Steel Flexible End Plate Connection to AS4100

This calculator designs a flexible end plate connection, performing the critical required checks for the weld, bolts, end plate, supported member (beam) and supporting member (beam or column). A flexible end plate connection is typical of a beam to column flange or web connection that acts as a pin support for the beam.

All calculations are performed in accordance with AS4100-2020.

Design checks for an end plate connection are not explicitly stated in AS4100. The design methods presented below are based on Design Guide 4: Flexible end plate connections published by the Australian Steel Institute (ASI).





Summary Results

Calculation

1. Properties

1.1 Supported Member

1.1.1 Beam section





Beam_section

:410 UB 53.7​







d

:403​







d1

:381​







bf

:178​







tf

:10.9​







twb

:7.6​







r

:11.4​







fyw

:320​













1.1.2 Minimum design actions

Clause 9.1.4 specifies minimum design actions on connections. A flexible end plate connection is considered a "connection to beam in simple construction", and therefore the minimum design shear force is:



$V^*_{min}=\max(0.15\times\phi V_{vm}, 40 \text{kN})$

As per Clause 5.12.3,



$V_{vm}$

is the member shear capacity in the presence of bending moment. For simplicity and conservatism, the calculator assumes



$M^{\ast }\le 0.75\varphi M_s$

so that



$V_{vm}=V_v$

for the calculation of minimum design actions. The member shear capacity



$V_v$

, for minimum design actions on connections, is taken from the "red book". This resource assumes the steel beam is Grade 300.





phi_Vv

:529.0​







$\varphi V_{vm}=\varphi V_v=\varphi \times \{\begin{array}{l}{V}_w=0.6f_y{A}_w\\ V_b={\alpha }_v{V}_w\end{array}$



Cl 5.12.3





Vmin

:79.4 kN​







$V_{min}^{\ast }=\max (0.15\times \varphi V_{vm},40\text{kN})$



Cl 9.1.4





1.2 Supporting Member

1.2.1 Type

The supporting member can either be a beam web; or column web or flange. This will influence the last design check considering the local stability of the supporting member.





For ease, the notation "col" and "column" are used throughout this calculator to describe the supporting member.





Type

:Column web​







1.2.2 Section

The member section and material properties are taken from Liberty GFG's steel products catalogue, assuming steel Grade 300.





Section

:250 UC 89.5​







d_col

:260​







bf_col

:256​







tf_col

:17.3​







tw_col

:10.5​







r_col

:14​







fyc

:320​







fuc

:440​















1.3 End Plate

1.3.1 Geometry

Typical steel end plate thicknesses are taken as per manufacturer availability, for example, Steel Supplies catalogue.

A minimum plate thickness of 10 mm is recommended for flexible end plate connections. This is to reduce distortion of the end plate due to weld shrinkage during cooling.





ti

:10mm​









bi

:150 mm​







$b_i=s_g+2a_{e3}$







di_min

:202 mm​







$d_{i\text{, min}}=0.5d$







di

:210 mm​







$d_i=\max ((n_p-1)s_p+2a_{e1},d_{i\text{, min}})$





1.3.2 Grade

End plates will either be a standard size flat bar (Grade 300) or plate cut to suit (Grade 250).

As per Table 2.1 of AS4100-2020, the plate yield stress



$f_{yi}$

and tensile strength



$f_{ui}$

are automatically calculated depending on the user selected grade. Yield stress varies based on thickness of steel, which has been incorporated in this calculator.





Cleat grade

:300​







fyi

:320​







fui

:440​











1.4 Bolt

1.4.1 Bolt size and category

As per Table 9.2.1, "grades" and "method of tensioning" are descriptions used to classify bolts.

Bolt grades:

1. 4.6 bolts are made from a low carbon steel. The value
   

   $f_{uf}=430MPa$
   .

1. 8.8 bolts are made from a high-strength, heat-treated, medium carbon steel. The value
   

   $f_{uf}=830MPa$
   .
2. 10.9 bolts are higher-grade structural bolts susceptible to brittle failure, that are used in special circumstances where very large forces are transmitted and space is limited. The value
   

   $f_{uf}=1090MPa$
   .

Bolt tensioning specifications:

1. "S" is a snug-tightened bolt
2. "TB" is a fully tensioned bolt using the bearing types
3. "TF" is a fully tensioned bolt using the friction type and should only be used where bolt slip needs to be limited, such as movement-sensitive installations or equipment with vibrations

This calculator assumes the tensioning specifications is "S", as "TB" and "TF" are uneconomic since they provide the same design capacity as 8.8/S but require tensioning, which isn't needed in these connections (though is needed in moment end plate connections).

Note, in Australian, class 8.8/S bolts are most commonly only available in M20 or M24 bolt diameters.





Bolt_size

:M20​







Bolt category

:8.8​









1.4.2 Bolt shear capacity

As per Cl 9.2.2.1, the shear capacity of a bolt



$\varphi V_f$

is given by:



$\phi V_f=\phi \space 0.62 \space k_{rd} \space k_rf_{uf}(n_nA_c+n_xA_o)$

Where:

1. 
   

   $\varphi$
   is the capacity reduction factor and is always 0.8, as per Table 3.4 of AS4100

1. 
   

   $k_{rd}$
   is the ductility reduction factor for grade 10.9 threaded bolts

1. 
   

   $k_r$
   is the reduction factor for bolted splice connections
2. 
   

   $f_{uf}$
   is the minimum tensile strength of the bolt
3. 
   

   $A_c$
   is the core area (at the root of the threads)

1. 
   

   $A_o$
   is the shank area of the bolt

1. 
   

   $n_n$
   is the # of shear planes in the threaded regions
2. 
   

   $n_x$
   is the # of shear planes in the unthreaded region

A bolt will either be classed with "threads included" which is standard practice, or "threads excluded" which is non-standard practice. Therefore the



$n_n{A}_c$

or



$n_x{A}_o$

will become zero in the equation above, respectively.

It is common for textbooks to tabulate bolt capacities per bolt size, for example Australian Guidebook for Structural Engineers which is used in this calculator.





Threads?

:Threaded​









phi_Vf

:92.6​







$\varphi V_f=\varphi 0.62k_r{f}_{uf}(n_n{A}_c+n_x{A}_o)$



Cl 9.2.2.1



1.4.4 Bolt geometry

ASI Guide 4 recommends the horizontal bolt spacing



$s_g$

range to be:



$9t_i\leq s_g \leq 14t_i$

ASI Guide 4 does not recommend minimum and maximum spacings for the vertical bolt spacing



$s_p$

, so this calculator adopts what is in AS4100-2020. The code specifies minimum



$s_{\text{p, min}}$

(Clause 9.5.1) and maximum



$s_{\text{p, max}}$

(Clause 9.5.3) bolt spacings. In summary, where



$d_f$

is the bolt diameter:



$s_\text{p, min} = 2.5 d_f$

In non-corrosive environments, where



$t_f$

is the thickness of the thinner ply connected:



$s_\text{p, max} = \min(32 t_f, 300 \text{ mm})$

In corrosive environments:



$s_\text{p, max} = \min(15 t_f, 200 \text{ mm})$

For minimum bolt edge distance, ASI Guide 4 takes what is provided in Table 9.5.2 AS4100-2020, which is



$a_{e\text{, min}}=1.5d_f$

.



Table 9.5.2 AS4100-2020





np

:3​







sg

:90 mm​







sp

:70 mm​







ae1

:35 mm​







ae3

:30 mm​







a

:120 mm​





Adapted from Figure 12 of ASI Design Guide 4









Horizontal spacing check

:9ti ≤ sg ≤ 14ti 🟢​







$9t_i\le s_g\le 14t_i$







sp_min

:50 mm​







$s_{\text{p, min}}=2.5d_f$



Cl 9.5.1





Corrosive_environment

:N​







sp_max

:200 mm​







$s_{\text{p, max}}=\{\begin{array}{ll}\min (32t_f,300\text{ mm}& \text{in non-corrosive environments}\\ \min (15t_f,200\text{ mm})& \text{in corrosive environments}\end{array}$



Cl 9.5.3





Vertical spacing check

:sp,min ≤ sp ≤ sp,max 🟢​







$s_{\text{p, min}}\le s_p\le s_{\text{p, max}}$







ae_min

:30 mm​







$a_{e\text{, min}}=1.5d_f$



Table 9.5.2





Edge check

:ae ≥ ae_min 🟢​







$a_e\ge a_{\text{e, min}}$







1.5 Weld

The supported member (beam) web is welded to the end plate on both sides of the web.

1.5.1 Fillet weld size

As per Cl 9.6.3.1, a fillet weld is approximately triangular in section and its size is specified by the leg length,



$t_w$

but it's strength is governed by the throat thickness,



$t_t$

. For an equal leg fillet weld,



$t_t=\frac{t_w}{\sqrt{2}}$

which is assumed in this calculator.

For economy, the fillet welds for a flexible end plate connection should be sized to be a single pass weld, which generally means 6mm or 8mm fillet welds.

The minimum weld size is provided in Table 9.6.3.2 based on the thickness of the end plate or the supported member's web, whichever is more.



Exert from Figure 9.6.3.1 of AS4100-2020



Table 9.6.3.2 AS 4100-2020





tw

:6mm​







tw_min

:4 mm​







Weld thickness check

:tw ≥ tw,min 🟢​











1.5.2 Weld category

Weld groups are categorised as either General Purpose (GP) or Special Purpose (SP). GP welds are typically used for static loaded or lower-stressed members and SP welds are selected for dynamic-loaded or higher-stressed members.

The weld category affects the capacity reduction factor:

1. 
   

   $\varphi =0.6$
   for GP
2. 
   

   $\varphi =0.8$
   for SP

For end plate connections, weld category SP is normally used.





Weld category

:SP​









Φ,w

:0.8​







${\varphi }_w=\{\begin{array}{ll}0.6& \text{for GP}\\ 0.8& \text{for SP}\end{array}$



Table 3.4



1.5.3 Weld electrode type

The electrode type defines the nominal tensile strength of the weld metal,



$f_{uw}$

. The options of electrode types are:

1. 43 = E43XX

1. 49 = E49XX
2. 55 = E55XX

The



$f_{uw}$

is simply the electrode type number x 10, for example, E43 has



$f_{uw}$

= 430MPa. See Table 9.6.3.10(A) of AS4100:2020 for all nominal strength of weld metal based on the weld electrode type.





Electrode_type

:49​







fuw

:490.0​







1.5.4 Weld capacity

Regardless of the direction of loading of a fillet weld, its strength depends on the cross sectional area of the throat, which will generally be in shear. Adapted from Cl 9.6.3.10 of AS4100, the capacity of each weld line,



$\varphi v_w(N/mm)$

is given by:



$\phi v_w = \phi \times 0.6 \times t_t \times f_{uw}$





t_t

:4.242640687119271​







$t_t=\frac{t_w}{\sqrt{2}}$







phi_vw

:997.8690896104525​







$\varphi v_w=\varphi \times 0.6\times t_t\times f_{uw}$



Cl 9.6.3.10









2. Design Actions





3. Design Checks

3. Design Checks

3.6 Supported Member Rotation Check

As per Section 10.8 of Design Guide 4, the touching of the beam lower flange against the support can be avoided by restricting the distance between the lower edge of the end plate and the lower flange



$a_c$

. The limit on



$a_c$

is because the centre of rotation of the connection has been found to be very close to the bottom of the end plate.

In order that the supported member (beam) does not rotate so that it touches the supporting member:



$\theta_b \leq t_i/a_c$





To determine the beam rotation



${\theta }_b$

at the end of a simply supported beam, we can assume a UDL and derive two equations:



$\theta_b =\dfrac{wL^3}{24EI} \hspace{1cm} \Delta=\dfrac{5wL^4}{384EI}$

Where



$\Delta$

is the mid-span deflection.







We can combine the two equations to determine the end rotation of a beam



${\theta }_b$

with respect to the mid-span deflection



$\Delta$

, which can be simplified to:



$\theta_b = \dfrac{16 \Delta}{5L}$

This calculator allows you to enter the length of the beam



$L$

and the mid-span deflection



$\Delta$

in order to calculate



${\theta }_b$

. Otherwise you can use your calculated value of



${\theta }_b$

and compare it to



${\theta }_{b\text{, limit}}=t_i/a_c$

.