Comparison of the seismic and wind analyses of two tower cranes

1.1. Past studies

Few studies have been performed on tower cranes under seismic and wind loads, even though there are several magazines announcing products related to cranes. A few papers performed dynamic analyses considering loads such as live loads, pendulum action, maneuver operations or slewing operations [4-7]. Takanashi et al. [2] performed an earthquake analysis. Alămoreanu et al. [8] used sinusoidal input to check earthquake responses. Gu et al. [9] analyzed the effect of wind loads. Gu et al. [10] and Li-Jeng et al. [11] used the FEM to study this topic.

During the Japan earthquake Hyogo-ken Nanbu in 1995 the need of a standard to ensure seismic-resistant cranes was first highlighted. Many problems were reported with tower cranes, especially those working on top of high-rise buildings [2]. As a consequence, ISO prepared a first draft of a norm on “Cranes: Principles for Seismically Resistant Design” [12]. Since then, several organizations have been working on the problems of earthquake and window effects on cranes, namely, the Eurocodes [13].

More recently, Shen et al., [14] looked into the introduction of TMD to control vibrations under earthquake loads, and Tarak et al., [15] present a text on modelling and control of tower cranes motion using analytical formulation and small-scale lab test.

1.2. Tower foundation

In the course of this section, both structures are described sequentially, from the foundation to the top, highlighting and comparing the differences between them in terms of the geometry, mass, etc.

First, the two tower cranes have different types of supports that are identical in terms of how they are designed by installing large masses of concrete.

While the tower crane located in Arco do Cego (AC) has a mass of 55 tons made up of concrete beams arranged on the four sides of the base resting on two IPE 400 beams, the tower crane located in Alto do Olival (AO) has a lower mass of 32 tons consisting of concrete slabs arranged on two sides of the base also resting on steel IPE beams (Fig. 3).

However, in terms of translation, while the Arco do Cego Crane (AC) is fixed in a pit foundation, the Alto do Olival Crane (AO) is supported by steel rails that can present translations according to the rail directions, thus enabling a change in position and, consequently, the perimeter of influence of the jib. The different mass assignments on the tower crane’s foundation depend on the size of each structure, its reach and the capacity to transport loads in accordance with its distance from the tower axis.

As will be described below, the AC tower crane has larger dimensions than the AO tower crane. Note also that while in the stack on AC base, concrete slabs cannot move as they are intertwined, on AO base they are just superposed allowing sliding in case of high vertical shaking.

Fig. 3Top and side view of Arco do Cego and Alto do Olival Tower Cranes

a) Arco do Cego

b) Alto do Olival

1.3. Tower mast

The tower mast has a spiral layout composed of modules in square sections corresponding to a large triangulated lattice structure connected to the base, which gives the crane its strength and height. The AC tower crane has the same module in height, while the AO tower crane has a tower composed of different modules (as shown in Fig. 4).

On the one hand, in the AC tower crane, SHS 140×140×8 mm cross-sections are used in the corners of the square section, and rectangular (100×50) mm cross-sections are used in the diagonal members, where both remain constant in height.

On the other hand, the AO tower crane has L-shaped cross-sections (angles with equal legs) in the corners of the square section, and U and L are used in the diagonal lines, where both gradually decrease in height.

Fig. 4Tower Crane mast modules: a) Arco do Cego and b) Alto do Olival

a)

b)

1.4. Jibs

Finally, the connection between the jibs and mast is ensured in the same way through ties (steel suspension cables) as shown in Figs. 5 and 6. It should be noted that the requirements of the first crane’s ties are higher than those of the second crane. Once again, in terms of dimensions, the AC tower crane has a longer reach, having a jib length of 60.00 m, and the AO tower crane has a 35.00 m length. The counter-jibs have dimensions of approximately 16 m and 13 m, respectively, and both are designed in different ways. While the AC counter-jib is made up of RHS 300×150×10 mm beams, the AOs are made up of a triangular truss with tubular cross-sections [16], such as the jibs of both structures. These are designed as truss structures composed of CHS and RHS cross-sections, decreasing the dimensions in the upper chord along the jib.

The two cranes are different in size and element characteristics. While the mast of the first tower crane has a square section of 1.60×1.60 m and a total height of 43.50 m, the second has a square section that decreases in height from 1.20×1.20 m to 0.90×0.90 m and has a total height of 36.00 m.

Fig. 5Arco do Cego tower-jibs connection

Fig. 6Alto do Olival tower-jibs connection

3.1. In situ dynamic characterization by forced-balance accelerometer

To not only ensure a closer proximity between the numerical model and the actual structure, but to also provide greater credibility of the results exposed in this work, a dynamic identification test based on ambient vibrations was performed for both structures under analysis.

Due to the low frequency of fundamental mode shapes of these structures together with the difficulty in placing instrumentation in several locations, prior to initiating the measurement campaign, we tested our instrumentation for the conditions we face at the site and evaluated the operational procedure to ensure that the collected information was correct and accurate. For the first topic, we tested an 18-bit accelerometer with a 0.1 Hz high cut off measuring the motion of a few centimeters for a 7 m long pendulum and obtained good results. For the second problem, we prepared a time trigger giving the time for a crane maneuverer to climb up the ladder and place the instrument at an adequate location. The instrument recorded the free vibration of the top of the tower for several minutes and repeated the test a few times with a $\mathrm{\Delta }t=$0.005 sec. Fig. 10 shows the time record obtained at the top of the tower, exhibiting the low frequencies and amplitudes of motion of the order of 5 mg in the longitudinal direction and amplitudes of motion, and Fig. 11 shows the corresponding FFT.

Fig. 10Representative time history record made at the top of the Alto do Olival Tower Crane

Fig. 11Frequencies in the x direction (longitudinal) obtained through the dynamic identification test

From the analysis of the two graphs, it can be concluded that this type of structure is able to offer a wide range of results with great clarity and quality, thus facilitating the identification of the structure’s natural frequencies and, consequently, the model calibration.

3.2. By optical measurements

Due to a lucky coincidence, we were able to follow in very close connection and with a view at the level of the jib the operation of one of the cranes in a construction shipyard. Beyond the accelerometer testing, we perform in-situ analysis by optical techniques, filming the motion of the tower and jib under several loads conditions, actually with much larger amplitude values than the one obtained at the time of instrument testing. Frequencies were easily obtained by accelerating the film and trigonometric relations permitted the computation of displacements. Comparing these measurements with the ones obtained with the accelerometer station, the results for the first frequencies in the longitudinal and transversal directions were the same to the centesimal point.

3.3. Vibration modes

Tables 2 and 3 show the frequency values obtained according to the different directions for both structures under analysis. As seen for the first vibration modes according to the translation directions, $x$ and $y$, the Arco do Cego tower crane has more flexible dynamic behavior, characterized by lower frequency values.

Note that after comparing the values obtained through the in situ tests and the numerical models, frequencies according to z and torsional movements were identified in the Arco do Cego tower crane. This fact is most likely associated with placing the equipment eccentrically in relation to the tower axis. This eccentricity may have been higher in the Arco do Cego tower crane, thus contributing to obtaining a torsional frequency.

3.4. Vibration modes

In this phase, using numerical modeling, the vibration modes and respective dynamic characteristics of the structure under analysis are described. It should be noted that Tables 4 and 5 are composed of values that were already adjusted and calibrated based on the results obtained in the in-situ dynamic identification test.

As is generally known, the overall response of the structure must be composed of all the vibration modes with a substantial contribution.

For the Arco do Cego tower crane case (Table 4), it was not possible to reach a minimum of 90 % of the total mass of the structure, having been included in the analysis of 50 modes contributing to 69 % of the mass according to $x$ and $y$ and 99 % according to $z$ and torsion around the vertical axis.

But for the sum of the mass participation factors of the Alto do Olival tower crane (Table 5), to reach a minimum value of 90 % of the total mass of the structure, a total of 94 vibration modes were computed.

From the analysis of the vibration modes and their respective mass participation factors, an interesting fact is highlighted.

For the Alto do Olival tower crane, the first twelve vibration modes do not generate high percentages of excited mass (≈ 34 %) for the $x$ and $y$ translation modes; thus, the number of vibration modes under analysis has been widened to reach the minimum condition of 90 % of the excited mass of the structure. Consequently, it has been noted that the higher percentages of excited mass are associated with the structure’s base translation in each direction, $x$ and $y$, which in turn involves the more rigid vibration modes.

Regarding the Arco do Cego tower crane, we have widened the modes under analysis, but even so, no more relevant vibration modes were identified in the structure dynamic behavior. Unlike the Alto do Olival tower crane, the mass located at the base of the structure was not even excited, which is due to the way the concrete masses are intertwined with each other, providing a steady and fixed base. In Tables 6 and 7 the results of the numerical model and the experimental test are compared.

From the analysis of the results, it is concluded that the values obtained from the in situ test reveal great quality and are close to some vibration modes in both structures, thus proving a good approximation between the numerical models and real structures.

From this comparison, the lowest errors obtained are approximately 2.6 % and 1.2 % for the AO and AC tower cranes, respectively, in the x direction, and the maximum obtained errors are approximately 10.1 % and 6.8 % in the $x$ directions (second modes). It should be noted that these maximum errors are associated with a second vibration mode in the x and y directions and as such may possibly correspond to fewer clear modes compared to the first two translation vibration modes, which does not cause a substantial influence on the model calibration. Although, the maximum error is 10,1 %, this is not an important issue as the mass participation factor is not so high and spectral values for these frequencies do not contribute much to the response of the structure as the first modes.

The following is a brief description of the most influential vibration modes in the structure behavior.

3.4.1. 1st Vibration mode

The first vibration modes of the Arco do Cego tower crane (Fig. 12) correspond to a torsional mode with a period of 6.59 sec, a mass participation factor of 92 %, and Alto do Olival a period of 7.61 sec and a mass participation factor of 98 %.

As shown in Fig. 12, the structural movement corresponds to a rotation of both jibs around the tower axis, guaranteeing a high percentage of excited mass.

Fig. 121st Vibration mode: Torsion around the tower axis

a) Arco do Cego

b) Alto do Olival

3.4.2. 2nd Vibration mode

The second vibration modes of the two cranes (Fig. 13) represent the vibration of the structure in the $x$ direction, that is, in the direction of the jibs, with a period of 5.14 s and a mass participation factor of 37 % and with a period of 3.37 s and a mass participation factor of 11 %, respectively.

Unlike the first vibration mode, this mode has a reduced percentage of excited mass. However, the Arco do Cego tower crane has a higher percentage, which is associated with the existence of a heavier counterweight and the fact that it has larger dimensions.

Fig. 132nd Vibration mode: Translation in the x direction

a) Arco do Cego

b) Alto do Olival

3.4.3. 3rd vibration mode

The cranes’ third vibration mode (Fig. 14) is characterized by a translation in the y direction, the direction transverse to the jibs, with a period of 4.78 s and a mass participation factor of 54 % and with a period of 2.99 s and a mass participation factor of 25 %.

Once again, it is verified that the Arco do Cego tower crane has a higher percentage of excited mass due to the greater presence of mass of this tower crane for both the entire structure and the counterweight.

Fig. 143rd Vibration mode: Translation in the y direction

a) Arco do Cego

b) Alto do Olival

3.4.4. 4th Vibration mode

The crane’s fourth vibration mode (Fig. 15) is characterized by a translation in the $x$ direction, the direction transverse to the jibs, with a period of 1.82 s and a mass participation factor of 22 % and with a period of 1.55 s and a mass participation factor of 18 %.

Fig. 154th Vibration mode: translation in the x direction

a) Arco do Cego

b) Alto do Olival

3.4.5. 5th vibration mode

The crane’s fifth vibration mode (Fig. 16) is characterized by a translation in the $y$ direction, the direction transverse to the jibs, with a period of 1.74 s and a mass participation factor of 3 % and with a period of 1.06 s and a mass participation factor of 4 %.

The following vibration modes have a higher influence on the dynamic behavior of the tower crane since they concentrate mainly on the mass excitation located at the base of the structure. These types of modes occur only in the Alto do Olival, and one must take into consideration the high discrepancy between the mass of the base of the structure and the rest of it.

Thus, the dynamic behavior of a tower crane is largely dependent on the way its base is designed.

Fig. 165th vibration mode: translation in the y direction

a) Arco do Cego

b) Alto do Olival

3.4.6. 42nd and 94th vibration modes (Alto do Olival Tower Crane)

The 42nd vibration mode (Fig. 17(a)) represents a translation of the structure base in the $y$ direction with a period of 0.042 s, and a mass participation factor of 32 % and the 94th vibration mode (Fig. 17(b)) is characterized by a translation of the base of the structure in the $x$ direction with a period of 0.017 s and a mass participation factor of 51 %.

These modes represent rather rigid modes with a considerable excited mass percentage.

As a result, it is critical to not neglect the influence of these last rigid vibration modes on the dynamic behavior of the structure. This type of mode is important for all cranes which stand on rails and may move under moderate to strong loads.

Fig. 17a) 42nd vibration mode: translation of the concrete ballasts in the x direction and b) 94th vibration mode: translation of the concrete ballasts in the y direction

a)

b)

4.1. Actions

The structures were analyzed for seismic and wind action plus dead load. In terms of dead loads, the crane is only subjected to its own weight, i.e., when it is not carrying any load.

4.2. Structural analysis

Based on each type of combination of actions, the action effects in each structural member on the base reactions and the resistance of the restraints that prevent the movement of the tower crane base of Alto do Olival tower crane were evaluated. As it is supported on rails, to prevent translation of foundations, we added steel profiles welded to the rails. Tables 8 and 9 present the maximum displacements of the jib and counter-jib tips due to seismic and wind action.

As seen, not only does the Arco do Cego tower crane have substantially higher displacements than the Alto do Olival tower crane, which is normal regarding the higher lengths of the former but also, in general, the wind action tends to be the more critical. The high displacement values are three times larger than the values of displacements obtained for a daily operational loading.

In terms of forces, it is observed that while the axial forces prevail in the members of the structure, shear forces and bending moments are negligible, as expected in a truss structure (Fig. 18).

Fig. 18Axial forces in different structural members (red and green – compression and blue – tension)

Therefore, we evaluated and compared the design effects and resistance of some cross-sections of both tower cranes (Figs. 19 and 20). In the case of a steel structure, the influence of the bending lengths and the reduction coefficients according to the possible directions are fundamental and must be taken into account [21]. Fortunately, a tower crane consists of modules of small lengths between vertical profiles.

From Figs. 19 and 20 presented above, the following conclusions can be obtained:

– The wind action effects are higher than those of seismic action in the tower cross-sections (SHS 140×140×8, diagonal – 100×50, base knee brace, L15 and L7) of both tower cranes; only in the L12 cross-section does the seismic action cause a higher axial force;

– In the jib cross-sections (SHS 90×90×5, SHS 70×70×4, CHS 60.3, CHS 42.4, RHS 300×150×12.5, SHS 80×80×5 and CHS 76.1) [16] of both tower cranes, the seismic action effects are higher than those of wind action;

– Regarding the suspension of steel cables, in general, the seismic action is also superior to that of wind, except for the Alto do Olival tower’s counter-jib, where the effects between wind and seismic activity are very similar;

– In general, the design values of the actions at the Arco do Cego crane are higher than those at the Alto do Olival crane, which is normal, taking into account the difference in geometry, weight, etc.

Fig. 19Arco do Cego tower crane security analysis for several sections

Fig. 20Alto do Olival tower crane security analysis for several sections

As shown in Fig. 21, the cross-sections of both structures in the most critical zones always meet the safety requirements (ratios below 1.0). It means that these structures can stand about 20 % more loads than the ones selected for analysis.

Fig. 21Tower crane security analysis ratios for most critical sections

a) Arco do Cego

b) Alto do Olival

From the analysis of the base reactions for the Alto do Olival tower crane that is standing on wheels, we can conclude that the wind has a greater affect than the seismic action (Table 10) and that the restraints, made of welded steel profiles, have a higher resistance than the effects due to both actions (Table 11).

4.3. A few test measurements for checking deformations

From all results obtained in this Section, we confirm the large deformations of these structures under moderate seismic and wind loads attesting their flexibility. These numbers were confronted with values provided by the analytical model for current operational conditions (a point load at the tip of the jib) and by optical inspection during some loading transportation. Not entering in details, the transport of large loads and sometimes the drop or hitting of these loads provoke large displacements compatible with the analytical results. We did not check local instability in the heavier loaded elements, but for larger actions we may have problems.