The behavior of top and seat bolted angle connections under blast loading

Journal of Constructional Steel Research 67 (2011) 1463–1474

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Journal of Constructional Steel Research

The behavior of top and seat bolted angle connections under blast loading Amir Saedi Daryan a,⁎, Masoud Ziaei a, Seyed Amirodin Sadrnejad b a b

Civil Engineering Department, K.N.Toosi University, Tehran, Iran Civil Engineering Department, K.N.Toosi University of Technology, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 5 January 2010 Accepted 16 March 2011 Available online 20 May 2011 Keywords: Bolted angle connection Blast loading Finite element analysis

a b s t r a c t Abnormal loading generated by blast or impact may cause local damage in a building that may evolve to affect the whole structural system. Therefore, structures have to be designed to prevent such disproportional consequences. Connection is an important contributor to ductility and robustness of the structural steel systems in mitigating such consequences. Considering this importance, finite element analysis is used in this paper to study the behavior of top and seat bolted angle connections under blast loading. The two frequent angle connections including top and seat angle bolted connections with and without web angles are studied using the ANSYS finite element software. The finite element models are verified by comparing the predicted results obtained from the models and the values measured in the experimental tests. Simplified blast loading is then applied to the verified connection models and the behavior of these connections under blast loads is evaluated with the connection critical areas being determined. The connection failure modes as well as the applicability of the connection under blast loading are briefly discussed. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction Considering the significant effect of connection behavior on behavior, survival time and efficiency of a structure, studying the connection behavior in different structures under different loads is of great importance. The vulnerability of steel connections has been emphasized by many studies. Most of them were performed for the purpose of mitigating seismic risk [1–4] or fire risk [5–10]. Study of steel connections subjected to dynamic loads was initiated in the 1960s by Popov [11] and some experimental tests were conducted to study the cyclic behavior of steel moment-resisting connections. Since these early studies, investigations have generally focused on the behavior under cyclic loads, such as those generated during an earthquake. However, since September 11th, there is rising concern in the United States over the safety of building structures subjected to blast loads. When a structural steel frame is subjected to blast loads, the beam-to-column connections, which are responsible for load transferring between different members within the frame, play a major role in structural response. Thus, a better understanding of the behavior of structural steel connections under blast loading is of prime importance. Nevertheless, few studies have been conducted to investigate the interaction of blast loads and structural components in buildings. Some case studies based on past blast attacks on buildings have been carried out, such as the work conducted by Caldwell [12]. This study ⁎ Corresponding author. Tel.: + 98 2188779473×5; fax: + 98 2188779476. E-mail addresses: [email protected] (A. Saedi Daryan), [email protected] (M. Ziaei), [email protected] (S.A. Sadrnejad). 0143-974X/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2011.03.020

was focused on the pattern and intensity of blast damages formed in the structures. However, most of these studies had a macro view of the situation and studied the buildings as a unique structure, instead of identifying the behavior of individual structural components of the building structure under blast loads. Little test data exists to quantify the performance of steel connections directly loaded by blast. Furthermore, numerical studies investigating blast loaded steel connections are also quite limited. Krauthammer's research team emphasized severe deformations and brittle failures of the connection components subjected to high-speed loads in their studies and investigated the strain rate effect on numerical analyses of structures after a blast considering the nonlinear behavior [13,14]. The post-blast behavior of such structures could be assessed by numerical simulations considering highly nonlinear behaviors, brittle failure, strain effects, and so on. They aimed at assessing connection damage using the pressure–impulse diagram for blast-like loadings. The blast responses of large-scaled three-dimensional connection models were determined using ABAQUS. Based on the analyses results from the full models, the characterized property was used to simplify the configurations which are feasible in three-dimensional multi-story frame analysis. [15] One of the important studies carried out to investigate the blast loading effect on connection behavior is the study conducted by Tapan Sabuwala et al. [16]. In some countries including Iran, steel structures with semi rigid connections and bracing system are widely used. The semi-rigid connections that are used in these steel frames are different types of bolted and welded angle connections. Thus, the effect of blast on these connection details is studied in this paper.

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2. Study theory 2.1. Simulation of blast effects Blast effects are associated with either small nuclear (e.g., tactical size) or conventional explosive devices. The associated technical problems include many serious issues that could be far more complicated to address than blast effects on buildings. Therefore, nuclear weapon effects are not addressed in this paper. The most common form of blast scaling is the Hopkinson–Cranz, or cube-root scaling [17,18]. It states that self-similar blast waves are produced at identical scaled distances when two explosive charges of similar geometry and of the same explosive, but of different sizes, are detonated in the same atmospheric conditions. It is customary to use as a scaled distance a dimensional parameter, Z as follows: Z = R= E

1=3

or

Z = R= W

1=3

ð1Þ

where R is the distance from the center of the explosive source, E is the total explosive energy released by the detonation (represented by the heat of detonation of the explosive, H), and W is the total weight of a standard explosive, such as TNT, that can represent the explosive energy. Blast data at a distance R from the center of an explosive source of characteristic dimension d will be subjected to a blast wave with amplitude of P, duration td, and a characteristic time history. The integral of the pressure–time history is defined as the impulse I. The Hopkinson– Cranz scaling law then states that such data at a distance ZR from the center of a similar explosive source of characteristic dimension Zd detonated in the same atmosphere will define a blast wave of similar form with amplitude P, duration Ztd and impulse ZI. All characteristic times are scaled by the same factor as the length scale factor Z. In Hopkinson–Cranz scaling, pressures, temperatures, densities, and velocities are unchanged at homologous times. The Hopkinson–Cranz scaling law has been thoroughly verified by many experiments conducted over a large range of explosive charge energies. In this study, the same method is used to simulate the effect of blast. Since the main purpose of this paper is about confined blasts, for instance a blast in a room, explanations about such explosions are presented in the following discussions. 2.2. Confined explosions Confined and contained explosions within structures result in complicated pressure–time histories on the inside surfaces. Such loading cannot be predicted exactly, but approximations and model relationships exist to define blast loads with good confidence. These include procedures for blast load determination due to initial and reflected shocks, quasi-static pressure, directional and uniform venting effects, and vent closure effects. The loading from a highexplosive detonation within a confined (vented) or contained (unvented) structure consists of two almost distinct phases. The first is the shock phase, where incident and reflected shocks inside structures consist of the initial high-pressure, short-duration reflected wave, and several later reflected shock reverberations of the initial shock within the structure. The second is called the gas loading phase that attenuates in amplitude because of an irreversible thermodynamic process. These are complicated wave forms because of the involved reflection processes within the vented or unvented structure. The overpressure at the wall surface is termed the normally reflected overpressure, and is designated Pr. Following the initial internal blast loading, the shock waves reflected inward will usually strengthen, as they implode toward the center of the structure, and then attenuate, as they move through the air and re-reflect to load the structure again. The secondary shocks will usually be weaker than the

initial pulse. The shock phase of the loading will end after several such reflection cycles. When an explosion from a high-explosive source occurs within a structure, the blast wave reflects from the inner surfaces of the structure, implodes toward the center, and re-reflects one or more times. The amplitude of the re-reflected waves usually decays with each reflection, and eventually the pressure settles to what is termed the gas pressure loading phase. Considering poorly vented or unvented chambers, the gas load duration can be much longer than the response time of the structure, appearing nearly static over the time to maximum response. Under this condition, the gas load is often referred to as a quasi-static load. For vented chambers, the gas pressure drops more quickly in time as a function of room volume; vent area, mass of vent panels, and energy release of the explosion. Depending on the response time of structural elements under consideration, it may not be considered quasi-static. The gas load starts at time zero and overlaps the shock load phase without adding to the shock load, as illustrated in Fig. 1, where the shock phase and the gas phase are idealized as triangular pulses. In a numerical study, it is necessary to calculate the shock and gas pressure curves against time according to the explosive charge weight. Considering the complication of calculating these curves, different computer codes can be used to calculate these curves including SHOCK [19] and FRANG [20] that are respectively used to calculate shock and gas pressure curves. SHOCK is a computer code for estimating internal shock loads. This code can be used to calculate the blast impulse and pressure on all or part of a cubicle surface bounded by one to four rigid reflecting surfaces. The code calculates the maximum average pressure on the blast surface from the incident and each reflected wave and the total average impulse from the sum of all the waves. The duration of this impulse is also calculated by assuming a linear decay from the peak pressure. This code is based on the procedures in TM 5-1300. Shock impulse and pressure are calculated for each grid point for the incident wave and for the shock reflecting off each adjacent surface. The program includes a reduced area option which allows determination of the average shock impulse over a portion of the blast surface or at a single point on the surface. The quasi static portion of the pressure pulse (gas load) can be obtained with the computer code FRANG to predict of the load history and combining the two curves to form the complete pressure–time history. It should be noted that the shock and quasi-static pressures are not added where they overlap, but are merely intersected to define the load history. 2.3. Study procedure In this paper, to study the behavior of steel bolted angle connections under confined explosion, the connection is considered as a part of an assumed room in which the explosion occurs. The peak pressures produced by the blast are then calculated according to the

Fig. 1. Typical combined shock and gas load in a small chamber.

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Table 1 Properties of connection components tested by Aziznamini. Specimen number

Bolt diameter (mm)

Column section

Beam section

Top and seat angles Angle

Length (mm)

Gauge (mm)

Bolt spacing (p)(mm)

Angle

Length (mm)

8S1 8S2 8S3 8S4 8S5 8S6 8S7 8S8 8S9 8S10 14S1 14S2 14S3 14S4 14S5 14S6 14S8

19.1 19.1 19.1 19.1 19.1 19.1 19.1 22.3 22.3 22.3 19.1 19.1 19.1 19.1 22.3 22.3 22.3

W12X58 W12X58 W12X58 W12X58 W12X58 W12X58 W12X58 W12X58 W12X58 W12X58 W12X96 W12X96 W12X96 W12X96 W12X96 W12X96 W12X96

W8X21 W8X21 W8X21 W8X21 W8X21 W8X21 W8X21 W8X21 W8X21 W8X21 W14X38 W14X38 W14X38 W14X38 W14X38 W14X38 W14X38

L6X3-1/2X5/16 L6X3-1/2X3/8 L6X3-1/2X5/16 L6X6X3/8 L6X4X3/8 L6X4X5/16 L6X4X3/8 L6X3-1/2X5/16 L6X3-1/2X3/16 L6X3-1/2X1/2 L6X4X3/8 L6X4X1/2 L6X4X3/8 L6X4X3/8 L6X4X3/8 L6X4X1/2 L6X4X5/8

152.4 152.4 203.2 152.4 203.2 152.4 152.4 152.4 152.4 152.4 20.32 20.32 20.32 20.32 20.32 20.32 20.32

50.8 50.8 50.8 137.2 63.5 63.5 63.5 50.8 50.8 50.8 6.35 6.35 6.35 6.35 6.35 6.35 6.35

88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9 13.97 13.97 13.97 13.97 13.97 13.97 13.97

2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X3/8 2L4X3-1/2X1/4 2L4X3-1/2X1/4 2L4X3-1/2X1/4

139.7 139.7 139.7 139.7 139.7 139.7 139.7 139.7 139.7 139.7 215.9 215.9 139.7 215.9 215.9 215.9 215.9

criteria of TM 5-1300 code. The charge weight that is to be located at the room center is determined based on the peak pressures obtained by the code as well as the room geometrical sizes. Having determined these values, SHOCK and FRANG codes are used to determine the combined shock and gas pressure curve and this blast pressure curve is applied to the side walls as a uniformly distributed load. Finally, after determination of blast-induced pressures in the room, ANSYS software is used to develop the finite element model of the room and the model is analyzed under the mentioned pressures. Details of the modeling procedure, loading pattern, pressure distribution pattern, boundary conditions, etc. are fully presented in the following discussions. As it can be clearly understood from the descriptions mentioned in the study procedure, the main body of this paper is modeling and analysis of bolted angle connections under equivalent blast pressure loads (quasi-static loads). Thus, it should firstly prove the ability of the finite element software in modeling and analysis of behavior of these types of connections. Some experimental tests in the field of angle connections are selected as reference and the finite element modeling and analysis are verified using the results of these tests. 3. Verification of the models 3.1. Experimental tests The experimental tests carried out by Aziznamini et al. in South California, Columbia University in 1982, 1985 and 1989 are valid references in the field of bolted angle connection behavior [21–23]. The behavior of these connections under monotonic and cyclic loads is studied in the mentioned tests. Moreover, different parameters including the initial stiffness of connection, moment-rotation behavior and etc are also studied. Citipitioglu and Haj-Ali in 2002 modeled

Web angle

and analyzed the Aziznamini test specimens using ABAQUS finite element software by 3D detailed models [24,25]. Afterwards, many researchers have used the results of these tests and finite element models in the field of angle connections [26–29]. Considering the validity of these tests, Aziznamini's test results are used for verification and the results obtained by numerical model analyses are compared with those of Aziznamini's test and Citipitioglu's numerical study. Dimensions, sizes and detailed properties of the test specimens are tabulated in Table 1. The test arrangement used by Aziznamini is shown in Fig. 2. 3.2. Finite element model The ANSYS multi-purpose finite element modeling code is used to perform numerical modeling of the connections. FE models are created using ANSYS Parametric Design Language (APDL). The geometrical and mechanical properties of the connection models are used as the parameters, thus the time required to create new models is considerably reduced. Numerical modeling of the connections is performed with the following considerations: all components of connections such as beam, column, angles and bolt heads and bolt shanks are modeled using eight node first order SOLID64 elements which can consider thermal gradient applied for pretension force of bolts. Bolt holes are 1.6 mm larger than the bolt diameter. The finite element model of the connection is shown in Fig. 3. Stress distribution produced by applying pretensioning force on bolt before conducting the main analysis is shown in Fig. 4. ANSYS can model contact problems using contact pair elements: CONTA174 and TARGE170 pair together in such a way that no penetration occurs during the loading process. The interaction between adjacent surfaces, including angle–beam flange, bolt head–nut, bolt hole–bolt

Fig. 2. Details of the specimen used by Aziznamini et al.

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Fig. 5. Selected contact surfaces considered in the finite element model.

Fig. 3. Finite element model of the connection.

shank and the effect of friction are modeled using these contact elements. Selected contact surfaces are shown in Fig. 5. The value of Coulomb friction coefficient is one of the significant parameters in studying the bolted connections that is used to consider the friction forces. AISC provision [30] proposes the value of 0.33 for A class surfaces. However, references [31,32] have considered the value of 0.1 for this coefficient. [31,32]. In the present study, in contrast to the studies carried out in references [31,32], nuts and bolt heads are modeled as hexahedral which is similar to the real shape. According to the sensitivity studies carried out by the first author, the value of 0.25 is found to be the best value for these types of connections [33,34]. The value of 0.25 as the friction coefficient proper for these types of connections is used in different studies [26–28] when detailed connection simulation were to be conducted and thus, the same value is considered in the current study. 3.3. Boundary conditions and applied loads Considering the test arrangement that is cruciform as well as the profile type, connection geometry has two symmetry planes that are shown in Fig. 6. Consequently, to decrease the analysis operation, just one-fourth of the connections is modeled and the degrees of freedom

on symmetry planes are restrained perpendicular to the symmetry planes to simulate the symmetry in the models. Considering the high rigidity of column due to the stiffeners as well as the nature of cruciform arrangement used in the tests, the column web did not experiment any deformation and rotation and remained elastic. This is confirmed by the results of experimental tests. Thus, column web is not modeled and column flange and stiffeners are just modeled and the rigidity produced by column is simulated by restraining the freedom degrees at the stiffener end points. It is noted that since the beams of the connections are compact sections, the local buckling instabilities occur in the inelastic range or high stress levels. The Von Mises stress distribution in FE models clarifies that the beam remains nearly elastic and so the local buckling failure mode can be ignored in the FE models. For the specimens tested at ambient temperature, 50 mm vertical displacement is applied monotonically on the nodes located at the end of beam to apply the moment on the connections. This displacement at the end of the beam causes an approximately 0.03 rad rotation. The location where this displacement is applied is shown in Fig. 6. The amount of bending moment and relative rotation of connection can be computed by Eqs. (2) and (3): M = p⁎L R=

ε1 −ε2 h

ð2Þ ð3Þ

where M is the applied connection moment, p is the summation of reaction forces formed by the applied displacement on beam end nodes, L corresponds to beam length, R is relative rotation of connection, h is beam depth, and ε1 and ε2 are the top and bottom flange horizontal displacements respectively. The rotational degrees of freedom are not active for solid elements in ANSYS; therefore, the vertical deflection is determined at a certain point along the beam from which the connection rotation Φ can be estimated using the following equation: Φ¼ Arctanðu=LÞ

ð3Þ

where u is the vertical deflection of the point along the beam, and L is the distance from connection centerline to the point where the deflection is measured. 3.4. Material properties

Fig. 4. Distribution of pretensioning force in bolt by applying thermal gradient.

The stress–strain relation for all connection components, except for bolts, was represented using a three-linear constitutive model. An isotropic hardening rule with a Von Mises yielding criterion was used

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Fig. 6. Boundary condition and loading (verification part).

to simulate plastic deformations of connection components, and fracture of material is not considered. Since the steel properties of connection components are not clearly mentioned in references [21–23], the properties that were assumed by Citipitioglu et al. for Aziznamini's tests [24,25] are used here and provide good results. The yield stress and ultimate strength of bolts are assumed based on nominal properties of A325 bolts. Bolt materials are modeled as bilinear with 634.3 MPa yield stress and an ultimate stress of 930 MPa at 8% strain. Modulus of elasticity and Poisson's ratio are considered, respectively, as 210 GPa and 0.3. Fig. 7 shows the stress–strain relation of A36 steel used for beam and angle materials in A.M. Citipitioglu et al.'s study.

3.5. Model verification To evaluate the accuracy of the numerical models, 17 finite element models are developed according to the specimens tested by Aziznamini and the results are compared. In Fig. 8, moment-rotation curves obtained by analysis of finite element models are compared to those from the experimental tests conducted by Aziznamini and those obtained by Citipitiuglu using numerical methods. Fig. 8 shows that the results of the finite element models are in close agreement with the experimental test results. Differences between the numerical simulations and the experimental results may be due to several causes, such as numerical modeling simplification, test specimen defects, residual stress and contact surface interactions, frictional forces, and bolt pretensioning forces. Bolt pretension and the friction coefficient were two major factors that affect the behavior of the connections, especially in the nonlinear regime. These factors are difficult to estimate. Another

600

stress(MPa)

500 strain=0.0485 stress= 510

400 300 strain=0.0013 stress=276.9

200 100

A36 steel

0 0

0.02

0.04 strain

0.06

Fig. 7. Stress–strain curve for A36 steel [35].

0.08

major influence on connection behavior arises from the nonlinear constitutive laws for materials, especially for situations where only uniaxial values of the stress–strain curves are available. This is the cause for the increased difference between the curves in the nonlinear portion of the curve. As can be seen from Fig. 8, good agreement is achieved between the results of experimental tests (Aziznamini) and that of numerical analyses (Citipitioglu and the current study) both in linear and nonlinear regions. The only exceptions are 8S3 and 8S4 models (there are significant differences between the results in both linear and nonlinear regions) where the results of numerical method are shifted from experimental test results. Since the results of this study and results of citipitioglu are the same, it seems that a problem might exist in the test geometrical size or bolt pretensioning force and thus, the finite element models can be trusted. 4. Behavior of the connections under blast loading The study theory as well as the general procedure of blast simulation analysis of the connections is briefly described in part 2. In part 3, some tested bolted connection specimens are modeled by ANSYS software and the analyses are carried out. The results are compared to that of the experimental test results to ensure the software capability in modeling and analysis of angle connection behavior. Now, the details of the procedure mentioned in part 2 (i.e. calculation of quasi-static pressure on structure, details of the assumed room with angle connections, modeling technique, material properties and etc) will be described in details. 4.1. Determination of experimental/theoretical load To study the behavior of these connections under blast loads, the magnitude of blast load and the application method should be determined. Since this study is carried out to investigate the connections used in structures in Iran and considering the construction procedure in this country, the Iranian code for Protection against classic weapons [36] should be used. This provision is based on TM 5-1300 [37] code and thus, TM 5-1300 code is selected to be used in this study. The procedure presented in TM 5-1300 code for estimation of an explosive charge size provides blast pressure for walls of containment structures or cubicles due to an internal or external explosion. Thus, it is necessary to consider the connection details as part of a hypothetical room within which the explosion occurs. An important point here is the determination of the assumed room characteristics including the application, sizes, dead and live load on

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14S1

14S2 150 125

80 60 40 TEST FE Citipitioglu et al

20

moment(kNm)

moment(kNm)

100

100 75 50

TEST FE Citipitioglu et al

25

0

0 0

5

10

15

20

25

30

0

5

rotation(mrad)

10

80

100

60 40 TEST FE Citipitioglu et al

60 40

TEST FE Citipitioglu et al

5

10

15

20

25

30

0

5

10

15

20

25

30

rotation(mrad)

rotation(mrad) 8S4

14S5

30

100

24

moment(kNm)

moment(kNm)

30

0 0

18 12 TEST FE Citipitioglu et al

6

80 60 40 TEST FE Citipitioglu et al

20 0

0 0

8

16

24

32

40

0

5

rotation(mrad)

10

125

160

moment(kNm)

200

100 75 TEST FE Citipitioglu et al

25

20

25

30

14S8

150

50

15

rotation(mrad)

14S6

moment(kNm)

25

80

20

0

120 80 TEST FE Citipitioglu et al

40 0

0 0

5

10

15

20

25

0

30

5

rotation(mrad)

moment(kNm)

27 18 TEST FE Citipitioglu et al

5

10 15 20 rotation(m rad)

20

25

30

25

44 33 22 TEST FE Citipitioglu et al

11

0 0

15

8S2

55

36

9

10

rotation(mrad)

8S1

45

moment(kNm)

20

14S4 120

moment(kNm)

moment(kNm)

14S3 100

20

15

rotation(mrad)

30

0

0

5

10 15 20 rotation(m rad)

Fig. 8. Comparison between the results of finite element and experimental test.

25

30

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8S3

8S5 50

40

moment(kNm)

moment(kNm)

50

30 20 TEST FE Citipitioglu et al

10

40 30 20 TEST FE Citipitioglu et al

10 0

0 0

5

10

15

20

25

0

30

8

8S6

32 24 16 TEST FE Citipitioglu et al

8

24

32

40

8S7

45

moment(kNm)

moment(kNm)

40

16

rotation(mrad)

rotation(mrad)

36 27 18 TEST FE Citipitioglu et al

9 0

0 0

8

16

24

32

40

0

8

rotation(mrad)

16

32

40

8S9

65

moment(kNm)

40 30 20 TEST

10

24

rotation(mrad)

8S8

50

moment(kNm)

1469

FE

52 39 26 TEST FE Citipitioglu et al

13 0

0 0

5

10

15

20

25

30

0

8

rotation(m rad)

24

32

40

8S10

85

moment(kNm)

16

rotation(mrad)

68 51 34 TEST FE Citipitioglu et al

17 0 0

5

10

15

20

25

30

rotation(mrad) Fig. 8 (continued).

room ceiling and so on. Since the assumed structure is placed in Iran, it is ssumed that the room is a part of a 10-story official building. The values of dead and live loads are 600 kg/m2 and 250 kg/m2 respectively according to the frequent construction method in Iran. The room dimension is 5.5 ⁎ 5.5 ⁎ 5.5 meters. These values are consistent with the size of existing rooms in official buildings in Iran. The size and characteristics of the mentioned room is shown in Fig. 9. To calculate the equivalent pressure on room walls, the following method is used: Firstly, the design methods of TM 5-1300 outlined in Section 5 were used to evaluate the maximum blast load that can be applied to the beam and column members for the structure. Then, the computer

codes SHOCK and FRANG were employed to find the weight of an equivalent TNT charge that will produce these pressures by trial-anderror method. (i.e. an initial value is firstly assumed for TNT weight. This value is entered to SHOCK and FRANGE codes and the pressure curve is calculated. This value is compared with the peak pressure value obtained by the TM 5-1300 code and if it is lower than the provision code value, the TNT charge weight is increased at the next try.) By repeating some trial-and-error steps, the TNT weight that produces the peak pressure equal to the TM 5-1300 code value is calculated to be about 15 lbs of TNT. Having determined the TNT weight, the results of SHOCK and FRANG codes in the form of time–pressure curves are applied as uniform pressure to the side

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Fig. 9. Theoretical room used for the blast study.

walls as the pressure induced by explosion of a 15 lb TNT charge at the geometrical center of the room floor. Since the angle bolted connections used in this study are widely used in steel structures in Iran and the construction methods and materials are different in each country area, different behaviors of the simulated room under blast load are considered. In this way, the results may be generalized for any condition connection. The behavior of room sidewalls under blast pressure may collapse, or reflect. In other words, three cases can be considered for the two sidewalls considered in the model and these three cases are described in Table 2 [38]. It should be noted that the SHOCK and FRANG codes are capable of considering the effect of wall behavior (fracture of wall due to shock wave and reflection of it) on the blast-induced time–pressure curve. In this part, the blast induced pressure is calculated for three cases of different behaviors of side walls. In the following discussions, after determination of blast details at geometrical center of the room, finite element models of this scenario are developed in full details. 4.2. Finite element model of angle connection under blast load 4.2.1. Boundary condition and loading It should be noted firstly that the details including the type of used elements, method of considering the contact effect, modeling of the bolts and bolt holes, friction coefficient etc. are the same as what had been mentioned in part 3–2. As it can be clearly observed from Fig. 9, the room space is divided into four equal sections by the symmetry planes (beam symmetry plane). To this reason and to reduce the calculation size, just onefourth of the room between these two symmetry planes is modeled in

Fig. 10. Boundary condition applied in the model.

the software. In addition to these two planes, another symmetry plane exists at the top of the column (column symmetry plane), since this story is one of the 10 stories of the structure. Thus, the column is continued in the second story and consequently, half of the column in the second story is modeled. Considering the three symmetry planes and the complexity of boundary conditions, the boundary conditions are numbered in Fig. 10 from 1 to 4. Number 1: As it was mentioned, just half of the column at the second floor is modeled. The marked place in the figure is the half modeled column. The nodes in this section are restrained in Y direction. Number 2: This is related to the symmetry line of side wall 1 and just half of the wall is modeled due to the symmetry existence. The nodes in this section are restrained in Z direction. Number 3: This is related to the symmetry line of side wall 2 and just half of the wall is modeled due to the symmetry existence. The nodes in this section are restrained in X direction. Number 4: This is related to three sections including the lower part of side wall 1, lower part of side wall 2 and column base. The nodes in these sections are restrained in all freedom degrees to provide the required boundary condition at the structure base.

Table 2 Numerical blast pressures. Case no

Sidewalls case

1

Two failed

2

One sidewall failed another sidewall reflects

3

Two sidewalls reflect

Member

Sidewalls Floor Sidewalls Floor Sidewalls Floor

Shock pressure

Gas pressure

Peak pressure (Mpa)

Time (ms)

Peak pressure (Mpa)

Time (ms)

1.07 0.2 1.07 0.2 1.07 0.2

1.81 7.19 2.23 9.06 2.65 11.17

0.19 0.19 0.19 0.19 0.19 0.19

29.95 31.08 43.5 44.52 5864.63 5866.79

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In the case of structure loading, as it was mentioned in the previous parts, the results of SHOCK and FRANG codes in the form of time–pressure curves (equivalent to the desired blast loading) are applied to the side walls as a surface load. The connections under the three cases presented in Table 2 are studied under simplified blast loading. It should be noted that according to TM 5-1300, only the peak response from the first cycle of the structure is important for a blast-resistant design. This first response cycle is minimally affected by damping of the system and thus, damping effects are neglected in the theoretical procedure given in TM 5-1300 for evaluating blast load response. Thus, damping is not included in the numerical models. Analyses are carried out over a time duration which would produce one cycle of structural response. Peak displacements and rotations of structural members are subsequently judged based on their response during this first cycle. 4.2.2. Material property High loading rates can influence the mechanical properties of structural materials and the use of dynamic increase factors (DIFs) for describing strain rate enhancement is well known. A DIF is the ratio of strain rate enhanced strength to static strength (e.g., the ratio of the dynamic and static yield stresses for a material). This effect of higher strain rates on the mechanical properties of steel is important for a blast-resistant design. DIFs are used for both design and approximate analyses (e.g., single-degree-of-freedom calculations). Nevertheless, DIFs have to be used with care in advanced numerical simulations. It is well known that the steel yield stress is enhanced by strain rates while the ultimate stress is affected much less. The effects of high rate dynamic loadings on the structural responses were investigated in references [39,40] by employing the recommended DIF values in TM 5-1300 for both the design and the numerical simulation [39,40]. These researches show the validity of the factors proposed by the codes for modeling the behavior of connections under blast loading. Considering the descriptions presented in this paper, dynamic increase factors (DIF) developed by Department of the US Army Corps of Engineers are taken into account for strain-rate effect [15,16]. These coefficients are presented in Table 3. Moreover, the elasto-plastic isotropic model is used for definition of material properties. One of the connections is shown in Fig. 11 in a blast simulation model. 4.3. Evaluation of connection behavior Since one of the purposes of this paper is to evaluate the criteria of TM 5-1300 and compare it with the results of finite element numerical simulation, evaluation based on the procedures mentioned in TM 5-1300 is carried out to be compared with that of ANSYS software. In the following, the results of numerical analyses for the room will be presented. In this way, the results of numerical methods can be compared to that of TM 5-1300 code and its limiting criteria. The responses and failure criteria based on TM 5-1300 criteria are shown in Table 4. Structure response is characterized in terms of the maximum deflection at mid-span,Xm and the corresponding rotational deformation at the member end, i.e. θ. It can be seen that the representative room could withstand the loads from the explosive charge.

Fig. 11. Finite element model of connection in blast loading.

5. Results and discussion Beam response is evaluated based on end rotation, end displacement, Von Mises stress and deformed shape of the connection. The rotations and displacements obtained from the analyses are presented in Table 5 for some of the connections under blast loading. It should be noted that only the results of some models are presented since the result trend is similar for all connections and the other connections have similar results. The predicted global rotations of beams are close to the TM 5-1300 results for the frangible wall case (case 1). However, the beams in the case of reflecting walls (one reflecting wall case 2 or two reflecting walls case 3) are rotated much higher than TM 5-1300 prediction for all connection details, and greater impulse and energy are transferred to the beam and column in the room. All local rotations for all different load cases and connection details exceeded the limit of 2 degrees specified in TM 5-1300. It should be noted that the beams twisted severely horizontally in all connections and the 3 loading cases and clearly exceeded the TM 5-1300 limit criteria. The reason may be that the realistic internal blast pressures radiate outward in three dimensions. These findings indicate that severe damage in the connections comes from the blast radiating in three dimensions as well as the vertically applied pressure. The column rotations indicate that the columns do not significantly affect the connection damage. This is observed for all connections and load cases. A brief review of observed stresses for 8S5 is presented in Table 6. As it can be seen, the maximum stresses are formed in the vertical bolt shafts in bottom angles. This is observed in all connections and all

Table 3 Dynamic increase factors (DIF) for accounting for strain rate effect. Component

DIF for Fy

DIF for Fu

Beam Column Angle Bolt

1.29 1.1 1.29 1.1

1.1 1.05 1.1 1.05

Table 4 Theoretical response to blast loads, based on TM 5-1300. Member Max Deflection. Xm (mm) Rotation, O, (deg) Rotational limit (deg ) Beam Column

47.1 90.84

0.95 1.65

2 2

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Table 5 Rotations and displacements of some of the connections. Response quantity of beam

Vertical

Global Local

Horizontal

Global Local

Displacement (mm) Rotation (deg) Displacement (mm) Rotation (deg) Displacement (mm) Rotation (deg) Displacement (mm) Rotation (deg)

Peak numerical value 8S10

8S7

8S6

8S5

8S2

8S1

240.25 5.4 157.12 17.08 180.3 4.09 109.47 13.44

303.91 6.83 198.75 21.71 228.07 5.17 138.47 17

343.41 7.71 224.58 24.53 257.71 5.84 156.47 19.21

276.28 6.21 180.68 19.74 207.34 4.7 125.89 15.45

357.25 10.31 255.17 25.37 302.75 8.81 198.47 26.45

403.69 11.65 288.34 28.66 342.1 9.95 224.27 29.88

Table 6 A brief review of observed stresses. Component

Stress concentration region

Maximum stress (Mpa)

Dynamic yield stress (Mpa)

Comment

Beam Column Top angle Seat angle Web angle Bolts ( web angle) Bolts (seat angle)

Near seat angle Upper and lower connection point Crossing of the legs Crossing of the legs Crossing of the legs Bolt shank Bolt shank

341.58 138.9 323.13 329.98 327.9 687.62 698.1

357.2 304.59 357.2 357.2 357.2 697.4 697.4

Near local yielding – Near failure Near failure Near failure Failure Failure

loading cases. The maximum stress is 698.1 MPa that is higher than bolt dynamic yield stress (697.4 MPa) and shows that the connection fails from this region. The column response to the blast simulated loads is elastic and the stresses and deformations are not significant. In addition stresses near the dynamic yield stress is observed in bolts of web angle. These stresses are lower than the stresses formed in bolts of seat angle by the value of 1.5% that is caused by high local rotation of connection in the plastic hinge area. It should be noted that in all connection details and all loading cases, the stresses in the angles are close to the yield stress. It should be noted that the results presented in the table below are obtained by investigating the stress distribution history during the analysis, i.e. the analysis is stopped when the first failure occurs in the system. In this way, it is assured that the presented procedure for the occurrence of deformations as well as stresses is similar to the real ones. It means that in real connections similar deformations will occur in the connection component before system failure. The predicted deformed shapes for connection 8S5 are shown in Fig. 12. As it can be seen from the figure, the bottom angles have high deformations. Moreover, web angles have deformed severely and the beam twisted horizontally, but the column has no significant deformation and remained in the elastic range. 5.1. Connection failure modes Considering the definition of Von Mises criteria in the software and deformation and stress distribution in connection components during and after the analysis, the following conclusions can be made about the failure mode of angle connections under equivalent quasi-static: The failure mode is approximately similar for all specimens and yielding firstly occurs at the top and seat angles. Then the web angles slowly yield due to the torsional buckling of the beam and finally, bolt failure (particularly the bolts that connect the seat angle to the column) occurs. Theoretically, the desirable failure mode in angle connections is the formation of two plastic hinges at the top angle (or seat angle depending on the loading direction), as it can be seen from Fig. 13a. The connection will be ductile when the failure of connection occurs due to this mechanism.

Fig. 12. Predicted deformation of the connection 8S5.

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advantageous to incorporate a strength based criterion into the provision that would augment existing serviceability criteria to evaluate steel frame performance under blast loads. Considering the inadequacy of the Iranian code for Protection against classic weapons, that is based on TM 5-1300 it seems that the equation mentioned in the current code should be replaced with the equation of UFC [41] that is a substitution for TM 5-1300. 2. The moment–rotation curves in vertical and horizontal directions shows that under blast condition, the stiffness and strength of connection is higher in vertical direction than in horizontal direction. The connection is weak in horizontal direction and a retrofitting method should be found to improve the behavior of this connection under blast loading. 3. Although the connection failure under blast loading finally begins from the bolt locations, the study of the stress distribution and deformations in the angles show that plastic hinges are formed at vertical and horizontal legs of top and seat angles and even web angles. Comparing this failure mode with the theory failure mode of the connections shows that the behavior of these connections under blast load is accompanied with formation of several hinges before the occurrence of failure. This means that these types of connections have ductile behavior under blast loading. Acknowledgments The authors would like to thank the Y.M.A Engineering Company for their great support which is much appreciated. Fig. 13. Pattern of plastic hinge formation in seat angle, (a) theoretical (b) numerical.

References The results of the current study show that the final failure of these connections were also from the bolt location, the procedure of plastic hinge formation in vertical legs of top and seat angle connections occurred before the failure of the bolts. This can be clearly observed comparing the theoretical formation of plastic hinges in angle that is shown in Fig. 13a with the deformation of seat angle after the analysis that is shown in Fig. 13b. Consequently, the behavior of these connections is ductile under blast loading. 6. Conclusion In this paper the behavior of top and seat bolted angle connections with and without web angle is studied. Firstly, the finite element models are verified using the results of experimental test carried out under static loading. Then the pseudo-static loading that simulates the blast loads are applied to the finite element models and analyses are conducted. The results are presented in the form of connection rotations in vertical and horizontal directions, the displacement of beam end, the deformation of connection components, Von Mises stress and the connection failure modes. Comparing the results of finite element analyses and the Iranian code for Protection against the classic weapons based on TM 5-1300 code, it can be concluded that: 1. Results of finite elements analyses carried out in this study reveal the worth of investigating structural connections by high-resolution finite-element analysis. For example, a semi-rigid connection that is judged to be safe based on Iranian code criteria failed in the finiteelement simulations. Moreover, according to the findings of this research, Iranian code criteria may need revision to reflect findings based on more complex behavior. These conclusions appear to indicate that criteria presented in the provision used to judge the adequacy of a steel frame based purely on rotations of the structural members are not adequate and should be revised. It is observed that high stress localization occurs in the connections due to blast loading that is a main cause of failure. Consequently, it would be

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