AISC 360: Moment Connection Design Example

If you read our previous article, AISC 360: Shear Connection Design, you would have a good sense of how simple connections are designed under AISC 360. A shear connection only has to deliver the beam end reaction. A moment connection has to deliver that reaction and the end moment with it, which brings the supporting column into the problem. In this article we work through an example moment connection between two I-shaped members and go through the design criteria that have to be satisfied. We can also get to the same results directly through the SkyCiv Connection Design module, which checks these connections to AISC 360-16 in ASD or LRFD.

As in the shear connection example, the calculations here use the Allowable Stress Design (ASD) method. If you aren’t familiar with the difference between ASD and LRFD in structural design, make sure to check out our video explaining this.

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In this example, we evaluate the capacity of a Bolted Flange-Plated Fully-Restrained (FR) Moment connection between a W18x50 beam and a W14x99 column, using the dimensions, welds and loads shown below. The connection has to support the beam end vertical reaction and the developed end moment. Compared with a shear connection, the difference is the pair of plates carrying the beam flange forces onto the supporting column flange.

The flange plates turn the beam end moment into a tension and compression couple. The top plate pulls, the bottom plate pushes, and both forces land on the column flange as concentrated forces. That is why a moment connection needs the column local checks that a shear connection does not.

Given:

Service Level Loads & Material:

Vertical Shear from Dead Load (VD) = 7.0 kips
Vertical Shear from Live Load (VL) = 21.0 kips

Moment from Dead Load (MD) = 42.0 kip-ft
Moment from Live Load (ML) = 126.0 kip-ft

Plate Material: ASTM A36, Fy = 36 ksi, Fu = 58 ksi
Beam and Column Material: ASTM A992, Fy = 50 ksi, Fu = 65 ksi

Beam and Column Geometry:

Beam: W18x50; bf = 7.50 in, tf = 0.570 in, d = 18.0 in, tw = 0.355 in, Sx = 88.9 in^3
Column: W14x99; bf = 14.6 in, tf = 0.780 in, d = 14.2 in, tw = 0.485 in, kdes = 1.38 in
Flange Plate: 3/4 in thick; 7.0 in x 12.5 in dimensions
Web Plate: 3/8 in thick; 5.0 in x 9.0 in dimensions

Fixtures (Bolts and Welds):
Flange: (8) – 7/8-in.-diameter ASTM F3125 Grade A325-N bolts in standard holes
Web Plate: (3) – 7/8-in.-diameter ASTM F3125 Grade A325-N bolts in standard holes

70-ksi electrode fillets. A325 and A490 are grades within ASTM F3125, which consolidated the older standalone bolt specifications.

Load Calculations:

LRFD Loads (Reference only):

Ultimate Vertical Reaction (R_u) = 1.2 (7.0 kips) + 1.6 (21.0 kips) = 42.0 kips
Ultimate Moment (M_u) = 1.2 (42.0 kip-ft) + 1.6 (126.0 kip-ft) = 252.0 kip-ft

ASD Loads:

Allowable Vertical Reaction (R_a) = 7.0 kips + 21 kips = 28.0 kips
Allowable Moment (M_a) = 42.0 kip-ft + 126 kip-ft = 168.0 kip-ft

Everything below is checked against the ASD loads. Keep the two methods apart: ASD compares service loads to allowable strength, LRFD compares factored loads to design strength, and the LRFD figures above are carried only so you can compare the two.

Solution based on SkyCiv Connection Design Software:
ERRATUM: The flange plate width in this example was 7.0 in but the width used in the calculations is 7.50 in, hence the difference in values.

 

Flange Force
Every check that follows is driven by one number, the force in the flange plate. The end moment is resolved into a couple acting at the plate centroids, so the lever arm is the beam depth plus one plate thickness:
P_af = [ 168.0 kip-ft (12 in/ft) ] / (18.0 in + 0.75 in) = 107.5 kips

 

Flange Plate to W14x99 Flange, Weld Strength
Strength of Fillet Welds, Ω = 2.0
Weld Size, t = 0.375 in
F_nw = 0.6 F_EXX [ 1.0 + 0.5 sin^1.5 (θ) ]
Where, θ = the angle which the load makes with the weld axis
= 90, for transversely loaded welds
= 0, for longitudinally loaded welds

Strength per unit size of weld:
Allowable weld stress, F_aw = 0.6 (70ksi) / 2.0 = 21 ksi
transverse length, l_t = 7 in
longitudinal length, l_l = 0 in
total effective length, l = l_t (1.5) + l_l (1.0) = 10.5 in
The 1.5 on the transverse length is the directional strength increase, 1.0 + 0.5 sin^1.5(90).
(R_a / a) = 21 ksi (10.5 in) = 220.5 kips / in

Effective size (throat) of fillet weld, a:
0.707 = the cosine or sine of 45 degrees
a = (0.707) t = 0.265 in

Two welds, one each side of the plate:
R_a = (R_a / a) a (2) = 220.50 (0.265 in) 2 = 116.9 kips
Design capacity ratio, DCR:
required load, R = 107.5 kips
overall capacity, R_a = 116.9 kips
DCR = (107.5 / 116.9) = 0.919, OK

 

Column Local Checks
These four checks ask whether the W14x99 can accept the flange force without local stiffening. All of them are compared against the same flange force:

Flange Force, P_af = 107.5 kips

• Web Local Yielding, Ω = 1.5
  R_n / Ω = [ F_yw t_w (5k + l_b) ] / Ω = 50ksi (0.485in) [ 5(1.38in) + 0.75in ] / 1.5 = 123.7 kips
  Here t_w is the column web thickness and l_b the bearing length, taken as the flange plate thickness.
  Design capacity ratio, DCR:
  Flange Force, P_af = 107.5 kips
  Overall capacity, R_a = 123.7 kips
  DCR = (107.5 / 123.7) = 0.869, OK

• Flange Local Bending, Ω = 1.67
  R_n / Ω = [ 6.25 F_y t_f² ] / Ω = [ 6.25 (50ksi) (0.78in)² ] / 1.67 = 113.8 kips
  Design capacity ratio, DCR:
  Flange Force, P_af = 107.5 kips
  Overall capacity, R_a = 113.8 kips
  DCR = (107.5 / 113.8) = 0.944, OK

• Web Local Crippling, Ω = 2.0
  R_n / Ω = 0.8 t_w² [ 1 + 3 ( l_b / d ) ( t_w / t_f )^1.5 ] ( E F_y t_f / t_w)^0.5 / Ω
  = 0.8 (0.485in)² [ 1 + 3 (0.05) (0.62)^1.5 ] [ (29000ksi) (50ksi) (0.78in) / 0.485in ] ^0.5 / 2.0
  = 154.8 kips
  Design capacity ratio, DCR:
  Flange Force, P_af = 107.5 kips
  Overall capacity, R_a = 154.8 kips
  DCR = (107.5 / 154.8) = 0.694, OK

• Web Compression Buckling, Ω = 1.67
  R_n / Ω = [ 24 t_w³ ( E F_y )^0.5 / h ] / Ω
  = 24 (0.485in)³ [ (29000ksi) (50ksi) ] ^0.5 / 14.2in (1.67)
  = 139.0 kips
  The full column depth is used here in place of h, the clear distance between flanges less the fillets, which is conservative.
  Design capacity ratio, DCR:
  Flange Force, P_af = 107.5 kips
  Overall capacity, R_a = 139.0 kips
  DCR = (107.5 / 139.0) = 0.773, OK

None of the four column local checks governs, so the W14x99 takes the flange force without transverse stiffeners for these limit states. Had any of them exceeded 1.0, the fix would be stiffeners or a doubler plate rather than a larger flange plate, because the capacity that ran out belongs to the column.

 

W18x50 Flange, Flange Plate Tensile Yielding
Strength of Element in Tension, Ω = 1.67

R_n / Ω = F_y A_g / Ω = (36ksi) (7.5in) (0.75in) / 1.67 = 121.3 kips

Design capacity ratio, DCR:
Flange Force, P_af = 107.5 kips
Overall capacity, R_a = 121.3 kips
DCR = (107.5 / 121.3) = 0.887, OK

 

W18x50 Flange, Flange Plate Compression Yielding
Strength of Element in Compression, Ω = 1.67

R_n / Ω = F_y A_g / Ω = (36ksi) (7.5in) (0.75in) / 1.67 = 121.3 kips

The compression plate is checked on the gross section because the bolt holes are filled in bearing. It matches the tension yielding value because the plate is short enough between the column face and the first bolt line for slenderness not to reduce it.

Design capacity ratio, DCR:
Flange Force, P_af = 107.5 kips
Overall capacity, R_a = 121.3 kips
DCR = (107.5 / 121.3) = 0.887, OK

 

W18x50 Flange, Flange Plate Tensile Rupture
Strength of Element in Rupture, Ω = 2.0
Shear Lag Factor, U from AISC Specification Table D3.1: 1.0

R_n / Ω = F_u A_e / Ω = (58ksi) [ 7.5in – 2 (1in) ] (0.75in) (1.0) / 2.0 = 119.6 kips

Two holes are deducted across the plate width. The 1 in deduction is the 7/8 in bolt diameter plus 1/8 in, which is the standard hole allowance used for net area.

Design capacity ratio, DCR:
Flange Force, P_af = 107.5 kips
Overall capacity, R_a = 119.6 kips
DCR = (107.5 / 119.6) = 0.899, OK

 

Summary Table of All the Results Check
Below is the SkyCiv Connection Design module Summary Table of all the necessary design checks completed for this connection. Not all of these checks were shown in this article but they are available via PDF which you may download here: Connection-Design-Report-EXAMPLE II.B-1-ASD

Of the checks worked through above, flange local bending governs at 0.944. That is the one to watch if the beam end moment grows, and it is a column property, so a heavier flange plate would not help.

Similarly, the LRFD version example can be found in this link: Connection-Design-Report-EXAMPLE II.B-1-LRFD

Run This Example Yourself
Enter the W18x50, the W14x99 and the flange plates, and the module returns every check above with its utilization ratio and the clause behind it. It runs in the browser, with nothing to install.

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References

• AISC 360-16, Specification for Structural Steel Buildings
• AISC Design Examples v14.1 (EXAMPLE II.B-1, pages IIB-2 to 13)
• SkyCiv Connection Design Software: https://skyciv.com/structural-software/connection-design/
• Flange plate connection calculator: https://skyciv.com/structural-software/connection-design/flange-plate-connection-calculator/