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Civil Engineering

CIVE 462

Colin A Rogers

Fall

Description

Load Combinations
1.25 D + 1.5 L + 0.5 S 1.25 D + 1.4 W + 0.5 S
1.25 D + 1.5 S + 0.5 L SLS: 0.9 D + 0.75 W + (0.5 S or 0.5 L)
1.25 D + 1.4 W + 0.5 L
Member Resistance Calculation
Tension Resistance (Cl. 13.2)
1. Check gross cross-section yielding: 3. Slenderness ratio:
2. Check net cross-section fracture
a. Bolt shear lag (CL.12.3.3.2) (p 1-30 HB) 4. Check bolt shear and bearing
b. Weld connection shear lag (p 1-11)
*In the case of combined members, check individual and built-
up section
Axial Compression Resistance (Cl. 13.3) (p 1-12)
1. Check beam class (Table 1 HB, p 1-126)
a. b can be found from p 2-24 HB 3. Calculate
el
b. Also for web supported on both a. ;
edges b. n=2.24 for HSS class H ; n=1.34 for other shapes
2. Check slenderness limit: *In the case of combined members, check individual and built-up
a. Find k at p 1-13 and r from tables
section
Flexural Resistance
1. Check beam class (Table 2 HB, p 1-127) or (Table 4-3 c. Can double check M from table p 5-86 HB (if
r
HB, 4-7) 350W)
a. belan be found from p 2-24 HB 3. Check shear resistance
b. (to check for webs’ class) a.
2. Check moment resistance b. Fs= 0.66F y
a. If laterally supported, see cl. 13.5 (p 1-36 HB)
c. Check that
L<=L u
b. If not, see cl. 13.6 (Go see torsional buckling 4. Check deflection (Use service load)
Resistance section of crib sheet) a. Get from HB Table D-1 (p 1-146)
b. Get From HB 5-146
Single Storey Building
Interior Columns
1. Find acting loads 3. Find factored loads based on tributary width
2. Pick largest load combination 4. Find reaction forces from joists on gerber
a. 1.25D + 1.5L + 0.5S 5. Select column section (Green pages HB)
b. 1.25D + 1.5S + 0.5L a. Lu: can subtract joist height
Interior Gerber and Link Beams
1. Use load combination to find Max & Min factored a. Use max w onfcenter span
load 3. Calculate max moment for link beam
2. Max moment located at center span
Wind Loading *Try all load combinations p 2-13. Pick largest
1. Calculate wind load from p 2-21 Notes (Calculate all 4 F ) 8. Check
a. ; C C from Figure
g p 9. Plug Agback into
2. Consider roof as a beam and find reactions (simply cut in half)
3. Calculate gravity load separately for D, S & L 10. Find lateral drift
4. Pick a load combination with wind. C F D + S or D + L 11. Magnification factor:
5. Calculate notional load = a. Amplified force = T x U (check w/ T )
6. Find total horizontal load and find F 2 R
b. Amplified deflection = x U 2
, where a = bay width (Check w/ from HB Table D-1 (p 1-146))
12. Calculate (p 1-3), then check
7. Set Tr=Tfand solve for Ag:
Pick corresponding member 13. Transfer brace load to column Beam Bearing Plates (p 3-3)
1. Find largest reaction force. Use tables (p 5-159 HB) for 6. Find bending length: , where k is from beam
indeterminate beams properties tables
2. Calculate concrete bearing stress:
2 7. Find
3. Calculate bearing area required (mm ):
4. Set the maximum plate width (C) as (wall width – 25 8. Set M r M afd solve for t: , where
mm)
5. Find a plate length : a. Use next round value for t
a. Make sure plate length > (Flange width + 25 9. Check deflections: ,
mm) 10. Check web crippling
Column Base Plates (p 3-4)
Concentric axial load (p 3-4)
1. Calculate factored axial load
2. Calculate bearing stress of concrete/grout:
3. Calculate bearing area required (mm ): 2
4. From handbook, find d and b for the column
5. Try a plate with an area larger than A m
6. Calculate actual bearing stress:
7. Calculate m & n. Largest governs.
a.
b.
c. For HSS sections:
8. Calculate
9. Set M r M afd solve for t: , where
a. Use next larger round value for t
10. Check deflections: t>(m/5 and n/5)
Lightly loaded column base plate (p 3-16)
1. Use concentric design to get plate size (Steps 1 to 5)
4. Calculate
2. Assume a square base plate: .
3. Solve for m: 5. Check deflections: t>(m/5 and n/5)
Eccentric axial load or combined axial load and moment (p 3-8)
Small eccentricity
1. Use concentric design to get plate size (Steps 1 to 5)
2. Calculate actual uniform bearing stress on reduced area
a. Might need to increase B & C to insure A > A required
3. Calculate m & n and check that they are relatively equal. Largest governs.
a.
b.
c. For HSS sections:
4. Calculate
5. Set M r M afd solve for t: , where
a. Use next larger round value for t
6. Check deflections: t>(m/5 and n/5)
Moderate eccentricity
1. Use concentric design to estimate plate size, B and C (Steps 1 to 5)
2. Calculate
3. Calculate 4. Combine and to solve for B=
a. Solve for C using
5. Calculate from similar triangles:
6. Calculate M af a combination of rectangular stress and triangular stress:
7. Set M r M anf solve for t: , where
a. Use next larger round value for t
8. Check deflections: t>(m/5 and n/5)
Large eccentricity
1. Assume B and C dimension
a. C has to be large enough so that bolt and columns fit on the plate
2. Calculate
3. Solve for a:
4. Solve for rod tension T:
5. Guess rod diameter. Find corresponding pitch size (P) from (p 6-166 HB)
6. Calculate
7. Check that
8. Find moment and shear on plate caused by rod
a. Set
b.
c.
9. Solve for t:
10. Check . If not, adjust t.
11. Check plate for bending moment
a. Calculate
b. Set and solve for t:
12. Check deflections: t>(m/5 and n/5)
Combined Axial Tension and Bending (p 4-1)
1. Find factored load and moment ( ) 4. Check buckling when member is laterally
2. Check beam class unsupported
3. Check cross-section strength: a. For class 1,2: ; For class 3:
a. For class 1,2: ; For class 3:
b. M rs calculated from clause (lateral
b. torsional buckling
Combined Axial Compression and Bending (p 4-3) or (p 1-40 HB)
1. Find factored load and moment. Find e (distance from the middle, )
2. Check beam class (Table 2 HB, p 1-127) or (Table 4-3 HB, 4-7)
a. b eln be found from p 2-24 HB
b. (to check for webs’ class)
3. Calculate (x and y axis)
a. Constant BMD or uniform lateral load (worst case):
b. Single point lateral load or moment between supports:
c. Applied end moments:
i. Double curvature:
ii. Single curvature:
4. Check that for every steps: (note that is the moment where the largest simultaneous load occurs) Class 1,2 Class 3
Cross-
section
strength ; ;
(p 4-8)
Overall
in-plane
member for members in unbraced frames * for members in unbraced frames
strength is unrestricted for braced frames is unrestricted for braced frames
(p4-16) ; ;
Flexural
buckling
is unrestricted for braced frames is unrestricted for braced frames
stability
(p 4-21) for members in unbraced frames for members in unbraced frames
(*For strong axis bending only: *For strong axis bending only:
Crcalculated on for max. slenderness ratio Crcalculated on for max. slenderness ratio
)
k is based on end restraints (see p 1-13) k is based on end restraints (see p 1-13)
; ;
: Mrxust account for LTB ; M dory not : Mrxust account for LTB ; M doerynot
*Final amplified deflection: see p 4-6
5. Check for Lateral-torsional buckling (only if L>L ) in utrong axis
a. Find . Worst case
i. M : Factored BM at ¼ point of unbraced segment
a
ii. M :bFactored BM at mid-point of unbraced segment
iii. M : Factored BM at ¾ point of unbraced segment
c
iv. For distributed loads: ;
v. For single point load in center: ;
b. Find
i. IyJ, Cwfrom beam properties tables. C = 0 fow HSS. ALTERNATIVELY, FROM 7-75 HB
ii. G=77,000 MPa, E = 200,000 MPa
c. Check that (Else take M )r
-6 -6
Class 1,2 (M =ZpF xx y) Class 3 (M =SyF xx y)
If M <0.67M If M 0.67M If M <0.67M If M 0.67M
u p u p u y u y
; ;
d. Check with new Connections
Bolted connections in tension
1. Find factored tensile load on bolt
c.
2. To find bolt size:
a. Set T rT afd solve for A : b d. Calculate ,
i. ; F uan be found from table 3-3 (p 3-8 HB) i.
ii. Use an A > in table 3-4 (p 3-8 HB)
b. From table 3-4, select a bolt size ii.
3. To find the fatigue loading: iii. Plate won’t separate
a. Find unfactored load (
5. Check for Prying forces (p 5-16)
b. Calculate : and check that a. for a T or I section
i. i. t=thickness of plate/flange
ii.
4. To estimate load at plate separation: ii.
iii.
a. Find pre-tension load from table 7 (p 1-130 HB)
b. Determine bolt gauge ‘g’ (p 6-168 HB) b.
5. Check for Prying forces p 3-20 HB(detailed method)
Bolted connections in shear in tension (p 5-21)
1. Calculate factored load T , unfactored load T and V s f b. Solve for T(e.g. 2x2 bolts in tension):
2. Check bearing capacity
a. t=plate thickness(*0.9 if HSS), d b bolt diameter, F ou plate i. From similar triangles: .
b. Check accuracy (p 1-27)
i. Max centre to centre spacing (pitch/gauge)= 2.7 5. Check ( )
ii. Max edge distance = 150 mm or 12 t of outside a. (Bolt)
connected part
b. (Bolt)t
iii. For more than 2 rows of bolts, see Table 6 c. if threads included in shear plane
iv. Min end distance = 1.5 d b 6. For SLS (slip critical connections):
3. Calculate pure shear force
solve for n
4. Calculate tension forces from connection moment
a. a. (Values from Table 3-
10 p 3-15 HB) F ofubolt
Eccentrically loaded connections (p 5-25)
Bolt Connections: Traditional Method (p 5-26)
1. Find the center of gravity of bolt group a. ;
2. Calculate Vertical (P ) vnd Horizontal (P ) coHponents
b.
and resulting moment about CG
3. Find all the moment arms (r , r ,a…,br) andicalc. 5. ;
4. For each “critical” bolt: a. if threads included in shear plane
Welded Connections: Traditional Method (p 5-31)
1. Find the center of gravity of the weld 5. Calculate
2. Calculate and :
6. Determine fillet weld size ( ) see p S110 Pick smallest:
a. a. Base metal:
b. Weld metal:
3. Calculate
i. ;
4. Calculate 7. . Pick next bigger electrode
a. Check with max/min weld sizes (p S111)
a. ;
ICR Method (p 5-35)
Bolt Connections Welded Connections
1. Calculate shear (V )fper brackets of bolts 1. Find center of gravity of the weld
2. From tables (p 3-29 HB) determine C (Interpolation) 2. Go to appropriate table (p 3-44 HB) and find
a. Check
a.
3. Calculate V r b.
a. 3. Interpolate to find C.
b. if threads included in shear plane 4. Check with max/min weld sizes (p S111)
4. Check V frr the bracket = V * Cr Vf Design of Plate Girder Construction (P 6-1)
1. Find M f 5. Calculate flexural resistance M r
2. Preliminary Sizing: a. Calculate , from HB 7-75
a. Estimate web height:
i.
b. For class 3 or less:
b. Estimate flange area:
c. For class 4: or if
,
c. Estimate web area:
i.
3. Check class 3: 6. If no lat. support check for LTB (p 6-4) Find M using M ’
r r
4. Estimate web thickness considering:
***density of steel: 7850 kg/m *** 3
a. Max web slenderness:
b. (corrosion protection)
Shear Stiffeners (p 6-9)
1. Calculate unstiffened web shear resistance. 4. Check (kv= 5.34 if no shear stiffeners)
If , shear stiffeners are needed. a. If then F s F cre(dtn’t use F fortend panel)
a. If
i. ;
b. If

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