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Steel Flexible End Plate Connection to AS4100's banner

Steel Flexible End Plate Connection to AS4100

Verified by the CalcTree engineering team on October 16, 2024

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

Summary 
Design Check
Capacity
Utilisation
Status
Weld
Va = 718.5 kN
0.11
🟢
Bolt
Vb = 171.6 kN
0.46
🟢
End plate
min(Vc, Vd) = 2268.0 kN
0.03
🟢
Supported member web
Ve = 472.8 kN
0.17
🟢
Supported member shear
Vf = 529.3 kN
0.15
🟢
Supported member rotation
θb = 19.2 millimeter / meter kN
12.34 millimeter / meter
🟢
Supporting member
min(Vg, Vh) = 815.1 kN
0.10
🟢
Can’t display the image because of an internal error. Our team is looking at the issue.


Calculation

Technical notes

Assumptions:
  1. Flexible end plate connection is considered a "flexible connection", where no moment is assumed to develop at the supported member (beam) end and is able to rotate.
  2. The recommended design model in Design Guide 4 treats the end plate as an extension of the supported beam web, with no bending assumed in either the bolts, the weld, or the plate.
  1. Regarding Cl 9.1.4, flexible end plate connections fall under "connections to beam in simple construction" for the minimum design actions on connections. For simplicity, this calculator assumes
    
    on the supported member (beam) so that
    
    for the calculation of minimum design actions on connections.
    
    decreases
    
    from
    
    to
    
    , therefore the assumption is conservative.
  1. Section size of the supported member (beam) and supporting member are to be chosen by the user from a catalogue of available sections in Australia.
  1. Supported member (beam) grade is 300, so that
    
    and the
    
    from capacity tables taken from the "red book" are valid.
  1. Supporting member (column or beam) grade is 300.
  2. End plate may be either cut from plate (Grade 250) or be a standard flat bar (Grade 300). As per Table 2.1 of AS4100-2020, the end plate yield stress
    
    and tensile strength
    
    are automatically calculated depending the user selected grade.
  1. Bolt hole oversize is taken as
    
    , so the connection accommodates tolerances in the end plate and supported member (beam) and allows some rotation of the beam itself.
  1. Bolt tensioning specification is taken as "S", as "TB" & "TF" are not recommended for flexible connections.
  1. Fillet welds are assumed to be equal leg fillet weld, so that
    
    .
Exclusions::
  1. Supported member (beam) and supporting member are only considered as an I-section, hollow sections and PFCs are excluded.
  1. The web of the beam I-section is welded to the end plate using a double sided fillet weld only, full or partial penetration butt welds are not considered.
  1. Double-sided connections are excluded. This calculator assumes a single-sided connection, that is the supporting member only has one beam connecting into it.

1. Properties

1.1 Supported Member

1.1.1 Beam section

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


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:

Vmin∗=max⁡(0.15×ϕVvm,40kN)V^*_{min}=\max(0.15\times\phi V_{vm}, 40 \text{kN})
As per Clause 5.12.3,

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

so that

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

, 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​




Cl 5.12.3


Vmin
:79.4 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​






di_min
:202 mm​






di
:210 mm​






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

and tensile strength

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

is given by:

ϕVf=ϕ 0.62 krd krfuf(nnAc+nxAo)\phi V_f=\phi \space 0.62 \space k_{rd} \space k_rf_{uf}(n_nA_c+n_xA_o)
Where:
  1. 
    
    is the capacity reduction factor and is always 0.8, as per Table 3.4 of AS4100
  1. 
    
    is the ductility reduction factor for grade 10.9 threaded bolts
  1. 
    
    is the reduction factor for bolted splice connections
  2. 
    
    is the minimum tensile strength of the bolt
  3. 
    
    is the core area (at the root of the threads)
  1. 
    
    is the shank area of the bolt
  1. 
    
    is the # of shear planes in the threaded regions
  2. 
    
    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

or

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​




Cl 9.2.2.1


1.4.4 Bolt geometry

ASI Guide 4 recommends the horizontal bolt spacing

range to be:

9ti≤sg≤14ti9t_i\leq s_g \leq 14t_i
ASI Guide 4 does not recommend minimum and maximum spacings for the vertical bolt spacing

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

(Clause 9.5.1) and maximum

(Clause 9.5.3) bolt spacings. In summary, where

is the bolt diameter:

sp, min=2.5dfs_\text{p, min} = 2.5 d_f
In non-corrosive environments, where

is the thickness of the thinner ply connected:

sp, max=min⁡(32tf,300 mm)s_\text{p, max} = \min(32 t_f, 300 \text{ mm})
In corrosive environments:

sp, max=min⁡(15tf,200 mm)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

.
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 🟢​






sp_min
:50 mm​




Cl 9.5.1


Corrosive_environment
:N​



sp_max
:200 mm​




Cl 9.5.3


Vertical spacing check
:sp,min ≤ sp ≤ sp,max 🟢​






ae_min
:30 mm​




Table 9.5.2


Edge check
:ae ≥ ae_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,

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

. For an equal leg fillet weld,

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. 
    
    for GP
  2. 
    
    for SP
For end plate connections, weld category SP is normally used.


Weld category
:SP​




Φ,w
:0.8​




Table 3.4


1.5.3 Weld electrode type

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

. The options of electrode types are:
  1. 43 = E43XX
  1. 49 = E49XX
  2. 55 = E55XX
The

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

= 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,

is given by:

ϕvw=ϕ×0.6×tt×fuw\phi v_w = \phi \times 0.6 \times t_t \times f_{uw}


t_t
:4.242640687119271​






phi_vw
:997.8690896104525​




Cl 9.6.3.10



2. Design Actions



V
:250.0 kN​




V_d
:250.0 kN​






3. Design Checks

The below design checks follow the procedures outlined in Design Guide 4: Flexible end plate connections.

3. Design Checks

3.1 Weld Check

As per Section 10.2 of Design Guide 4, the design capacity of the weld to the supported member's web in shear is given by:

V∗≤Va=ϕvw×2diV^*\leq V_a = \phi v_w \times 2d_i
Where:
  1. 
    
    is the depth of the end (web) plate
  1. 
    
    is the capacity of a single fillet weld in
    
    , as provided in Section 1.5 of this calculator where
    
    depends on the weld category selected (GP or SP)


Va
:419.1 kN​






weld_util
:0.60​



weld_check
:V* ≤ Va 🟢​






3.2 Bolts Check

As per Section 10.3 of Design Guide 4, the design capacity of the bolts to the end plate is given by:

V∗≤Vb=2np×ϕVdfV^*\leq V_{b} = 2n_p \times \phi V_{df}
Where:
  1. 
    
    is the number of bolts
  1. 
    
    is the design capacity of a single bolt in shear in ULS
  2. 
    
    is the design capacity of a single bolt in shear as provided in Section 1.4 of this calculator, where
    
    is taken as 0.8 as per Table 3.4 of AS4100-2020
  1. 
    
    is the design capacity related to local bearing or end plate tear-out of a single bolt in the end plate, where
    
    is taken as 0.9 as per Table 3.4 of AS4100-2020
  1. 
    
    is the thickness of the end plate
  1. 
    
    is the bolt diameter
  1. 
    
    is the tensile strength of the end plate
  2. 
    
    are tear-out distances, where
    
    is the vertical bolt edge distance and
    
    
  1. 
    
    is the bolt hole diameter, assuming a 2mm oversize for tolerances
  1. 
    
    is the bolt vertical spacing



ae2
:59 mm​






aey
:35 mm​






ΦVbi
:138.6 kN​






ΦVdf
:92.6 kN​






Vb
:555.6 kN​






bolt_util
:0.45​



bolt_check
:V* ≤ Vb 🟢​






3.3 End Plate Check

As per Section 10.4 of Design Guide 4, the design capacity of an end plate in shear involves two checks given by:
a) flexible end plate in shear:

V∗≤Vc=ϕ×0.5fyiti2diV^* \leq V_c = \phi \times 0.5 f_{yi} t_i 2 d_i
Where:
  1. 
    
    is taken as 0.9, as per Table 3.4 AS4100-2020
  2. 
    
    is the yield strength of the end plate
  1. 
    
    is the thickness of the end plate
  1. 
    
    is the depth of the end plate
b) flexible end plate in block shear:

V∗≤Vd=ϕ×(Antfui+0.6fyiAgv)×2V^* \leq V_d = \phi \times (A_{nt}f_{ui}+0.6 f_{yi} A_{gv}) \times 2
Where:
  1. 
    
    is taken as 0.75, as per Section 10.4 of Design Guide 4
  1. 
    
    is the tensile strength of the end plate
  2. 
    
    are block shear areas, refer to Design Guide 4 for more details


Vc
:604.8 kN​






Agv
:1,750 mm^2​






Ant
:190 mm^2​






Vd
:629.4 kN​






endplate_util
:0.41​



endplate_check
:V* ≤ Vc and Vd 🟢​






3.4 Supported Member Web Check

As per Section 10.5 of Design Guide 4, the design capacity of the supported member's web at the end plate is given by:

V∗≤Ve=ϕ×(0.6fywtwebdi)V^*\leq V_{e} = \phi \times (0.6 f_{yw} t_{web}d_i)
Where:
  1. 
    
    is taken as 0.9, as per Table 3.4 AS4100-2020
  1. 
    
    is the yield strength of the supported member's web
  1. 
    
    is the thickness of the supported member's web
  1. 
    
    is the depth of the end plate


Ve
:275.8 kN​






beam_web_util
:0.91​



beam_web_check
:V* ≤ Ve 🟢​






3.5 Supported Member Shear Check

Supported member shear check is especially important for coped members. This calculator currently does not consider coped members. Therefore, the beam shear capacity is provided by the web, and is given by the web shear capacity of the full section.
As per Section 10.6 of Design Guide 4, the design capacity of the supported member in shear for an uncoped beam is given by:

V∗≤Vf=ϕVvo=ϕ×(0.6fywAw)V^*\leq V_{f} = \phi V_{vo} = \phi \times (0.6 f_{yw} A_w)
Where:
  1. 
    
    is taken as 0.9, as per Table 3.4 AS4100-2020
  1. 
    
    is the yield strength of the supported member's web
  1. 
    
    is the gross-sectional area of the web, given by
    
    for welded sections and
    
    for hot rolled (universal) sections


Vf
:529.3 kN​






beam_shear_util
:0.47​



beam_shear_check
:V* ≤ Vf 🟢​






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

. The limit on

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:

θb≤ti/ac\theta_b \leq t_i/a_c

To determine the beam rotation

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

θb=wL324EIΔ=5wL4384EI\theta_b =\dfrac{wL^3}{24EI} \hspace{1cm} \Delta=\dfrac{5wL^4}{384EI}
Where

is the mid-span deflection.


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

with respect to the mid-span deflection

, which can be simplified to:

θb=16Δ5L\theta_b = \dfrac{16 \Delta}{5L}
This calculator allows you to enter the length of the beam

and the mid-span deflection

in order to calculate

. Otherwise you can use your calculated value of

and compare it to

.


L
:10.00 m​



Delta
:50 mm​




θb
:0.9deg​






ac
:108 mm​






θb_limit
:5.3deg​






beam_rotation_util
:0.173​



beam_rotation_check
:θ ≤ ti/ac 🟢​






3.7 Supporting Member Check

As per Section 10.10 of Design Guide 4, the local capacity of the supporting member involves two checks given by:
a) local shear design capacity of the supporting member web:

V∗≤Vg=2ϕ×(0.6fycdb1tc)V^* \leq V_{g} = 2 \phi \times (0.6 f_{yc} d_{b1}t_{c})
Where:
  1. 
    
    is taken as 0.9, as per Table 3.4 AS4100-2020
  2. 
    
    is the yield strength of the supporting member (web or flange)
  1. 
    
    is the supporting member shear transfer depth
  1. 
    
    is the depth of the end plate
  1. 
    
    is the thickness of the supporting member (web
    
    or flange
    
    )
b) local bearing design capacity of the supporting member:

V∗≤Vh=2np×min⁡(ϕ3.2 tcdffuc, ϕ ae2tcfuc)V^* \leq V_{h} = 2n_p\times \min(\phi 3.2 \space t_c d_f f_{uc}, \space \phi \space a_{e2} t_c f_{uc})
Where:
  1. 
    
    is taken as 0.9, as per Table 3.4 AS4100-2020
  2. 
    
    is the tensile strength of the supporting member (web or flange)
  1. 
    
    is the bolt diameter
  1. 
    
    is the tear-out distance
Note, the above assumes a single-sided connection, that is the supporting member only has one beam connect into it. For double-sided connections, refer to Design Guide 4.


tc
:10.5​






Vg
:1,034.2 kN​






et
:100 mm​






eb
:45 mm​






db1
:285 mm​






ae2 (1)
:59 mm​






Vh
:1,471.9 kN​






column_util
:0.24​



column_check
:V* ≤ Vg and Vh 🟢​






Related Resources

  1. Steel Web Plate Connection to AS4100
  2. Steel Moment End Plate Connection to AS4100
  3. Fillet Weld Group Calculator to AS 4100
  4. Bolt Group Calculator to AS 4100
  5. Steel Beam and Column Designer to AS4100