede buckling are
presented in Table 4 for Element 2 (column) (Fig. 9), which is con-
General Information sidered as the most deformable.

Based on the calibrated model (Case 2A), a parametric concept for As mentioned earlier, to understand the collapse behavior, it
constructing a two-story scaffolding model is developed and ana- would be helpful to learn the deformation for each of the loading
lyzed using DAM as explained before. steps before the collapse (Fig. 12). The stable changes in the geome-
try form of the scaffolding include Steps 30–32, and the stability
Modeling the Two-Story Scaffoldings loss appears in Step 33. Under such conditions, the structural insta-
bility or buckle is assumed to occur. The structure experiencing
Two-story steel scaffoldings are made by stacking up two of the buckling cannot be used; thus, the loading condition in Step 33 does
one-story steel scaffolding frame modules discussed previously. not need to be examined further because it is obvious that it cannot
For its structural modeling, the column connection between the two be used. Therefore, it is necessary to review the maximum load
modules is considered as continuous. This condition is taken with before buckling, i.e., Steps 30–32. The check begins in Step 32, and
the assumption that although it takes the form of a connection
because it has been designed to be easy to set and dislodge, the con-
dition is considered precise enough and strong enough to distribute

© ASCE 04018028-9 Pract. Period. Struct. Des. Constr.

Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. Fig. 12. Deformation changes at each step approaching instability (Case 7).

Table 5. Column interaction check for the two-story model

Check Step Pu (kN) Mu (kN·m) Pu=f Pn R ¼ Pu þ 8 Mu Note
f Pn 9 f Mn
0.802 Not Ok
1 32 −93.46949 −1.623 0.789 1.245 Not Ok
0.773 1.011
2 31 −91.96898 −0.815 0.898 OK

3 30 −90.14139 −0.458

Fig. 13. Ultimate load response of one- and two-story steel scaffolding: (a) Case 2A; and (b) Case 7.

if it fails to fulfill the limit load condition then the lower loads in from the mean value of both, i.e., Pu = (91.97 þ 90.14)/2 % 91 kN.
Step 31 and smaller are checked. The ultimate load is obtained Compared with the one-story scaffolding, making a combination of
when the limit condition Pu % f Pn is fulfilled. stacked modules of two single-story scaffoldings will result in a
capacity that is 82% of the previous configuration.
Check the Available Strength of Element 2 (Column Left)
Discussions
Because the configuration of f 58 mm (L = 1.5 m) steel pipe
remains the same as earlier, the previously calculated data, i.e., Pn = An ultimate load analysis using DAM has been made using two
129.5 kN and Mn = 3.618 kN·m, are used. configurations of steel scaffolding, each consisting of the same
frame modules. One-story steel scaffolding (Figs. 4 and 5) is
The interaction of flexure and compression in doubly symmetric a single module. Two-story steel scaffolding consists of two mod-
members (pipe) will be limited by Eqs. H1–1 (AISC 2010) as seen ules, which are arranged stacked up (Figs. 9 and 10). Despite the
in Table 5. same constituent frame modules, the resulting carrying capacities
are different. The carrying capacity of one- and two-story steel
Judging from the results of Checks 2 and 3, it can be estimated
that the maximum load occurs between the Step 30 and Step 31
incremental loading stages. Briefly, the maximum load is taken

© ASCE 04018028-10 Pract. Period. Struct. Des. Constr.

Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. Fig. 14. Ultimate load response of standard and modified scaffolding: (a) Case 7; (b) Case 8; and (c) Case 9.

Fig. 15. Load-displacement curves of standard and modified scaffolding.

scaffolding is 111 kN (100%) and 91 kN (82%), respectively, and lateral restraint. To see the extent of the sway effect, a numeri-
which means that increasing the number of stories will decrease cal simulation using the previous model as modified is performed
the load capacity of the steel scaffolding. by adding new bracing in parts that had no previous bracing (Case
8) and by using an initial condition with additional lateral support at
DAM evaluates elements as beam-column; their capacities are the point of loading (Case 9). The ultimate load is taken at Pu = 91
determined by the interactions of flexure and compression accord- kN to enable its comparisons with the previous analysis (Fig. 14).
ing to Eqs. H1–1 (AISC 2010). Hence, the compression capacity is
correlated with the occurring moment. Therefore, when the load To see the effect of structural geometry changes (addition of
capacity is reduced it is due to the existence of a greater moment, new bracing in the parts of the frame with no previous bracing and
and vice versa. To prove this, DAM results will be shown regarding adding lateral support to the point of load at the column end) a rean-
the moments occurring for the axial load when it reaches the ulti- alysis is performed on the two-story scaffolding, which yields the
mate condition. P-D curves shown in Fig. 15.

The addition of stories results in the greater influence of P-D. Case 7 is a configuration of a steel scaffolding model, which is
This can be seen from the occurring moments when the load deemed as a standard, and Cases 8 and 9 are the modifications of
capacity of the steel scaffolding decreases (Fig. 13). The condition that standard model. Case 8 is made by adding new diagonal brac-
occurs because the structural system experiences sway deforma- ing to a part of the frame that had no previous bracing. The resulting
tions that are significantly influenced by the bracing configuration impact is highly significant; the bending moment, which results

© ASCE 04018028-11 Pract. Period. Struct. Des. Constr.

Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028

Downloaded from ascelibrary.org by Wiryanto Dewobroto on 08/29/18. Copyright ASCE. For personal use only; all rights reserved. from the second-order effect, decreases and seems even to disap- thank Mr. Sutadji Yuwasdiki, the chief of the experimental
pear. As a result, as can be seen in Fig. 15, the occurring P-D curve loading test executing team at the Research Institute for Human
takes the form of a vertical straight line. This means that during the Settlements, Ministry of Public Works, Bandung. Without them,
loading stages no buckling or instability occurs. This is possible this research on numerical analysis of steel scaffolding systems
because the behavior of the structural system in the frame shifts would have never been completed.
from the sway mode to the nonsway mode. This is the best solution
for a multistory steel scaffolding system. A similar influence References
appears for Case 9, which gives some lateral restraint to the point of
loading, although it does have some influence in increasing its load- Adam, J. M. 2013. “Special issue on analysis of structural failures using nu-
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Conclusion
AISC. 2005. Specification for structural steel buildings. ANSI/AISC 360-
The local product of the ring-lock scaffolding system is made 05. Chicago: AISC.
based on similar products abroad, and it has been proven reliable
as an aid for construction execution at a more economical price. AISC. 2010. Specification for structural steel buildings. ANSI/AISC 360-
To ensure its strengths when used on-site, an ultimate load 10. Chicago: AISC.
capacity analysis has been conducted to find the maximum load
that can be supported by the structure. Generally speaking, for AISC. 2016. Specification for structural steel buildings. ANSI/AISC 360-
such an analysis, a relatively sophisticated FEM-based computer 16. Chicago: AISC.
program and cumbersome procedure will be used. However, this
research has successfully completed the analysis by using a sim- Andresen, J. 2012. “Investigation of a collapsed scaffold structure.” Proc.
pler method, i.e., DAM, which is the latest structural steel design Inst. Civ. Eng. Forensic Eng. 165 (2): 95–104. https://doi.org/10.1680
method (AISC 2005, 2010, 2016). /feng.11.00021.

Despite its relatively simple structural modeling, the accuracy of CSI (Computers & Structure, Inc.). 2011. SAP2000 linear and nonlinear
its results can be improved by calibrating it against the experimental static and dynamic analysis and design of three-dimensional structure.
loading test result data, which are relatively costly. Therefore, it is Berkeley, CA: CSI.
used only for relatively small structural modules, which in this case
is one-story steel scaffolding. Furthermore, using a parametric Dewobroto, W. 2016. Steel structure–Behavior, analysis & design–
study technique, the numerical analysis is used for analyzing the AISC 2010. 2nd ed. Tangerang, Indonesia: Jurusan Teknik Sipil
ultimate load of more complex structural modules, i.e., two-story UPH.
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This research found that the steel scaffolding modules arranged in compared to experimental results.” In Proc., Geotechnical and
a stack up are highly susceptible to stability issues. As a result, this Structural Engineering Congress 2016, edited by C. Y. Chandran and
module’s load capacity is less than the one-story scaffolding module. M. I. Hoit, 201–211. Red Hook, NY: Curran Associates.
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against stability issues, hence, improving the load capacity. Hadipriono, F. C., and H. K. Wang. 1987. “Causes of falsework collapses
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The author would like to extend his gratitude to Mr. Susiato and Kim, S. E., K. W. Kang, and D. H. Lee. 2003. “Full-scale testing of space
Mr. Yosep Tan, the owner and head of PT. Putracipta steel frame subjected to proportional loads.” Eng. Struct. 25 (1): 69–79.
Jayasentosa, manufacturers of steel scaffoldings and funding of https://doi.org/10.1016/S0141-0296(02)00119-0.
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order inelastic analysis.” Eng. Struct. 14 (1): 7–14. https://doi.org/10
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© ASCE 04018028-12 Pract. Period. Struct. Des. Constr.
Pract. Period. Struct. Des. Constr., 2018, 23(4): 04018028