Behaviour of high-strength bolts at elevated temperatures

EUROSTEEL 2017, September 13–15, 2017, Copenhagen, Denmark

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

Behaviour of high-strength bolts at elevated temperatures under double-shear loading

Mina Seif *,a, Jonathan Weigand a, Rafaela Peixoto b, Luiz Vieira b a National Institute of Standards and Technology (NIST), MD, USA

[email protected], [email protected] b University of Campinas, Campinas, Brazil

[email protected], [email protected]

ABSTRACT During fire events, connections in steel structures may be subjected to large unanticipated deformations and loads. These fire effects can produce failures of connections, including local buckling of the connection zone, rupture of connection plates, shear rupture of bolts, and bolt tear-out rupture of beam webs. Thus, a key issue in evaluating the response of structural systems to fire effects is the proper representation of material behaviour, including fracture, at elevated temperatures. Temperature-dependent material behaviour of structural steel plates has been studied by many researchers, both experimentally and numerically. However, the behaviour of structural steel bolts at elevated temperatures, especially under shear loading, is not well established in the literature. This paper presents results from recently conducted tests of high-strength structural bolts subject to double shear loading at elevated temperatures. The parameters varied between tests included the bolt grade, bolt diameter, and temperature. Bolt grades A325 and A490 were tested. For each bolt grade, three different diameters were tested (19 mm, 22 mm, 25 mm) at five different temperatures (20 ºC, 200 ºC, 400 ºC, 500 ºC, and 600 ºC). Three tests were conducted for each combination of parameters. Degradation in the mechanical and material properties were characterized. In addition, a new component-based model for high-strength bolts was developed based on the experimental data. The component-based model is shown to accurately account for the temperature-dependent degradation of bolt shear strength and stiffness, while also providing the capability to model load reversal. Keywords: elevated-temperature; high-strength bolts; shear loading, structural fire effects

1 INTRODUCTION Structurally significant fires can subject steel framing and connections to loading scenarios that are largely unanticipated in current design specifications. Interactions between heated structural framing and the surrounding cooler structure can result in large compressive forces during heating followed by large tensile forces during cooling, potentially resulting in failures in the steel connections. Seif et al. [1, 2] examine the various failure modes that can occur in typical shear and moment connections at elevated temperatures, including fracture of connection plates, shear rupture of bolts, and bolt tear-out failure of beam web or connection plates, using explicit high-fidelity finite element analysis. The likelihood for connection failures to occur depends not only on the loads that can be sustained by the various components that comprise the connections, but also on their deformation capacities, since surviving until burnout requires the connections to accommodate both the forces and deformations induced by restraint of thermal expansion and contraction. Consequently, evaluating the performance of connections subjected to demands from both the fire-induced thermal loading and the restraint supplied by interaction with the surrounding structure, motivates a need for improved models. Proper representation of the components of steel connections, at elevated temperatures, is a key issue in evaluating the response of buildings to fire effects; and while temperature-dependent behaviours of structural plate materials (such as ASTM A36 [3], ASTM A572 [4], and ASTM A992 [5]), have been studied both experimentally and numerically [6-8], the behaviour of high-strength structural bolt material grades at elevated temperatures is not as well-characterized in the literature. Kodur et al. [9] studied the influence of elevated temperatures on the thermal and mechanical properties of high-


strength bolts, however only one bolt diameter was considered. Yu [10] investigated the effects of elevated temperatures on bolted connections, and his work did include a small set of experiments on bolts under shear loading. However, the experiments by Yu had large bearing deformations in the reaction plates imbedded in the results, creating difficulties when attempting to isolate the bolt shear load-deformation response. The current shortage of experimental data, especially for isolated bolts subjected to shear loading, has made proper characterization of the temperature-dependent behaviour of bolts challenging. A more comprehensive set of experimental data was needed to provide a more complete understanding of the behaviour of high-strength bolts under shear loading at elevated temperatures. The following sections describe the details of an experimental study on shear behaviour in high-strength bolts at elevated temperature, as well as a summary of a new component-based model for high-strength bolts developed based on the experimental data. The component-based model is shown to accurately account for the temperature-dependent degradation of bolt double-shear strength and stiffness. Such component-based models are computationally efficient, facilitating large building-level analyses where high-fidelity modelling of the bolts would be infeasible.

2 TEST PARAMETERS AND SETUP This section describes the full testing procedure of the high-strength structural bolts at elevated temperatures under double-shear loading. The parameters varied between tests included the bolt grade, bolt diameter, and temperature. Bolt grades ASTM A325 [11], with a specified nominal yield strength of 635 MPa (92 ksi) and specified nominal ultimate tensile strength of 825 MPa (120 ksi), and ASTM A490 [12], with a specified nominal yield strength of 895 MPa (130 ksi) and specified nominal ultimate tensile strength of 1035 MPa (150 ksi), were tested. Three different diameters (19 mm (3/4 in), 22 mm (7/8 in), and 25.4 mm (1 in)) were tested for each bolt grade at five different temperatures: 20 ºC, 200 ºC, 400 ºC, 500 ºC, and 600 ºC. At least three replicate tests were conducted for each combination of bolt material grade, diameter, and temperature. The bolt specimens were tested using specially manufactured testing blocks. The testing blocks were designed to be substantially stronger and stiffer than the bolt specimens, so that they could be used for multiple tests. Two separate sets of testing blocks were manufactured: one set for the 19 mm (3/4 in) and 22 mm (7/8 in) diameter bolts, and one set for the 25 mm (1 in) diameter bolts. The set for the smaller diameter bolts was manufactured using ASTM A36 [3] steel, with a specified nominal yield strength of 250 MPa (36 ksi) and a nominal ultimate tensile strength of 400 MPa (58 ksi), while the other set was manufactured using heat-treated AISI/SAE 8640 alloy steel, with a specified nominal yield strength of 560 MPa (81 ksi) and a specified nominal ultimate tensile strength of 750 MPa (109 ksi)). The configuration of the test setup, including dimensions for the reaction blocks are shown in Fig. 1. The temperature for each test was achieved by placing the entire test setup in an electric furnace, which was capable of achieving a temperature of 1200 ºC. A rate of temperature loading of 20 ºC/min was used for all tests. One thermocouple type K was placed inside the furnace to control the furnace temperature and three thermocouples type K were placed on the bolt specimens (touching the bolt surface) to ensure that the target temperature had been achieved in the bolt at the initiation of the shear loading. As stated by the thermocouple manufacturer, the precision of the measured temperature at 0 ºC is of 2.2 ºC. The shear loading on the bolt specimen was applied using a universal testing machine, which had a capacity of 980.7 kN and an uncertainty of measurement at 10kN of ± 0.1 kN, at a level of confidence of 95 %. Compression loading was applied at a rate of approximately 60 kN/min (13.49 kip/min) throughout the entire test. The loading was continued until the bolt ruptured in double-shear. The displacement of the universal testing machine was monitored using an external linear variable displacement transducer (LVDT), which had a range of 100 mm (3.94 in) and a precision of 1/1000 mm. The uncertainty in the displacement measurement was less than 0.1 %. Double-shear was achieved by applying the load through the middle block, shearing the bolt through two shear-planes. Temperature, forces, and displacements were monitored throughout the tests. For


all tested bolt specimens, both shear planes passed through the unthreaded portion of the bolt, so that the thread did not influence the bolt-shear response. Each test was assigned a unique name. The nomenclature included the bolt, diameter, type, test temperature, and specimen number. For example, for test “25A325T20-1”; the first two digits correspond to the bolt diameter (25 mm (1 in)), the next four characters correspond to the bolt type (A325), followed by the letter T and the temperature at which that bolt was tested (T20= 20 ºC (Ambient Temperature)), and lastly, the test-number for the specimen. A sample of the results is presented in the following section.

Fig. 1. Test blocks setup: (a) 3D view; (b) furnace enclosure; and (c) dimensions (in mm)

3 EXPERIMENTAL RESULTS This section presents a subset of the experimental results from the bolts tested under double-shear loading at elevated temperatures. Fig. 2(a) and Fig. 2(b) show the load-displacement responses of the 25 mm (1 in) diameter A325 and A490 bolts, respectively. Each plot contains results from fifteen individual tests, with three replicate tests at each of the five different temperature-levels. This paper only includes results from the 25 mm (1 in) diameter bolts. Results for the 19 mm (3/4 in) and 22 mm (7/8 in) diameter bolts are available in [13]. In general, higher temperatures led to decreased double-shear strengths and increased shear deformations at failure. At 200 ºC, the grade A325 bolts retained an average of 96.4 % (±1.3 %) of their double-shear strength, relative to their double-shear strength at ambient temperature, while at 400 ºC, and 500 ºC, and 600 ºC the grade A325 bolts retained averages of 78.9 % (±1.4 %), 56.6 % (±0.9 %), and 33.1 % (±1.0 %) of their double-shear strength, respectively. The grade A490 bolts had a 12.9 % (±0.6 %) larger average double-shear capacity at ambient temperature than did the grade A325 bolts. The grade A490 bolts exhibited similar levels of degradation at elevated temperatures as did the grade A325 bolts, retaining 98.5 % (±0.3 %), 81.3 % (±1.2 %), 59.8 % (±0.1 %), and 38.6 % (±2.7 %) of their double-shear strength at temperatures of 200 ºC, 400 ºC, 500 ºC, and 600 ºC. For the grade A325 bolts, increases in the shear deformation at failure were negligible at 200 ºC, but increased by 43 % at 400 ºC, 20 % at 500 ºC, and 76 % at 600 ºC, relative to the tests at ambient temperature. Deformation capacities for the grade A490 bolts followed similar trends, with increases in the shear deformation at failure of 44 %, 43 %, and 250 % at temperatures of 400 ºC, 500 ºC, and 600 ºC, respectively.

(a) (b) (c)


(a)

(b)

Fig. 2. Load-displacement curves for (a) 25 mm (1 in) diameter A325 bolts and (b) 25 mm (1 in) diameter A490 bolts.


4 DISCUSSION 4.1 Shear Strength The bolt double-shear strength is proportional to the cross-sectional area of the bolt shaft. The ratio between the areas of a 25 mm (1 in) diameter bolts and a 19 mm (3/4 in) diameter bolts is 1.73, while the ratio between the areas of the 22 mm (7/8 in) diameter bolt and the 19 mm (3/4 in) diameter bolts is 1.34. Fig. 3(a) shows the double-shear strength for each of the grade A325 bolts, with dashed lines plotted through the average value at each temperature (for each diameter). Fig. 3(b) shows a similar summary plot for the grade A490 bolts. At each temperature, and for both bolt grades, the ratio between the double-shear capacities for bolts with different diameters was similar to the ratio between their bolt cross-sectional areas, indicating that, beyond the differences in cross-sectional area, the geometry of the bolts had little to no influence on the bolt double-shear capacities. Figs. 3(a) and 3(b) also show that, for all diameters and for both material grades, the reductions in double-shear strength were relatively minor at 200 ºC, but were substantially more significant at temperatures of 400 ºC, 500 ºC, and 600 ºC. Between temperatures of 400 ºC and 600 ºC the degradation in double-shear strength was nearly linear with increasing temperature.

(a) (b)

Fig. 3. Failure load versus temperature for: (a) A325 bolts, (b) A490 bolts

4.2 Eurocode In this section, the retained double-shear strength in the tests is compared to the design reduction factors specified in the Eurocode [14] at different elevated temperatures. According to the Eurocode [14], the fire design resistance of bolts loaded in shear should be determined from:

𝐹𝐹𝑣𝑣,𝑡𝑡,𝑅𝑅𝑅𝑅 = 𝐹𝐹𝑣𝑣,𝑅𝑅𝑅𝑅 𝑘𝑘𝑏𝑏,𝜃𝜃𝛾𝛾𝑀𝑀2𝛾𝛾𝑀𝑀,𝑓𝑓𝑓𝑓

(1)

where 𝑘𝑘𝑏𝑏,𝜃𝜃 is the reduction factor determined at the appropriate temperature (Table D.1 of [14]),

𝐹𝐹𝑣𝑣,𝑅𝑅𝑅𝑅 is the design shear resistance of the bolt per shear plane (Table 3.4 of [14]),

𝛾𝛾𝑀𝑀2 is the partial factor at normal temperature, and

𝛾𝛾𝑀𝑀,𝑓𝑓𝑓𝑓 is the partial factor for fire conditions.

Fig. 4 and Table 1 show a comparison between the retained double-shear strength for all bolt diameters and for both bolt materials grades and the design reduction factors specified in the


Eurocode. The retention factors were relatively consistent across all three bolt diameters and for both bolt material grades. For temperatures up to 500 ºC, the Eurocode reduction factors were 5 % to 10 % more conservative than the bolt data. At 600 ºC, the Eurocode was roughly 40 % more conservative than the bolt data.

(a) (b)

Fig. 4. Reduction factor versus Temperature from experimental data and Eurocode: (a) A325 bolts, and (b) A490 bolts

Table 1. Reduction factor from Eurocode, A325 and A490 bolts

Reduction Factor

Temperature (ºC) Eurocode 19A325 19A490 22A325 22A490 25A325 25A325

20 1.000 1.000 1.000 1.000 1.000 1.000 1.000 200 0.935 1.028 0.978 0.960 0.948 0.964 0.985 400 0.775 0.826 0.848 0.845 0.807 0.789 0.813 500 0.550 0.588 0.620 0.583 0.620 0.566 0.598 600 0.220 0.336 0.384 0.334 0.373 0.331 0.386

5 COMPONENT-BASED MODELING Phenomenological component-based models provide a practical means for modelling shear behaviour in bolts at elevated temperatures, while also providing considerable advantages in computational efficiency over high-fidelity finite element models. In component-based models, the component is represented by a discrete nonlinear spring with fully prescribed force-deformation behaviours. Here, the component-based model for high-strength bolts in single-shear from [15], which uses the nonlinear four-parameter “Richard Equation” [16, 17], is extended to include multiple shear planes (i.e., two for double-shear behaviour) and temperature-dependent degradation in stiffness and strength. The bolt double-shear load-deformation response can be written as:

𝑅𝑅(∆,𝑇𝑇) = 𝑅𝑅𝑢𝑢𝑢𝑢𝑢𝑢 + (𝑘𝑘𝑓𝑓(𝑇𝑇)−𝑘𝑘𝑓𝑓(𝑇𝑇))(∆−∆𝑢𝑢𝑢𝑢𝑢𝑢)

�1+��𝑘𝑘𝑓𝑓(𝑇𝑇)−𝑘𝑘𝑝𝑝(𝑇𝑇)��∆−∆𝑢𝑢𝑢𝑢𝑢𝑢�

𝑅𝑅𝑢𝑢,𝑐𝑐𝑐𝑐𝑐𝑐(𝑇𝑇) �𝑢𝑢(𝑇𝑇)

�

� 1𝑢𝑢(𝑇𝑇)�

+ 𝑘𝑘𝑝𝑝(𝑇𝑇)(∆ − ∆𝑢𝑢𝑢𝑢𝑢𝑢) (2)


where Δ is the bolt shear-deformation, )(Tki and )(Tk p are the temperature-dependent elastic and plastic stiffnesses of the bolt

double-shear load-deformation response, ( )unlunl R,∆ are the coordinates of the last unload point,

cycnR , is the cyclic reference load, n is a shape parameter controlling the sharpness of the transition from the

elastic stiffness to the plastic stiffness, and )(T denotes dependence on temperature.

The cyclic reference load ( ) ( ) upvcycn TkTRTR δ−≈)(, during the initial cycle of loading and ( ) ( ) ( ) unlpunlvunlcycn TkRTRsignTR ∆+−∆−∆=)(, during the subsequent unload/reload cycles, where

( ) ( )TFAnTR ubspv 6.0= is the temperature-dependent double-shear capacity of the bolt, uδ is the deformation capacity of the bolt, 2=spn is the number of shear planes through the bolt, bA is the

bolt cross-sectional area, and uF is the ultimate tensile strength of the bolt material at elevated-temperature T . Best-fit values for parameters )(Tki , )(Tk p , )(TRn , and )(Tn from Eq. (2) were calculated directly from each bolt double-shear load-deformation data. The initial stiffness was calculated using least-squares linear regression of data within 95 % of the peak stiffness. The plastic stiffness was calculated based on least-squares linear regression of the last three points on the bolt double-shear load deformation curves at the bolts’ maximum plastic deformations, with the reference load corresponding to the projection of the plastic stiffness at a deformation of zero. The shape parameter was determined by using an iterative procedure to minimize the residual between Eq. (2) (using the already fitted values for )(Tki , )(Tk p , )(TRn ), and the load-deformation data from each individual bolt test. Fig. 5 shows a comparison between Eq. (2), with the fitted curve parameters, and the experimental data. Fig. 5 shows that the fitted curves match the experimental data within 3 % for all bolt tests.

(a)

(b)

Fig. 5. Comparison of Eq. (2) with fitted curves parameter to experimental double-shear load-deformation data from each bolt test; (a) A325 bolts, and (b) A490 bolts.

To develop an approach to predict the behaviour of the double-shear load-deformation response over all temperatures, the bolt-shear component-based model from [14] was used to transform the reference load and initial stiffness data from the 25 mm (1 in) diameter bolts into ultimate tensile


strengths and moduli of elasticity, respectively, of the bolt steel (Fig. 6). Power-law and cubic equations were fitted to the data for both bolt materials for the ultimate tensile strength and modulus of elasticity, respectively, providing the capability to model degradation in the bolt double-shear response in terms of the characteristic degradation behaviour of the bolt steel mechanical properties. Significantly more scatter was observed in the fitted parameters for the plastic stiffness and the shape parameter, and thus those parameters were fitted using multi-linear segments passing through their averages at each test-temperature. A complete description of the overall modelling approach, and extension of this approach to the 19 mm (3/4 in) and 22 mm (7/8 in) diameter bolts from [13] can be found in [18]. Fig. 7 shows a comparison of the component-based model, with parameters fitted as described in the previous paragraph, and the experimental data for the 25 mm (1 in) diameter bolts. In comparison to the data from the 25 mm (1 in) diameter bolt tests, the accuracy of the model is within the experimental uncertainty measured between replicated tests.

(a) (b)

Fig. 6. Fitted relationships for temperature-dependent (a) ultimate tensile strength of bolt material and (b) modulus of elasticity of bolt material.

(a) (b)

Fig. 7. Comparison of component-based model and the experimental data for the 25 mm (1 in) diameter bolts from [13].


6 SUMMARY AND CONCLUSIONS This paper presented a subset of the results from recently conducted tests on high-strength bolts subject to double-shear loading at elevated temperatures. Several parameters were varied between the tests, including the bolt grade, bolt diameter, and temperature. Bolt grades A325 and A490 were tested. For each bolt grade, three different diameters were tested (19 mm (3/4 in), 22 mm (7/8 in), and 25.4 mm (1 in)) at five different temperatures (20 ºC, 200 ºC, 400 ºC, 500 ºC, and 600 ºC). At least three tests were conducted for each combination of parameters. Degradations in both the stiffness and strength of the bolts were characterized. Results from these experiments help to fill a critical knowledge gap in the literature on the behavior of high-strength structural bolts under shear loading at elevated temperatures. Results from the tests showed that at temperatures below 200 ºC, the bolts had little degradation in double-shear strength when compared to their double-shear strength at ambient temperature; however, their deformations at failure were larger. In excess of 200 ºC, the double-shear strength of the bolts decreased more significantly. At 400 ºC, 500 ºC, and 600 ºC, the bolts retained roughly 82 %, 60 %, and 35 % of their ambient-temperature double-shear strength, respectively. This paper also presented a newly developed component-based model for the high-strength bolts at elevated temperatures, developed based on the experimental data. Nonlinear curves fitted to the experimental data for the ultimate tensile strength and modulus of elasticity, respectively, provided the capability to model degradation in the bolt double-shear response in terms of the degradation in the bolt steel mechanical properties. The component-based model was shown to accurately account for the temperature-dependent degradation of bolt double-shear strength and stiffness.

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Behaviour of high-strength bolts at elevated temperatures