V. AISC ASD - Deflection Check for a Steel Beam with Web Opening
Determine the deflection of a beam with a web opening.
Details
Design Method : ASD
Beam No : 5
Beam Section : W21X50
- d = 20.83 in
- tw = 0.38 in
- bf = 6.53 in
- tf = 0.535 in
- Z = 110 in3
- L = 30 ft
- E = 29,732 ksi
Opening Type: Rectangular
Number of openings : 1
- Section location of Opening, sopen = 0.3
- a0 = 20 in
- h0 = 10 in
- e = 0 in ( concentric opening )
- Fy = 36 ksi
Loading at critical location:
- V u = 9.51 kip
- Mu = 344.36 kip-inch
Location of maximum deflection from start of the member : Lcritical = 120 in
Tee Properties :
- st = 5.415 in
- sb = 5.415 in
- Moment Area =
- Area = bftf + tw(st - tf) = 5.34795 in2
-
Cyt = Moment Area / Area = 1.20632 in.
- (concentric opening)
-
Izz = Izz,t + Izz,b = 25.2872 in3
Vt = FyRt = 4.755
Vb = FyRb = 4.755
Δ0 = Δ0b + Δ0b = 0.03373 in
L0 = distance from high moment end of opening to adjacent support
L2 = distance from support to the point where deflection is maximum = L0 - Lcritical = 240 in
L3 = L0 - L2 = 74 in
Δ = Δp1 + Δp2 = 0.11377 in (extra deflection due to opening)
displacement factor: Δfactor = 750
Ratio of Δactual/Δallow = 0.66 (without web opening)
Thus, Δactual= 0.3168 in (from analysis considering stiffness of unperforated member without web opening)
Total deflection considering the effect of web hole,
Δactual,wb= Δ + Δactual = 0.4306 in
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Interaction Ratio, R | 0.897 | 0.899 | < 1% | |
Total deflection, in | 0.4306 | 0.4315* | < 1% |
* STAAD.Pro does not directly report the deflection, but rather the ratio of deflection with length, dff, for comparison with a limiting displacement factor.
Δactual,wb = L / dff = 360 in / 834.32 = 0.4315 in
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples\Verification Models\09 Steel Design\US\AISC\AISC ASD - Deflection of Steel Beam with Web Opening.std is typically installed with the program.
STAAD PLANE Deflection of Steel Beam with Web Opening
START JOB INFORMATION
ENGINEER DATE 18-May-05
END JOB INFORMATION
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 30 0 0; 3 0 20 0; 4 10 20 0; 5 20 20 0; 6 30 20 0; 7 0 35 0;
8 30 35 0; 9 7.5 35 0; 10 22.5 35 0; 11 15 35 0; 12 5 38 0; 13 25 38 0;
14 10 41 0; 15 20 41 0; 16 15 44 0;
MEMBER INCIDENCES
1 1 3; 2 3 7; 3 2 6; 4 6 8; 5 3 4; 6 4 5; 7 5 6; 8 7 12; 9 12 14;
10 14 16; 11 15 16; 12 13 15; 13 8 13; 14 9 12; 15 9 14; 16 11 14;
17 11 15; 18 10 15; 19 10 13; 20 7 9; 21 9 11; 22 10 11; 23 8 10;
MEMBER PROPERTY AMERICAN
1 3 4 TABLE ST W14X90
2 TABLE ST W10X49
5 6 7 TABLE ST W21X50
8 TO 13 TABLE ST W18X35
14 TO 23 TABLE ST L40404
MEMBER TRUSS
14 TO 23
MEMBER RELEASE
5 START MZ
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 29000
POISSON 0.3
DENSITY 0.000283
ISOTROPIC STEEL
E 29732.7
POISSON 0.3
DENSITY 0.000283
ALPHA 1.2e-005
DAMP 0.03
END DEFINE MATERIAL
CONSTANTS
BETA 90 MEMB 3 4
MATERIAL MATERIAL1 MEMB 1 TO 4 6 TO 23
MATERIAL STEEL MEMB 5
UNIT FEET KIP
SUPPORTS
1 FIXED
2 PINNED
PRINT MEMBER INFORMATION LIST 1 5 14
PRINT MEMBER PROPERTIES LIST 1 2 5 8 14
LOAD 1 DEAD AND LIVE LOAD
SELFWEIGHT X 1
SELFWEIGHT Y -1
JOINT LOAD
4 5 FY -15
11 FY -35
MEMBER LOAD
8 TO 13 UNI Y -0.9
6 UNI GY -1.2
CALCULATE RAYLEIGH FREQUENCY
LOAD 2 WIND FROM LEFT
MEMBER LOAD
1 2 UNI GX 0.6
8 TO 10 UNI Y -1
* 1/3 RD INCREASE IS ACCOMPLISHED BY 75% LOAD
LOAD COMB 3 75 PERCENT DL LL WL
1 0.75 2 0.75
PERFORM ANALYSIS
LOAD LIST 3
UNIT INCHES KIP
PARAMETER
CODE AISC
TRACK 2 MEMB 5
DFF 750
DJ1 3 MEMB 5
DJ2 6 MEMB 5
*WEB OPENINGS
*********************
RHOLE 0.3 MEMB 5
RDIM 20.0 10.0 MEMB 5
*********************
CHECK CODE MEMB 5
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - (AISC 9TH EDITION) v1.0 ******************************************** |--------------------------------------------------------------------------| | Y PROPERTIES | |************* | IN INCH UNIT | | * |=============================| ===|=== ------------ | |MEMBER 5 * | AISC SECTIONS | | AX = 14.70 | | * | ST W21X50 | | --Z AY = 6.94 | |DESIGN CODE * | | | AZ = 4.69 | | AISC-1989 * =============================== ===|=== SY = 7.63 | | * SZ = 94.62 | | * |<---LENGTH (FT)= 10.00 --->| RY = 1.30 | |************* RZ = 8.18 | | | | 94.4 (KIP-FEET) | |PARAMETER | L3 STRESSES | |IN KIP INCH | L3 L3 IN KIP INCH | |--------------- + L3 -------------| | KL/R-Y= 92.20 | L3 FA = 21.60 | | KL/R-Z= 14.67 + L3 fa = 0.94 | | UNL = 120.00 | L3 FCZ = 19.35 | | CB = 1.00 + FTZ = 21.60 | | CMY = 0.85 | L3 FCY = 27.00 | | CMZ = 0.85 + L3 FTY = 27.00 | | FYLD = 36.00 |L0 L0 fbz = 11.97 | | NSF = 1.00 +---+---+---+---+---+---+---+---+---+---| fby = 0.00 | | DFF = 750.00 -5.2 Fey = 18.01 | | dff= 834.32 ABSOLUTE MZ ENVELOPE Fez = 711.71 | | (KL/R)max = 92.20 (WITH LOAD NO.) FV = 14.40 | | fv = 1.33 | | | | MAX FORCE/ MOMENT SUMMARY (KIP-FEET) | | ------------------------- | | | | AXIAL SHEAR-Y SHEAR-Z MOMENT-Y MOMENT-Z | | | | VALUE -14.2 9.6 0.0 0.0 94.4 | | LOCATION 0.0 0.0 0.0 0.0 10.0 | | LOADING 3 3 0 0 3 | | | |**************************************************************************| |* *| |* DESIGN SUMMARY (KIP-FEET) *| |* -------------- *| |* *| |* RESULT/ CRITICAL COND/ RATIO/ LOADING/ *| | FX MY MZ LOCATION | | ====================================================== | | PASS DEFLECTION 0.899 3 | | 13.81 T 0.00 -94.36 10.00 | |* *| | | |--------------------------------------------------------------------------| DEFLECTION OF STEEL BEAM WITH WEB OPENING -- PAGE NO. 7 OUTPUT FOR WEB OPENING ---------------------- SECTION LOAD MZ/ FY/ IR MOM. CAP. (Mm) SHR. CAP. (Vm) ((MZ/Mm)^3+(FY/Vm)^3)^0.33 ======================================================================= 0.300 3 344.36 9.51 3618.00 38.44 0.25 ======================= END WEB OPENING OUTPUT ======================== 79. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 14,2023 TIME= 10: 8:26 **** DEFLECTION OF STEEL BEAM WITH WEB OPENING -- PAGE NO. 8 ************************************************************