Columns Subjected to Tensile Stress in RF-/JOINTS Steel - Column Base

Technical Article

The product range of Dlubal Software contains various modules for design of steel and timber connections. The RF-/JOINTS Steel - Column Base add-on module allows you to analyse footings of hinged or restrained steel column bases. For the cost-effective and safe design of the column base, the fastener selection, foundation geometry, and material quality are crucial.

This article presents designs of a rigid column applied to the tension area of the connection. The model is based on an example in the reference literature [1].

System

The column comprises of the cross-section HEB 280 and structural steel S 235 JR.

Figure 01 - System and Loading According to [1]

In Window 1.4 of RF-/JOINTS, the dimensions of the foundation are specified as 140 ∙ 120 ∙ 80 cm. The class of concrete is C20/25.

Parameters of the base plate are defined in Window 1.5 as illustrated in Figure 02.

Figure 02 - Window '1.5 Base Plate and Welds' in RF-/JOINTS

In Window 1.6, the dimensions and positions of the anchors are defined (see Figure 03).

Figure 03 - Window '1.6 Anchors' in RF-/JOINTS

Internal Forces

RF-/JOINTS allows you to define internal forces manually and thus independently of the RFEM/RSTAB model.

The following design internal forces are specified in Window 1.3:

NEd = -396.0 kN
VEd = 21.5 kN
MEd = -110.0 kN

Anchor Forces

In order to determine the design-relevant internal forces, the following case distinctions are necessary:

Figure 04 - Case Distinction According to [1]

For the connection design in the tension area, the 'Case F1 < 0 and F2 ≥ 0' should be applied as governing.

$${\mathrm F}_1\;=\;\frac{{\mathrm N}_\mathrm{Ed}}2\;-\;\frac{{\mathrm M}_{\mathrm y,\mathrm{Ed}}}{2\;\cdot\;{\mathrm a}_\mathrm D}\;=\;\frac{396}2\;-\;\frac{11,000}{2\;\cdot\;13.1}\;=\;-221.84\;\mathrm{kN}$$

$${\mathrm Z}_1\;=\;\frac{-2\;\cdot\;{\mathrm F}_1}{1\;+\;\frac{{\mathrm a}_\mathrm Z}{{\mathrm a}_\mathrm D}}\;=\;\frac{-2\;\cdot\;-221.84}{1\;+\;\frac{24.0}{13.1}}\;=\;156.7\;\mathrm{kN}$$

The following part of the article presents designs of the connection in the tension area with regard to the anchor and the concrete.

Tensile Stress of Anchor

Using the anchor M30 (strength 5.6, AS = 5.61 cm²), the design is performed according to [2], Table 3.4, as follows:

$${\mathrm F}_{\mathrm t,\mathrm{Rd}}\;=\;\frac{{\mathrm k}_2\;\cdot\;{\mathrm f}_\mathrm{ub}\;\cdot\;{\mathrm A}_\mathrm S}{{\mathrm\gamma}_{\mathrm M2}}\;=\;\frac{0.9\;\cdot\;50.0\;\cdot\;5.61}{1.25}\;=\;201.96\;\mathrm{kN}$$

Figure 05 - Window '3.1 Design - Summary' Including Details of Anchor in Tension

Anchor Pull Out

The resistance to pulling out the anchor is determined according to [4], Section 15.1.2.3, as follows:

$${\mathrm F}_{\mathrm t,\mathrm{bond},\mathrm{Rd}}\;=\;11\;\cdot\;{\mathrm f}_\mathrm{ck}\;\cdot\;\frac{{\mathrm d}_\mathrm h\;\cdot\;{\mathrm l}_\mathrm h\;-\;\frac{\mathrm\pi\;\cdot\;\mathrm d^2}4}{{\mathrm\gamma}_\mathrm{Mc}}\;=\;11\;\cdot\;20.0\;\cdot\;\frac{80\;\cdot\;80\;-\;\frac{\mathrm\pi\;\cdot\;30^2}4}{1.50}\;=\;834.99\;\mathrm{kN}$$

Figure 06 - Window '3.1 Design - Summary' Including Details of Anchor Pull Out

Concrete Cone Failure

In the case of the concrete cone failure, a conical break arises from the end of the anchorage element. The concrete cone failure design is performed according to [4], Section 9.2.4.

$${\mathrm F}_{\mathrm t,\mathrm{cone},\mathrm{Rd}}\;=\;\frac{{\mathrm N}_{\mathrm{Rk},\mathrm c}}{{\mathrm\gamma}_\mathrm{Mc}\;\cdot\;{\mathrm\gamma}_{{\mathrm M}_2}}\;=\;\frac{290.09}{1.5\;\cdot\;1.2}\;=\;161.16\;\mathrm{kN}$$

Figure 07 - Window '3.1 Design - Summary' Including Details of Concrete Cone Failure

Splitting Failure

Splitting forces cause splitting cracks in the concrete. They occur as radially circumferential around the anchors and thus perpendicular to the tensile force. The splitting failure is also analysed according to [4], Section 9.2.4.

$${\mathrm F}_{\mathrm t,\mathrm{sp},\mathrm{Rd}}\;=\;\frac{{\mathrm N}_{\mathrm{Rk},\mathrm{sp}}}{{\mathrm\gamma}_\mathrm{Mc}\;\cdot\;{\mathrm\gamma}_{{\mathrm M}_2}}\;=\;\frac{278.05}{1.5\;\cdot\;1.2}\;=\;154.47\;\mathrm{kN}$$

Figure 08 - Window '3.1 Design - Summary' Including Details of Splitting Failure

The tension force resistance of the concrete is slightly exceeded. In this case, the splitting failure is governing for the design in the tension areas of the connection.

The analysis for the tension area is completed in the program by designing the tension force introduction. However, this is not further described in this article. Furthermore, it is necessary to design the connection parts in the compression area, the bending resistance of the connection, the shear resistance, and the welds.

Summary

RF-/JOINTS Steel - Column Base designs footings of hinged and restrained column bases. In the case of a column with a base plate subjected to tensile stress, it is necessary to consider the tensile stresses, which arise in the concrete due to the load introduction on the fastener. The tension resistance of the concrete is often governing for the loads that can be transferred by the joint.

Reference

[1]  Kahlmeyer, E., Hebestreit, K., & Vogt, W. (2012). Stahlbau nach EC 3 (6th ed.). Cologne: Werner.
[2]  Eurocode 3: Design of steel structures - Part 1-8: Design of joints; EN 1993-1-8:2005 + AC:2009
[3]  Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings; EN 1992-1-1:2004 + AC:2010
[4]  Comité euro-international du béton (CEB): Design of Fastenings in Concrete Design Guide. (1997). London: ICE Publishing.
[5]  Manual RF-/JOINTS. (2015). Tiefenbach: Dlubal Software. Download.

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