3 Restrained Beams - 2012
-
Upload
melinda-gordon -
Category
Documents
-
view
225 -
download
0
Transcript of 3 Restrained Beams - 2012
-
7/30/2019 3 Restrained Beams - 2012
1/14
14/8
Liew
Restrained Beams
8/14/2012
1
Introduction
ShearResistancePlasticShearResistance
ShearArea
ShearBucklingResistance
MomentResistanceMomentResistancewithHighShear
ServiceabilityBeamDeflections
Examples
ExampleRB
1(Section
resistance
and
deflection
of
UB)
Outline
8/14/2012
2
-
7/30/2019 3 Restrained Beams - 2012
2/14
14/8
Liew
Beams are structural members which transfer transverse loads on the
member to the supports through bending and shear.
Beams which are unable to deflect laterally are termed restrained .
Restrained beams are often designed on the basis of bending momentresistance which is dependent on section classification.
Deflection is normally significant and has to be checked at serviceabilitylimit state.
Introduction
8/14/2012
3
Full lateral restraint may be assumed to exist if the frictional orpositive connection of a floor (or other)
construction to the compression flange of the member is capable of resisting a lateral force ofmore than
2.5% of the maximum force in the compression flange of the member. This load should be considered as
distributed uniformly along the flange. Examples of full lateral restraint are:
1) insitu or precast concrete slab which is supported directly on the top flange or cast around it
2) steel plate floor which is welded or bolted to the flange at closely spaced intervals
3) provision of closely spaced bracing elements so that the minor axis slenderness is low ( )
tw
Friction force
(h tf)
L
FullyRestrainedBeam
Min. friction or connection resistance reqd=2.5% * max. moment in member
(h tf) *L
C =M/(h-tf)
T
M =Applied Moment
8/14/2012
4
-
7/30/2019 3 Restrained Beams - 2012
3/14
14/8
Liew
Shear Resistance
8/14/2012
5
Shear Resistance
EN 1993-1-1 (Cl 6.2.6)
The design shear force, VEd, should satisfy:
Vc,Rdis the design shear resistance, which may be calculated based on a plastic or an
elastic distribution of shear stress. The usual approach is to use the plastic shearresistance, Vpl,Rd.
The design plastic shear resistance is given by:
PlasticShearResistance
whereAv is the shear area.
ShearCheck8/14/2012
6
-
7/30/2019 3 Restrained Beams - 2012
4/14
14/8
Liew
ShearArea
tf
b
tw
rRolledIandHsections,loadparalleltoweb
tf
b
tw
rRolledIandHsections,loadparalleltoflange
tw
hw
WeldedI,H&boxsections,loadparalleltoweb
twhw
hw
WeldedI,H&boxsections,loadparalleltoflange
hw
8/14/2012
7
ShearArea
tf
b
tw
rRolledchannelsections,loadparalleltoweb
b
tfRolledTsections,loadparalleltoweb
Rectangularhollowsections,loadparalleltodepth
Rectangularhollowsections,loadparalleltowidth
Circularhollowsections
8/14/2012
8
-
7/30/2019 3 Restrained Beams - 2012
5/14
14/8
Liew
The shear buckling resistance for webs should be checked if
Shear buckling is unlikely to affect rolled sections.
ShearBucklingEN 1993-1-5 (Cl 6.2.6(6))
8/14/2012
9
8/14/2012
Moment Resistance
10
-
7/30/2019 3 Restrained Beams - 2012
6/14
14/8
Liew
Moment Resistance
EN 1993-1-1 (Cl 6.2.6)
The design bending moment,MEd, should satisfy the following cross-section check:
The bending moment resistance,Mc,Rdabout a principal axis depends on the class of
the section:
MomentCheck
Class 1 and 2 sections
Class 3 sections
Class 4 sections
8/14/2012
11
8/14/2012
12
The following sections are class 3 (semi-compact), all other UB andUC sections are either class 1 (plastic) or class 2 (compact):
Grade S275 steel Grade S355 steel152 152 23 UC 152 152 23 UC
305 305 97 UC356 368 129 UC
Non of the UB and UC under bending is class 4.
Notes
The Corus Advance range of sections includes UB and UCs thatare not in BS446, these are included in the above.
Dimensions of all sections in the Advance range are given in SCIpublication No P-363.
Section classification for bending only
-
7/30/2019 3 Restrained Beams - 2012
7/14
14/8
Liew
EN 1993-1-1 (Cl 6.2.8)
When the design value of the shear force is less than 50% of the design plastic shear
resistance, i.e. VEd 0.5 Vpl,Rd, its effect on the moment resistance may be neglected.
MomentResistancewithHighShear
When the design value of the shear force exceeds 50% of the design plastic shear
resistance i.e. VEd> 0.5 Vpl,Rd, the yield strengthfy should be reduced by (1 ) in the
determination of the moment resistance,Mc,Rd.
where
Class1&2IsectionswithequalflangesandbendingaboutmajoraxisAn alternative approach is available to determine the reduced design plastic resistance moment
for class 1 and 2 I sections.
but
where
8/14/2012
13
Serviceability
8/14/2012
14
-
7/30/2019 3 Restrained Beams - 2012
8/14
14/8
Liew
Deflection Check
Maximum Deflection due to unfactored imposed load
Cantilevers Length/180
Internal beams carrying plaster or other brittle finish Span/360 or 40mm
Other beams (except purlins and sheeting rails) Span/200 or 40mm
Edge beam Span/300 to span/500 or
20mm
Vertical deflection due to stat ic vertical wheel loads from overhead
traveling cranes Span/600
Horizontal deflection (calculated on the top flange properties alone)
due to horizontal crane loads Span/500
EN 1993-1-1 (Cl 7.2)
Excessive deflection at service load may impair the function of a structure.
Deflection check should be carried using the unfactored variable actions Qk.
8/14/2012
15
Examples of simple beam and cantilever forcesBeamDeflections
8/14/2012
16
-
7/30/2019 3 Restrained Beams - 2012
9/14
14/8
Liew
Examples
8/14/2012
17
Eurocode3:DesignofSteelStructures RLiew&SDPang
Example RB-1: Section resistance and deflection of UBA beam of span 10 m is simply supported at its ends and fully restrained along its length. It
supports a uniformly distributed load across the entire span and a point load at its mid-span.
Check and verify if section UB 533210101 in S355 steel is suitable for this beam. Assume
that the beam carried plaster finish.
Unfactoredload values:
Dead Load UDL 5 kN/m Imposed Load UDL 10 kN/m
Point load 50 kN Point load 100 kN
18
5m 5m
50 kN + 100 kN5 kN/m + 10 kN/m
-
7/30/2019 3 Restrained Beams - 2012
10/14
14/8
Liew
Ultimate Limit State
Design Loads
Dead Load Distributed load 5 1.35 = 6.75 kN/m
Point load 50
1.35 = 67.5 kNImposed Load Distributed load 10 1.5 = 15 kN/m
Point load 100 1.5 = 150 kN
5m 5m
67.5 kN + 150 kN
6.75 kN/m + 15 kN/m
217.5 kN 217.5 kN
Design Moment
Maximum bending moment at mid-span:MEd= (6.75+15)*102
/8 + (67.5+150)*10/4 =816 kNm.
Design Shear
Maximum shearforce at the supports: VEd= 217.5 kN.
8/14/2012
19
Yield Strengthtw = 10.8mm, tf= 17.4mm.
Maximum thickness = 17.4mm
-
7/30/2019 3 Restrained Beams - 2012
11/14
14/8
Liew
Shear Resistance
Shear Area
hwtw =(h2tf)tw = 1.0*(536.7 2*17.4)*10.8 =5421 mm2.
Av =A2btf+ (tw + 2r)tf= 12900 2*210.0*17.4 + (10.8 + 2*12.7)*17.4 = 6222 mm2.
Plastic Shear Resistance
SinceVEd= 217.5 kN
-
7/30/2019 3 Restrained Beams - 2012
12/14
14/8
Liew
Serviceability L imit State
Check for Deflection
The deflection of the beam under unfactored imposed load is
Since the beam carries plaster finish,
the maximum deflection of the beam is within limit.
8/14/2012
23
Eurocode3:DesignofSteelStructures RLiew&SDPang
Using Design Table
UB 533210101 in S355 under pure bending
Page D-66:
Section is class 1
Moment Resistance about major axisMcy,Rd= 901kNm
(hand calculation 900 kNm)
Page D-103
Design shear resistanceVc,Rd= 1240kN
(hand calculation 1239 kN)
Note that the moment capacity given in the table is for low shear.
The moment needs to be reduced for high shear case.
24
-
7/30/2019 3 Restrained Beams - 2012
13/14
14/8
Liew
Eurocode3:DesignofSteelStructures RLiew&SDPang
Page D-66
25
Eurocode3:DesignofSteelStructures RLiew&SDPang
26
Page D-103
Design shear resistance
-
7/30/2019 3 Restrained Beams - 2012
14/14
14/8
8/14/2012
27
Homework
Consider a simply supported beam 914 x 419 x 388 UB, S275 steel subjected to a
factored shear force of 2500kN and moment of 4000kNm. Check the shear andbending resistance of the beam if it is fully restrained against lateral-torsional buckling.