DDCL Seated angle
All clauses and sections, unless specified otherwise, refer to IS 800: 2007
[Grey highlighted items TO BE IGNORED and SHOULD NOT COME IN THE FINAL WEB FORM]
[YELLOW highlighted items to come as (on click) display]
This is a cleaned-up version of DDCL - that could be used in a pdf form.
Start with assumed size of seated angle (as given by user)
a. Seated Angle
i. Bearing width of seated angle = width of beam [based on general practice]
ii. Bearing length (length of outstanding leg of seated angle) is governed by web local crippling of supporting beam
1) The length of the outstanding leg of the seat angle is calculated on the basis of web crippling of the beam. The seat leg length is kept more than the calculated bearing length given by [Cl 8.7.4]
\(b=R/(t_w * f_yw/\gamma_m0 )\)
Where,
R is the reaction from the beam,
\( t_w\) is the thickness of the web of the beam,
\(f_yw \) is the yield strength of the web of the beam
\(\gamma_m0\) is the partial safety factor for material = 1.10
[Cl 8.7.4] Bearing Stiffeners
Bearing stiffeners should be provided for webs where forces applied through a flange by loads or reactions exceeding the local capacity of the web at its connection to the flange given by (equation form modified in the preceding paras)
iii. Angle thickness is governed by shear yielding and flexural yielding of angle
1) Moment capacity of the outstanding leg
a) [Cl 8.2.1.2]
When the factored design shear force, V, does not exceed 0.6 \(V_d\)
Where,
\(V_d \) is the design shear strength of the cross-section (see 8.4), the design bending strength, \(M_d\) shall be taken as:
\(M_d= \beta_b Z_p f_y/\gamma_m0\)
To avoid irreversible deformation under serviceability loads, Md shall be less than
In case of simply supported: \((1.2 Z_e f_y)/\gamma_m0 \)
And in cantilever beams: \((1.5 Z_e f_y)/\gamma_m0 \)
Where,
\( \beta_b = 1.0\) for plastic and compact sections;
\(\beta_b =Z_e/ Z_p\) for semi-compact sections;
\(Z_p, Z_e\) = plastic and elastic section moduli of the cross-section, respectively;
\( f_y\) = yield stress of the material; and
\( \gamma_m0\) = partial safety factor for material
b) [CL 8.2.1.3]
When the design shear force (factored), V, exceeds 0.6 \(V_d\)
Where,
\( V_d\) is the design shear strength of the cross-section (see 8.4) the design bending strength, \(M_d\) shall be taken as \(M_dv\) = design bending strength under high shear as defined in 9.2
[Cl 9.2.2]
When the factored value of the applied shear force is high (exceeds the limit specified in Cl 9.2.1), the factored moment of the section should be less than the moment capacity of the section under higher shear force, M_dv, calculated as given below:
1) Plastic or compact section
\(M_dv =min{M_d − \beta(M_d−M_fd ) , (1.2 Z_e f_y)/\gamma_m0} \)
[#Assuming, M_fd= 0, as the shear resisting area and moment resisting area are the same for the cross section of the outstanding leg]
=min {(1−\beta)M_d , (1.2 Z_e f_y)/\gamma_m0 }
Where,
\beta = ( 2V/V_d −1 )^2
M_dv = design bending strength under high shear
M_d = plastic design moment of the whole section disregarding high shear force effect (see 8.2.1.2) considering web buckling effects (see 8.2.1.1)
V = factored applied shear force as governed by web yielding or web buckling
V_d= design shear strength as governed by web yielding or web buckling (see 8.4.1 or 8.4.2)
M_fd = plastic design strength of the area of the cross-section excluding the shear area, considering partial safety factor γ_m0, and
Z_e = elastic section modulus of the whole section
2) Semi-compact section
M_dv =(Z_e f_y)/\gamma_m0
2) Shear capacity of the outstanding leg of cleat
a) [Cl 8.4.1] Plastic shear resistance under pure shear
V_dp=(A_v f_yw)/√3 \gamma_m0
Where,
V_dp= design plastic shear resistance under pure shear
A_v=A=d_a t_a (#this formula is for a plate, assuming clear horizontal leg of the seated angle is a plate) [Cl 8.4.1.1]
d_a = clear length of outstanding leg of seated angle
t_a = thickness of seated angle
f_yw = yield strength of the web
\gamma_m0 = partial safety factor
b) [Cl 8.4.2] [Resistance to shear buckling]
[#This clause check does not need to be implemented as the outstanding leg of the seated angle will not buckle due to the low slenderness ratio]
b. Bolt
Bolt value and number of bolts
i. [Cl. 10.3.3] Shear capacity of bolt
1) V_dsb = (f_u (n_s A_(sb )+n_n A_(nb )))/(√3 \gamma_mb )
#currently, conservatively assuming n_n A_(nb )=0 that is, all shear planes pass through the threads.
The option to specify this as an input from the user is being implemented.
Thus,
V_dsb = (f_u n_n A_(nb ))/(√3 \gamma_mb )
Where,
V_dsb = design strength of bolt, as governed by shear strength
f_u = ultimate tensile strength of a bolt
n_s = number of shear planes without threads intercepting the shear plane
A_sb = nominal plain shank area of the bolt
n_n = number of shear planes with threads intercepting the shear plane
A_nb = net shear area of the bolt at threads, may be taken as the area corresponding to root diameter at the thread
γ_mb = partial safety factor for bolt
2) [Cl 10.3.3.1] Long joints [#assuming that this does not apply]
When the length of joint, l_j , of a splice or end connection in a compression or tension element containing more than two bolts (that is the distance between the first and last rows of bolts in the joint, measure in the direction of the load transfer) exceeds 15d in the direction of load, the nominal shear capacity (see 10.3.2) V_db shall be reduced by the factor \beta_lj , given by:
\beta_lj = 1.075 − l_j/200d but 0.75 ≤ \beta_lj ≤1.0
= 1.075 −0.005l_j/d
Where,
d = nominal diameter of the fastener
Note: This provision does not apply when the distribution of shear over the length of joint is uniform, as in the connection of web of a section to the flanges
3) [Cl 10.3.3.2] Large grip lengths [#assuming that this does not apply]
When the grip length, lg , (equal to the total thickness of the connected plates), exceeds 5 times the diameter, d of the bolts, the design shear capacity shall be reduced by a factor \beta_lg given by:
\beta_lg=8d/(3d+l_g )
=8/(3+l_g/d)
\beta_lg shall not be more than β_lj given in [Cl 10.3.3.1]. The grip length l_g shall in no case be greater than 8d
4) [Cl 10.3.3.3] Packing plates [#assuming that this does not apply]
The design shear capacity of bolts carrying shear through a packing plate in excess of 6 mm shall be decreased by a factor, \beta_lj , given by:
\beta_pk=1 − 0.0125 t_pk
Where,
t_pk = thickness of the thicker packing, in mm
ii. Bearing capacity of bolt
1) [Cl. 10.3.4] Bolt bearing on the seat angle (and column)
The design bearing strength of a bolt on any plate, V_dpb , as governed by bearing is given by:
V_dsb=2.5 k_b dtf_ub
Where,
k_b is smaller of
{e/(3d_0 ) , p/(3d_0 ) −0.25, f_ub/f_u , 1.0}
e, p = end and pitch distances of the fastener along bearing direction;
d_0 = diameter of the hole
f_ub,f_u = ultimate tensile stress of the bolt and the ultimate tensile stress of the plate, respectively;
d = nominal diameter of the bolt,
t = summation of the thicknesses of the connected plates experiencing bearing stress in the same direction, or if the bolts are countersunk, the thickness of the plate minus one half of the depth of countersinking.
t shall be minimum of {thickness of seat angle, thickness of support}
#assuming standard clearance holes; hence, reduction factors for long slotted holes and over size, and short slotted holes as given in [Cl 10.3.4] do not apply
iii. Number of bolts (N1) = reaction/capacity per bolt
c. Detailing
i. [Cl 10.2.2] Minimum spacing
The distance between centre of fasteners shall not be less than 2.5 times the nominal diameter of the fastener
ii. [Cl 10.2.3.1] Maximum spacing
The distance between the centres of any two adjacent fasteners shall not exceed 32t or 300mm, whichever is less, where t is the thickness of the thinner plate.
Bolt pitch (mm) ≥ 2.5* (bolt diameter) , ≤min(32*t, 300)
Bolt gauge (mm) ≥ 2.5*(bolt diameter) , ≤min(32*t, 300)
iii. [Cl 10.2.4] Edge and end distances
[Cl 10.2.4.2]
The minimum edge and end distances from the centre of any hole to the nearest edge of a plate shall not be less than 1.7 times the hole diameter in case of sheared or hand-flame cut edges; and 1.5 times the hole diameter in case of rolled, machine-flame cut, sawn and planed edges.
[Cl 10.2.4.3]
The maximum edge distance to the nearest line of fasteners from an edge of any un-stiffened part should not exceed 12tε, where ε = √(250/f_y ) and t is the thickness of the thinner outer plate.
End distance (mm) ≥ 1.7*(hole diameter), ≤ 12*t
Edge distance (mm) ≥ 1.7*(hole diameter), ≤ 12*t
d. Top Angle
#Literature suggests to use a 'nominal size' for the top angle (from stability consideration). However the term nominal size is not well defined.
The AISC Steel Construction Manual, 14th Ed, Page 10-84, suggests
A 1/4-in.-thick angle with a 4-in., vertical leg dimension will generally be adequate
#This translates to 6.35 mm thick angle with a 101.6 mm vertical leg
Can ISA 100 65x6 or ISA 100 65x8 be used?
Can we directly use the above sizes in the Indian context?