Post on 16-Apr-2017
HCM City, date 18 month 03 year 2016
HO CHI MINH UNIVERSITY OF ARCHITECTURE
Field: Structural Engineering
STRUCTURAL STEEL PART II
Project: Design Single Storey Steel Building.
NAME: NGUYỄN TRÍ THIỆN
Student ID number:
Grade: XD12A2
TUTOR: DR. TRẦN VĂN PHÚC
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 1
SYMBOLS USED IN THIS PROJECT A: is gross area of cross section.
An: is net cross section area.
Af: is cross section area of flange (chord).
Aw: is cross section area of web.
Abn: is cross section area of bolt.
b: is width.
bf: is flange (chord) width.
bef: is design width.
bs: is the width of stiffener.
h: is height.
hw: is height of web.
hf: is the height of fillet weld.
hfk: is distance between flange’s central axis.
i: is inertia radius of cross section.
ix, iy: is inertia radius of cross section relative to axes x-x, y-y respectively.
If: moment of inertia of flange (chord).
It: torsional constant.
Ix, Iy: moment of inertia about the principal axes.
Inx, Iny: moment of inertia about the principal axes referred to the net area.
L: is length of member.
l0: is design length of compression members.
lx, ly: are design lengths of component in planes perpendicular to axes x-x and y-
y respectively.
lw: is the length of weld seam.
S: is static moment of gross slid portion cross section relative to neutral axis.
t: is thickness.
tf, tw: is thickness of flange (chord), web respectively.
Wnmin: is the minimum moment resistence of net section.
Wx, Wy: are the moment resistance of gross section relative to axes x-x, y-y
respectively.
F, P: is force.
M: is moment or bending moment
Mx, My: are moment or bending moment relative to axis x-x, y-y respectively.
N: is longitudinal force.
V: is lateral force or shear force.
E: is modulus of elasticity.
f: is design yield strength.
fv: is ultimate shear strength.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 2
fc: is design crushing strength.
fub: is ultimate tension strength.
σ: is stress.
σc: is local stress.
σx, σy: are normal stresses which are parallel with axes x-x, y-y respectively.
σct, σc,ct: are normal critical stress and concentrated critical stress respectively.
τ: is shear (tangential) stress.
τct: is ultimate shear stress.
e: is eccentricity of force.
m: is relative eccentricity.
me: is reduced relative eccentricity.
nv: is the number of design section.
βf, βs: are factor for analysis of corner seam through seam metal and through
metal of melting boundary respectively.
γc: is working condition factor.
γb: is working condition factor of bolt.
γg, γp: is load factor (load coefficient).
nc: is load combination factor.
η: is factor of influence of cross section form.
λ: is flexibility (slenderness ratio).
: is fictitious flexibility.
w : is fictitious flexibility of web.
λx, λy: are design flexibility in planes perpendicular to axes x-x and y-y
respectively.
μ: is length coefficent.
φ: is buckling factor.
φb: is factor of reducing design resistence at bending-and-twisting form of beam
stability loss.
φc: is factor of reducing design resistence at eccentric compression.
Ψ: is intermidiate factor to calculate φb factor.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 3
CHAPTER 1. GIVEN DATA Name: Nguyễn Trí Thiện Student ID number:
Order number: 87 Grade: XD12A2
Design three span single storey building according to following data
given below:
Span
(m) Bay
(m)
Level
Crane
Q(T)
Wind
pressure
at 10 m
qo
(daN/m2)
Length
(m)
Slope
i% L1 L2 L3
Ground
(m)
Ground
floor
(m)
Rail
(m)
30 33 30 6,5 -0,65 0 12 10 85 162,5 10
Area type to calculate wind load is B.
A single model overhead crane is in the center span which is its load
capacity is given above. There is no crane on the side span, and the
dimension of side span is equal L1=L3.
Roof materia: tole. Using portal frame with I built-up beam, straight
column, and beam with variable section.
Material using : Steel CCT34, with following properties:
Design yield strength: f = 2100 daN/cm2
Ultimate shear strength: fv = 1200 daN/cm2
Design crushing strength: fc = 3200 daN/cm2
Ultimate tension strength: fu = 3400 daN/cm2
Using Shielding metal arc welding method and electrode wire N46 with
fwf = 2000 daN/cm2
Conection between beam and column: Rigid.
Conection between column and foundation: Fixed.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 4
CHAPTER 2. FRAME GEOMETRY
CHOSING CRANE.
Accroding to given data: Span L2 = 33m, load capacity Q = 3T, using
catalouge and find out a suitable crane:
Span: 33-0,75x2=31,5 m
Gabarit high HK = 875 mm
DEFINE VERTICAL DIMENSION.
Upper column length:
r dcct KhH h H C
HK: Gabarit height (the distance between upper surface of the rail and yop
of the crane) – According to catalouge: HK = 875mm.
C: the safety distance between crane and rafter
1 1
100 33000 100 265200 200
C L mm
hdcc: the height of runway beam
1 1 1 1
.6500 650 812,58 10 8 10
dcth B mm
Chose hdct = 800mm
hr: the height of rail 200mm
So 200 8 00 875 265 2140r dcc Kt h h H C mH m
Chose Ht = 2.2m
Lower column length:
– d r dcc r mH H h h h
Hr – upper surface of the rail level, Hr = 12 m
hm – ground floor level above ground level 0,65m, hm=0,65m (foundation
are refferd to be placed at the same ground level).
120 – 00 800 200 650 11650d r dcc r nH H h h h mm
Chose Hd = 12m
The length of column:
2200 12000 14200t dH H H mm
DEFINE HORIZONTAL DIMENSION:
The grid of reference axis shall be coincident with axis of column.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 5
The distance between reference axis and y-y axis of runway beam:
750mm to match up crane load capacity Q < 75 ton. To prevent
the impact between crane and column, shall be: 1 ( )tB h a D
B1 is the dimension of head crane B1 = 200(mm).
D is the safety clearence between crane and column D=
60(mm).
ht is the height of upper column:
1 1 1 12200 200 220( )
10 11 10 11t th H mm
Chose ht =250mm (ht is multiple of 250mm)
1750( ) ( ) 200 250 60 510tmm B h a D mm
1 1
14200 568 mm 60025 25
d dh H h mm
Distance between rail center point and outer edge of the middle
colum:
0.60
0.75 0.452 2
hZ m
JACK ROOF MONITOR DIMENSION.
Span of the roof:
1 133 3,3 ( )
10 10cmL L m
Height of the roof: Hcm =1.5(m).
HORIZONTAL FRAME MODEL OF CALCULATION.
Using straight column and beam with variable section.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 6
Horizontal frame model of calculation as follow :
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 7
CHAPTER 3. DEFINE LOAD.
DEAD LOAD.
Dead load apply to horizontal frame include in gravity load of purlins,
self weight of frame and runway beam. In this project, self weight of bracing
column and roof are neglected.
Self weight of structure.
It would be automatically calculated by software.
Envelope material.
Roof structure.
Roof system: using roof fill insulation, purlins and snag rods. Take
230 d /tc
mg aN m , load factor n = 1,1.
Normal load apply to roof:
1 . 30 6,5 195 /tc tc
kh mg g B daN m
Design load apply to roof:
1 1. 1,1 195 214,5 /tt tc
kh khg n g daN m
Building lateral side.
Sidewall girt, sidewall canopy system and tole is assumed to be
230 d /tc
bcg aN m , load factor n = 1,1
Normal load apply to outside column:
2 . 30 6,5 195 /tc tc
kh bcg g B daN m
Design load apply to outside column:
2 2. 1,1 195 214,5 /tt tc
kh khg n g daN m
Runway beam.
The height of runway beam Hdct = 0,8m. Preliminary self weight of
runway beam is assumed to be 200 daN/m, load factor n = 1,1. It is
reduced to concentrated load and eccentric moment is located at level of
junction of column and lower surface of rail:
Normal load:
200 6,5 1300 dtc tc
dct dctG g B aN
1300 0,75 975 d .tc tc
dct dct nM G L aN m
Design load:
. 1,1 1300 1430 dtt tc
dct dctG n G aN
1430 0,75 1072,5 d .tt tt
dct dct nM G L aN m
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 8
ROOF LIVE LOAD.
According to TCXDVN 2737: 1995, standard load of roof live load
should be taken as 30 daN/m2, load factor n = 1,3 (in case live load is
less than 200 daN/m2). It is reduced to distributed load apply to rafter:
Normal load: 30 6,5 195 /tc tc
htp p B daN m
Design load: . 1,3 195 253,5 /tt tc
pp n p daN m
CRANE LOAD.
This following table gives properties of 10 ton crane which is taken from crane catalouge :
Load
(T)
Span
(m)
Total
mass
Max
wheel
load Pmax
(T)
Min
wheel
load Pmin
(T)
Dimension
H3 B W C2 C1 H2 H1
10 31,5 7,76/8,28 6,60/6,85 1,55/1,56 1200 3500 3000 1230 1830 1640 875
Crane load apply to horizontal frame including vertical impact and
horizontal breaking focre:
Vertical impact.
The maximum wheel load used for the design of runway beams,
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 9
including monorails, their connections and support brackets, shall be
increased by the percentage given below to allow for the vertical impact
or vibration:
_ Monorail cranes (powered) .........................................................25
Cab-operated or radio operated bridge cranes (powered)…...........25
_ Pendant-operated bridge cranes (powered)…..............................10
_ Bridge cranes or monorail cranes with hand-geared bridge, trolley and
hoist…...............................................................................................0
_ Vertical impact shall not be required for the design of frames, support
columns, or the building foundation.
It should be calculated as follow:
max max 0.85 1.2 6850 1 0,908 6600 0,446 0,538
19955,48
tt
c iD n n P y
daN
min min 0.85 1.2 1550 1 0,908 1560 0,446 0,538
4582,29
tt
c iD n n P y
daN
Where:
n – is the load factor of crane, n = 1,2.
nc – is the load combination factor, nc = 0,85 is taken from SNiP
2.01.07-85*
_ If two cranes are taken into account, their loads ought to be multiplied by the following combination coefficient: nc= 0,85 – for crane operation mode groups 1K-6K
INFLUENCE LINE FOR REACTION TO DEFINE Dmax, Dmin
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 10
Through rail and runway beam, Dmax and Dmin would be transmited to
bracket support, thus eccentric of column may be e = L1 = 0,75m.
Eccentric moment is given by:
max max 19955,48 0.75 14966,61 .tt ttM D e daN m
min min 4582,29 0.75 3436,72 .tt ttM D e daN m
Breaking force of trolley and lifted load:
Lateral loads being bi-directional action are applied to the column
throught crane rail to account for such effects as acceleration and
breaking forces of trolley and lifted load, skewing of the travelling crane,
rail misalignment, and not picking up the load up vertically. It is defined
as :
max c kT n nT y
Where:
n – overload factor of crane, γp = 1,2
nc – load combination factor, nc = 0,85 is considered for crane
operation mode groups 1K-6K. Loads and effects SNiP 2.01.07-
85*
Tk – breaking force of single trolley wheel impact to rail
0
0,05 10000 8280 77600,05( )263
2
xck
Q GT daN
n
no – the number of driven wheels
1 0,908 0,446 0,538 2,892iy
max 0,85 1,2 263 2,892 775,81tc
c p iT n T y daN
WIND LOAD:
According to TCVN 2737-1995 or Loads and effects SNiP 2.01.07-85*, Upon calculation of internal pressure wi as well as upon calculation of high buildings up to 40 m and one-storey buildings up to 36 m – in case the ratio between the height and the span is less than 1,5 – that are located in areas of A and B types (see item 6.5), the pulsating component of wind load may be omitted. The standard average component of wind load W at the height of z over the ground surface is to be calculated under the following formula:
. . . .o
W W n c k B
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 11
Where:
Wo = 85 daN/m2: standard wind pressure (see item 6.4)
B – span 6,5B m
c – aerodynamic coefficient (see item 6.6)
Coefficient α degrees h1/l
0 0.5 1 ≥2
ce1
0 0 -0.6 -0.7 -0.8
20 +0.2 -0.4 -0.7 -0.8
40 +0.4 +0.3 -0.2 -0.4
60 +0.8 +0.8 +0.8 +0.8
ce2 ≤60 -0.4 -0.4 -0.5 -0.8
Aerodynamic coefficient
ce1: 1 13,550,452
30
h
l và 5 42'o ce1 = -0,44
n = 1,2 : confidence factor of service life (50 years).
k – coefficient of wind pressure change in height (see item 6.5), which
is to be calculated as following formula
2
( ) 1,844
tm
t z g
t
zk
z
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 12
Area type g
tz mt
A 250 0.07
B 300 0.19
C 400 0.14
According to given data, calculated area type is B so
300; 0,09g
t tz m . The height is lower than 10m take k = 1.
The coefficient k considering wind pressure change in height z is set
under following table:
Height z (m) k
0 1
10 1
13,55 1,056
15,05 1,090
15,2 1,093
According to TCVN 2737-1995 or Loads and effects SNiP 2.01.07-85*
if wind is perpendicular to the end wall of the building so it’s c = -0,7 for
the whole surface of the building.
Outside column
Left wind: c = +0,8
Level 10m: . . . . 85 1,2 0,8 1 6,5 530,4 /o
W W n c k B daN m
Level 13,55m:
. . . . 85 1,2 0,8 1,056 6,5 560,10 /o
W W n c k B daN m
Right wind: c = -0,4
Level 10m: . . . . 85 1,2 0,4 1 6,5 265,2 /o
W W n c k B daN m
Level 13,55m:
. . . . 85 1,2 0,4 1,056 6,5 280,05 /o
W W n c k B daN m
Longitudinal wind: c = -0,7
Level 10m: . . . . 85 1,2 0,7 1 6,5 464,1 /o
W W n c k B daN m
Level 13,55m:
. . . . 85 1,2 0,7 1,056 6,5 490,09 /o
W W n c k B daN m
Left roof’s L1-L2 span
Left wind: c = -0,442
Level 13,55m:
. . . . 85 1,2 0,442 1,056 6,5 309,46 /o
W W n c k B daN m
Level 15,050m:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 13
. . . . 85 1,2 0,442 1,090 6,5 319,42 /o
W W n c k B daN m
W 314,44 d /tb aN m
Right wind: c = - 0,4
Level 13,55m:
. . . . 85 1,2 0,4 1,056 6,5 280,05 /o
W W n c k B daN m
Level 15,050m:
. . . . 85 1,2 0,4 1,090 6,5 289,07 /o
W W n c k B daN m
W 284,56 d /tb aN m
Longitudinal wind: c = -0,7
Level 13,55m:
. . . . 85 1,2 0,7 1,056 6,5 490,09 /o
W W n c k B daN m
Level 15,050m:
. . . . 85 1,2 0,7 1,09 6,5 505,87 /o
W W n c k B daN m
W 497,98 d /tb aN m
Right roof’s L1-L2 span
Left wind: c = -0,6
Level 13,55m:
. . . . 85 1,2 0,6 1,056 6,5 420,08 /o
W W n c k B daN m
Level 15,05m:
. . . . 85 1,2 0,6 1,090 6,5 433,60 /o
W W n c k B daN m
W 426,84 d /tb aN m
Right wind: c = - 0,5
Level 13,55m:
. . . . 85 1,2 0,5 1,056 6,5 350,06 /o
W W n c k B daN m
Level 15,05m:
. . . . 85 1,2 0,5 1,090 6,5 361,34 /o
W W n c k B daN m
W 355,7 d /tb aN m
Longitudinal wind: c = -0,7
Level 13,55m:
. . . . 85 1,2 0,7 1,056 6,5 490,09 /o
W W n c k B daN m
Level 15,050m:
. . . . 85 1,2 0,7 1,090 6,5 505,87 /o
W W n c k B daN m
W 497,98 d /tb aN m
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 14
Center roof
Left wind: c = -0,2
Level 13,55m:
. . . . 85 1,2 0,2 1,056 6,5 140,03 /o
W W n c k B daN m
Level 15,2m:
. . . . 85 1,2 0,2 1,093 6,5 144,93 /o
W W n c k B daN m
W 142,48 d /tb aN m
Right wind c = - 0,5
Level 13,55m:
. . . . 85 1,2 0,5 1,056 6,5 350,06 /o
W W n c k B daN m
Level 15,2m:
. . . . 85 1,2 0,5 1,093 6,5 362,33 /o
W W n c k B daN m
W 356,20 d /tb aN m
Longitudinal wind c = - 0,7
Level 13,55m:
. . . . 85 1,2 0,7 1,056 6,5 490,09 /o
W W n c k B daN m
Level 15,2m:
. . . . 85 1,2 0,7 1,093 6,5 507,26 /o
W W n c k B daN m
W 498,68 d /tb aN m
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 15
CHAPTER 4. DETERMINE INTERNAL FORCE,
SHEAR AND MOMENT AT SAP 2000 V18
DEFINE MATERIAL AND SECTION PROPERTIES.
Material.
Properties of CCT34 steel:
Weight per unit volume 37850 /T daN m
Modulus of elasticity 10 22,1 10 /E daN m
Minimum yield stress 7 22,2 10 /yf daN m
Minimum tensile stress 7 23,4 10 /uf daN m
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 16
Section.
a) Column section: (reference book: Structural Steel - Pham Van
Hoi - page 225).
Wide – flange shape I preliminary sizing
Brace is located at level (code) +6,35m, ly = 7,0 m.
Chosing height h and width b:
1 1 1 114200 568 947( )
15 25 15 25h H mm
Chọn 700h mm
1 1 1 17000 233 350
30 20 30 20
0,3 0,5 0,3 0,5 700 210 350
yb l mm
b h mm
Chọn 350b mm
Chosing the thickness of flange tf and web tw:
w
w w
1 1 1 1 21350 12.5 10
28 35 21 28 35 21
1 1 1 1700 11.67 5.83
60 120 60 120
; 60 ; 8
f
f f
ft b mm
t h mm
t t t mm t mm
→Chose
w
14
10
ft mm
t mm
Both kinds of column side and center are defined at the same size as
straight element.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 17
a) Beam section: (reference book: Structural Steel - Pham Van Hoi -
page 225).
The height of beam is normally bigger than hmin
min
5 5 210 15000200 577
24 24 210000 1,1 cos(10 )o
tb
f l lh mm
E
=>Chose 700h mm
To preventing over all buckling and easier connecting with other
elements, the width is defined as follow:
1 1 1 1
700 140 3502 5 2 5
180 , /10
f
f f
b h mm
b mm b h
=>Chose 350b mm
To preventing vertical buckling of compression flange, the ratio between
width and the thickness of flange is defined as follow:
6
2100350 11,07
2,1 10
30030 10
30 30
ff
f
f f f
fb E t b mmEt f
bb t t mm
Chose 14ft mm
To preventing shear buckling of web, the thickness of the web is defined
as:
ww 6
700 2 14 21006,64
3,2 3,2 2,1 10
h ft mm
E
Chose w 10t mm
Both kinds of beam side and center are defined at the same size as
straight element.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 18
CREATING BUILDING MODEL.
The length of rafters are too long L1 = L3 = 30 (m), L2 = 33 (m), so to be
easier in transportation, the rafter is devided into 2 separated segment.
Side span’s rafter L1 = L3 = 30 (m), the conection between 2 segment is
loacated at 6 (m) in horizontal direction starting at side column, the rafter
is divided as follow:
60001 4 9 12 6092,56
cos10
90002 3 10 11 9138,84
cos10
o
o
D D D D mm
D D D D mm
Centre span’s rafter L2 = 33 (m), the conection between 2 segment is
loacated at 6 (m) in horizontal direction starting at side column, the rafter
is divided as follow:
60005 8 6092,56
cos10
105006 7 10661,98
cos10
o
o
D D mm
D D mm
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 19
DEFINE LOAD.
Dead loads include the following:
a) weight of structural parts including weight of bearing and
enclosing structures;
b) weight and pressure of ground (mounds and fillings), rock
pressure.
c) The prestressing forces remained in building structures and
foundations should be adopted in calculations as dead load forces.).
Crane load include in 6 load cases:
Dmax vertically impact on column E (Dmax LEFT)
Dmax vertically impact on column I (Dmax RIGHT)
T horizontally impact on column E, from right to left direction (T
LEFT)
T horizontally impact on column E, from left to right direction (-T
LEFT)
T horizontally impact on column I, from left to right direction (T
RIGHT)
T horizontally impact on column I, from right to left direction (-T
RIGHT)
Wind load include in 2 load cases:
Wind impact on building from left to right direction (LEFT WIND)
Wind impact on building from right to left direction (RIGHT WIND)
Live load include in 6 load cases: HT1, HT2, HT3, HT4, HT5, HT6.
Those kinds of loads could be occurred concurrent.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 20
Dead load
Defining load for building model at Sap 2000 to analysis, the Self
Weight Multiplier need to be 1.1
Live load.
HT1.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 21
HT2.
HT3.
HT4.
HT5.
HT6.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 22
Wind load.
Left wind.
Right wind.
Crane load.
Dmax Left.
Dmax phải.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 23
T LEFT.
-T LEFT.
T RIGHT.
-T RIGHT.
Longitudinal wind:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 24
DEAD LIVE1 LIVE2 LIVE3 LIVE4 LIVE5 LIVE6DMAX
LEFT
DMAX
RIGHTT LEFT - T LEFT T RIGHT - T RIGHT
LEFT
WIND
RIGHT
WIND
LO NGITUDINAL
WIND
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
M(KN.m) -13501.4 -4281.6 -3692.7 691.9 -1116.3 127.5 -1328.7 1971.1 -1622.2 -1309.5 1309.5 1313.6 -1313.6 37250.2 -5522.0 6554.8
N(KN) -10176.9 -2959.1 -800.4 165.6 31.9 -7.4 -57.4 115.2 -47.1 -35.9 35.9 51.4 -51.4 5161.2 3963.5 7205.7
V(KN) -2328.3 -923.6 -646.7 137.9 -85.6 8.1 -145.7 227.9 -167.8 -134.1 134.1 141.6 -141.6 8122.2 -1425.6 -888.9
M(KN.m) 19559.8 8833.1 5490.2 -1266.8 99.7 13.0 739.9 -1265.5 759.9 594.0 -594.0 -696.3 696.3 -24547.8 -12047.6 -27668.0
N(KN) -5105.3 -2959.1 -800.4 165.6 31.9 -7.4 -57.4 115.2 -47.1 -35.9 35.9 51.4 -51.4 5161.2 3963.5 7205.7
V(KN) -2328.3 -923.6 -646.7 137.9 -85.6 8.1 -145.7 227.9 -167.8 -134.1 134.1 141.6 -141.6 537.8 2366.6 5747.5
M(KN.m) -3086.1 3790.0 3651.2 -4520.5 -4157.7 617.5 -1306.9 -3075.6 -3360.6 -2237.4 2237.4 1497.6 -1497.6 9490.0 -11480.0 3843.8
N(KN) -15040.6 -894.9 -3144.7 -3483.8 -917.3 131.1 90.0 -19986.4 -4619.5 15.2 -15.2 -30.7 30.7 9368.7 10457.9 15961.9
V(KN) -459.6 638.9 762.8 -929.5 -705.9 108.1 -139.0 -948.7 -553.0 -323.2 323.2 177.0 -177.0 787.8 -1455.5 560.7
M(KN.m) 2267.8 -3653.4 -5235.9 6307.9 4066.1 -641.7 312.2 7976.7 3082.0 1528.3 -1528.3 -564.3 564.3 312.0 5476.9 -2688.8
N(KN) -13378.8 -894.9 -3144.7 -3483.8 -917.3 131.1 90.0 -19986.4 -4619.5 15.2 -15.2 -30.7 30.7 9368.7 10457.9 15961.9
V(KN) -459.6 638.9 762.8 -929.5 -705.9 108.1 -139.0 -948.7 -553.0 -323.2 323.2 177.0 -177.0 787.8 -1455.5 560.7
M(KN.m) 1195.3 -3653.4 -5235.9 6307.9 4066.1 -641.7 312.2 -6989.9 -354.7 1528.3 -1528.3 -564.3 564.3 312.0 5476.9 -2688.8
N(KN) -11948.8 -894.9 -3144.7 -3483.8 -917.3 131.1 90.0 -30.9 -37.2 15.2 -15.2 -30.7 30.7 9368.7 10457.9 15961.9
V(KN) -459.6 638.9 762.8 -929.5 -705.9 108.1 -139.0 -948.7 -553.0 -323.2 323.2 177.0 -177.0 787.8 -1455.5 560.7
M(KN.m) 2367.2 -5282.6 -7181.1 8678.1 5866.2 -917.3 666.6 -4570.7 1055.5 994.8 -994.8 -1015.6 1015.6 -1697.0 9188.5 -4118.7
N(KN) -11585.0 -894.9 -3144.7 -3483.8 -917.3 131.1 90.0 -30.9 -37.2 15.2 -15.2 -30.7 30.7 9368.7 10457.9 15961.9
V(KN) -459.6 638.9 762.8 -929.5 -705.9 108.1 -139.0 -948.7 -553.0 452.6 -452.6 177.0 -177.0 787.8 -1455.5 560.7
ELEMENT SECTIO NINTERNAL
FO RCE
LO AD PATTERN
C1
CO LUMN
BASE
CO LUMN
HEAD
C2
CO LUMN
BASE
LO WER
BRACKET
C3
UPPER
BRACKET
CO LUMN
HEAD
INTERIAL FORCE AND LOAD COMBINATION.
INTERNAL FORCE TABLE OF COLUMN
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 25
DEAD LIVE1 LIVE2 LIVE3 LIVE4 LIVE5 LIVE6DMAX
LEFT
DMAX
RIGHTT LEFT - T LEFT T RIGHT - T RIGHT
LEFT
WIND
RIGHT
WIND
LO NGITUDINAL
WIND
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
M(KN.m) -19559.75 -8833.08 -5490.22 1266.76 -99.68 -12.99 -739.87 1265.45 -759.94 -593.95 593.95 696.34 -696.34 24547.81 12047.57 27667.99
N(KN) -2824.69 -1213.43 -723.12 153.73 -82.04 7.29 -150.67 238.26 -171.61 -136.95 136.95 145.96 -145.96 1048.7 2749.27 6435.92
V(KN) -4848.31 -2852.54 -732.12 151.1 40.22 -8.14 -42.64 91.96 -30.2 -22.37 22.37 37.04 -37.04 5082.07 3708.38 6598.04
M(KN.m) 3214.44 3781.78 -1075.58 355.66 -342.2 36.1 -482.78 710.92 -577.84 -459.07 459.07 473.01 -473.01 -380.2 -5140.38 -3064.41
N(KN) -2610.4 -1061.33 -723.12 153.73 -82.04 7.29 -150.67 238.26 -171.61 -136.95 136.95 145.96 -145.96 1048.7 2749.27 6435.92
V(KN) -2705.41 -1331.54 -732.12 151.1 40.22 -8.14 -42.64 91.96 -30.2 -22.37 22.37 37.04 -37.04 3186.02 1992.5 3595.26
M(KN.m) 3214.44 3781.78 -1075.58 355.66 -342.2 36.1 -482.78 710.92 -577.84 -459.07 459.07 473.01 -473.01 -380.2 -5140.38 -3064.41
N(KN) -2610.4 -1061.33 -723.12 153.73 -82.04 7.29 -150.67 238.26 -171.61 -136.95 136.95 145.96 -145.96 1048.7 2749.27 6435.92
V(KN) -2705.41 -1331.54 -732.12 151.1 40.22 -8.14 -42.64 91.96 -30.2 -22.37 22.37 37.04 -37.04 3186.02 1992.5 3595.26
M(KN.m) 13147.86 5507.48 5546.37 -1010.99 -705.98 109.73 -97.15 -120.89 -304.68 -256.75 256.75 138.01 -138.01 -16335.27 -11522.44 -15213.23
N(KN) -2288.97 -833.18 -723.12 153.73 -82.04 7.29 -150.67 238.26 -171.61 -136.95 136.95 145.96 -145.96 1048.7 2749.27 6435.92
V(KN) 508.94 949.96 -732.12 151.1 40.22 -8.14 -42.64 91.96 -30.2 -22.37 22.37 37.04 -37.04 341.95 -581.31 -908.92
M(KN.m) 13147.86 5507.48 5546.37 -1010.99 -705.98 109.73 -97.15 -120.89 -304.68 -256.75 256.75 138.01 -138.01 -16335.27 -11522.44 -15213.23
N(KN) -2344.42 -1004.79 -563.83 120.77 -88.38 8.76 -139.24 215.33 -162.23 -129.81 129.81 135.73 -135.73 960.22 2809.94 6488.46
V(KN) 45.6 766.16 -860.82 178.55 23.18 -6.54 -71.63 137.32 -63.58 -49.04 49.04 65.21 -65.21 542.84 -25.39 383.52
M(KN.m) -1801.32 -1422.34 3014.4 -2625.92 -915.62 168.84 550.7 -1362.97 270.43 186.85 -186.85 -451.77 451.77 -3785.33 3257.1 1687.73
N(KN) -2665.86 -1004.79 -791.98 120.77 -88.38 8.76 -139.24 215.33 -162.23 -129.81 129.81 135.73 -135.73 960.22 2809.94 6488.46
V(KN) 3259.95 766.16 1420.68 178.55 23.18 -6.54 -71.63 137.32 -63.58 -49.04 49.04 65.21 -65.21 -3317.88 -3242.65 -4120.65
M(KN.m) -1801.32 -1422.34 3014.4 -2625.92 -915.62 168.84 550.7 -1362.97 270.43 186.85 -186.85 -451.77 451.77 -3785.33 3257.1 1687.73
N(KN) -2665.86 -1004.79 -791.98 120.77 -88.38 8.76 -139.24 215.33 -162.23 -129.81 129.81 135.73 -135.73 960.22 2809.94 6488.46
V(KN) 3259.95 766.16 1420.68 178.55 23.18 -6.54 -71.63 137.32 -63.58 -49.04 49.04 65.21 -65.21 -3317.88 -3242.65 -4120.65
M(KN.m) -27919.36 -6042.23 -10137.97 -3702.54 -1055.38 208.25 982.6 -2191.02 653.83 482.59 -482.59 -844.95 844.95 23981.18 29276.69 35588.23
N(KN) -2880.15 -1004.79 -944.08 120.77 -88.38 8.76 -139.24 215.33 -162.23 -129.81 129.81 135.73 -135.73 960.22 2809.94 6488.46
V(KN) 5402.85 766.16 2941.68 178.55 23.18 -6.54 -71.63 137.32 -63.58 -49.04 49.04 65.21 -65.21 -5891.69 -5387.5 -7123.43
M(KN.m) -30286.59 -759.59 -2956.89 -12380.59 -6921.59 1125.52 316.03 2379.71 -401.65 -512.22 512.22 170.68 -170.68 25678.17 20088.17 39706.95
N(KN) -3363.27 -286.48 103.26 -1117.78 -875.72 127.88 -279.99 -708.81 -725.58 314.9 -314.9 319.01 -319.01 1490.66 1279.75 7095.62
V(KN) -5615.58 -4.11 -134.65 -3222.9 -802.32 111.54 60.76 155.58 -12.15 -52.29 52.29 -11.1 11.1 3278.67 4713.55 7559.7
M(KN.m) -2885.82 -734.81 -2144.95 2467.52 -2083.64 452.95 -50.33 1441.55 -328.41 -196.94 196.94 237.63 -237.63 8498.32 -1858.45 3188.55
N(KN) -3148.98 -286.48 103.26 -965.68 -875.72 127.88 -279.99 -708.81 -725.58 314.9 -314.9 319.01 -319.01 1490.66 1279.75 7095.62
V(KN) -3472.68 -4.11 -134.65 -1701.9 -802.32 111.54 60.76 155.58 -12.15 -52.29 52.29 -11.1 11.1 2419.53 2565.69 4552.69
M(KN.m) -2885.82 -734.81 -2144.95 2467.52 -2083.64 452.95 -50.33 1441.55 -328.41 -196.94 196.94 237.63 -237.63 8498.32 -1858.45 3188.55
N(KN) -3148.98 -286.48 103.26 -965.68 -875.72 127.88 -279.99 -708.81 -725.58 314.9 -314.9 319.01 -319.01 1490.66 1279.75 7095.62
V(KN) -3472.68 -4.11 -134.65 -1701.9 -802.32 111.54 60.76 155.58 -12.15 -52.29 52.29 -11.1 11.1 2419.53 2565.69 4552.69
M(KN.m) 13973.08 -691.45 -724.04 6382.76 6382.76 -724.04 -691.45 -200.24 -200.24 354.81 -354.81 354.81 -354.81 -9100.66 -9100.66 -17088.52
N(KN) -2773.98 -286.48 103.26 -699.51 -875.72 127.88 -279.99 -708.81 -725.58 314.9 -314.9 319.01 -319.01 1490.66 1279.75 7095.62
V(KN) 277.4 -4.11 -134.65 959.85 -802.32 111.54 60.76 155.58 -12.15 -52.29 52.29 -11.1 11.1 916.02 -1193.07 -709.56
ELEMENT SECTIO NINTERNAL
FO RCE
LO AD PATTERN
B1
START
0m
END
6,03m
B2
START
0m
END
9,04m
B3
START
0m
END
9,04m
B6
START
0m
END
10,55m
B4
START
0m
END
6,03m
B5
START
0m
END
6,03m
INTERNAL FORCE TABLE OF RAFTER
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 26
Mmax, Ntư Mmin, Ntư |N|max, Mtư Mmax, Ntư Mmin, Ntư |N|max, Mtư Mmax, Ntư Mmin, Ntư |N|max, Mtư
1,14 1,2,3,5,7 1,2,3,6,71,4,6,8,11,1
4, 16
1,2,3,5,7,9
,13, 151,2,3,6,7,9,13
1,4,6,8,11,1
4, 16
1,2,3,5,7,9
,13, 151,2,3,6,7
M(KN.m) 23748.8 -23920.8 -22677.0 29613.1 -30490.9 -24401.6 29613.1 -30490.9 -22677.0
N(KN) -5015.7 -13962.0 -14001.2 1231.8 -10104.9 -13707.4 1231.8 -10104.9 -14001.2
V(KN) 5794.0 -4129.8 -4036.1 4638.9 -5511.1 -4143.7 4638.9 -5511.1 -4036.1
1,2,3,5,6,7 1, 16 1,2,3,6,71,2,3,5,6,7,9
,13
1,4,8,11,1
4, 161,2,3,6,7,9,13 1,2,3,5,6,7
1,4,8,11,1
4, 161,2,3,6,7
M(KN.m) 34735.6 -8108.2 34635.9 34528.7 -30248.0 34438.9 34735.6 -30248.0 34635.9
N(KN) -8897.8 2100.4 -8929.7 -8607.2 6309.9 -8635.9 -8897.8 6309.9 -8929.7
V(KN) -4121.8 3419.2 -4036.1 -4220.8 3778.4 -4143.7 -4121.8 3778.4 -4036.1
1,14 1, 15 1,8,111,2,3,6,14,
16
1,4,5,7,8,1
0, 151,2,3,4,5,8,11
1,2,3,6,14,
16
1,4,5,7,8,1
0, 15
1,2,3,4,5,8,1
1
M(KN.m) 6404.0 -14566.1 -3924.3 16167.2 -27186.3 -4953.8 16167.2 -27186.3 -4953.8
N(KN) -5671.9 -4582.8 -35042.2 4239.2 -27482.7 -40638.8 4239.2 -27482.7 -40638.8
V(KN) 328.3 -1915.1 -1085.0 2113.0 -4511.2 -1232.8 2113.0 -4511.2 -1232.8
1,4,5,7 1,2,3,6 1,8,111,4,5,7,8,10,
151,2,3,6, 16 1,2,3,4,5,8,11
1,4,5,7,8,10
, 151,2,3,6, 16
1,2,3,4,5,8,1
1
M(KN.m) 12954.1 -7263.1 8716.3 25369.1 -8729.9 9407.8 25369.1 -8729.9 9407.8
N(KN) -17689.9 -17287.3 -33380.4 -25820.8 -2530.7 -38976.9 -25820.8 -2530.7 -38976.9
V(KN) -2233.9 1050.3 -1085.0 -4511.2 1404.0 -1232.8 -4511.2 1404.0 -1232.8
1,4,5,7 1,2,3,6 1,2,3,4,51,4,5,7,9,13,
15
1,2,3,6,8,1
1, 161,2,3,4,5,9,12
1,4,5,7,9,13
, 15
1,2,3,6,8,1
1, 161,2,3,4,5
M(KN.m) 11881.6 -8335.6 2680.1 15930.8 -17468.8 1704.6 15930.8 -17468.8 2680.1
N(KN) -16259.9 -15857.3 -20389.5 -6422.5 -1142.2 -19606.5 -6422.5 -1142.2 -20389.5
V(KN) -2233.9 1050.3 -693.2 -4023.5 841.0 -1008.2 -4023.5 841.0 -693.2
1,4,5,7 1,2,3,6 1,2,3,4,51,4,5,7,9,13,
15
1,2,3,6,8,1
1,14, 161,2,3,4,5,9,12
1,4,5,7,9,13
, 15
1,2,3,6,8,1
1,14, 161,2,3,4,5
M(KN.m) 17578.1 -11013.8 4447.8 26190.7 -19918.8 4275.6 26190.7 -19918.8 4447.8
N(KN) -15896.1 -15493.6 -20025.8 -6058.8 7653.4 -19242.8 -6058.8 7653.4 -20025.8
V(KN) -2233.9 1050.3 -693.2 -4023.5 851.8 -1008.2 -4023.5 851.8 -693.2
INTERNAL FORCE DESIGN
ELEMENT SECTIONINTERNAL
FORCE
LOAD COMBINATION 1 LOAD COMBINATION 2
C3
START
0m
END
2,55m
C1
START
0m
END
14,2m
C2
START
0m
END
11,65m
LOAD COMBINATION OF COLUMN
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 27
Mmax, Ntư Mmin, Ntư |N|max, Mtư Mmax, Ntư Mmin, Ntư |N|max, Mtư Mmax, Ntư Mmin, Ntư |N|max, Mtư
1, 16 1,2,3,5,6,7 1,2,3,5,71,4,8,11,14,
16
1,2,3,5,6,7,9
,131,2,3,5,7,9,13
1,4,8,11,14,
161,2,3,5,6,7 1,2,3,5,7,9,13
M(KN.m) 8108.2 -34735.6 -34722.6 30248.0 -34528.7 -34517.0 30248.0 -34735.6 -34517.0
N(KN) 3611.2 -4986.7 -4994.0 4387.5 -5056.3 -5062.8 4387.5 -4986.7 -5062.8
V(KN) 1749.7 -8443.5 -8435.4 5902.7 -8144.5 -8137.2 5902.7 -8443.5 -8137.2
1,2,4,6 1, 15 1,2,3,5,7 1,2,4,6,8,111,3,5,7,9,13,
15, 161,2,3,5,7,9,13 1,2,4,6,8,11
1,3,5,7,9,13
, 15, 161,2,3,5,7,9,13
M(KN.m) 7388.0 -1925.9 5095.7 8023.6 -6826.1 3961.8 8023.6 -6826.1 3961.8
N(KN) -3510.7 138.9 -4627.6 -3083.0 4510.2 -4711.7 -3083.0 4510.2 -4711.7
V(KN) -3894.0 -712.9 -4771.5 -3672.2 1602.0 -4625.4 -3672.2 1602.0 -4625.4
1,2,4,6 1, 15 1,2,3,5,7 1,2,4,6,8,111,3,5,7,9,13,
15, 161,2,3,5,7,9,13 1,2,4,6,8,11
1,3,5,7,9,13
, 15, 161,2,3,5,7,9,13
M(KN.m) 7388.0 -1925.9 5095.7 8023.6 -6826.1 3961.8 8023.6 -6826.1 3961.8
N(KN) -3510.7 138.9 -4627.6 -3083.0 4510.2 -4711.7 -3083.0 4510.2 -4711.7
V(KN) -3894.0 -712.9 -4771.5 -3672.2 1602.0 -4625.4 -3672.2 1602.0 -4625.4
1,2,3,6 1,14 1, 16 1,2,3,6,8,111,4,5,7,9,13,
14, 161,2,3,5,7,9,13 1,2,3,6
1,4,5,7,9,13
,14, 161,2,3,5,7,9,13
M(KN.m) 24311.4 -3187.4 -2065.4 23317.4 -17276.9 21975.1 24311.4 -17276.9 21975.1
N(KN) -3838.0 -1240.3 4147.0 -3345.4 4090.3 -4184.9 -3838.0 4090.3 -4184.9
V(KN) 718.6 850.9 -400.0 800.6 72.0 642.3 718.6 72.0 642.3
1,2,3,6 1,14 1, 16 1,2,3,6,8,111,4,5,7,9,13,
14, 161,2,3,5,7,9,13 1,2,3,6
1,4,5,7,9,13
,14, 161,2,3,5,7,9,13
M(KN.m) 24311.4 -3187.4 -2065.4 23317.4 -17276.9 21975.1 24311.4 -17276.9 21975.1
N(KN) -3904.3 -1384.2 4144.0 -3437.7 3995.1 -4229.2 -3904.3 3995.1 -4229.2
V(KN) -55.6 588.4 429.1 122.2 880.5 -199.1 -55.6 880.5 -199.1
1,3,6,7 1,2,4,5 1,2,3,5,71,3,6,7,9,13,
15, 16
1,2,4,5,8,11,
141,2,3,5,7,9,13
1,3,6,7,9,13,
15, 16
1,2,4,5,8,11
,141,2,3,5,7,9,13
M(KN.m) 1932.6 -6765.2 -574.2 6659.6 -11070.4 -46.9 6659.6 -11070.4 -46.9
N(KN) -3588.3 -3638.3 -4690.3 4604.3 -2366.2 -4756.0 4604.3 -2366.2 -4756.0
V(KN) 4602.5 4227.8 5398.3 -2274.7 1312.7 5068.6 -2274.7 1312.7 5068.6
1,3,6,7 1,2,4,5 1,2,3,5,71,3,6,7,9,13,
15, 16
1,2,4,5,8,11,
141,2,3,5,7,9,13
1,3,6,7,9,13,
15, 16
1,2,4,5,8,11
,141,2,3,5,7,9,13
M(KN.m) 1932.6 -6765.2 -574.2 6659.6 -11070.4 -46.9 6659.6 -11070.4 -46.9
N(KN) -3588.3 -3638.3 -4690.3 4604.3 -2366.2 -4756.0 4604.3 -2366.2 -4756.0
V(KN) 4602.5 4227.8 5398.3 -2274.7 1312.7 5068.6 -2274.7 1312.7 5068.6
1, 16 1,2,3,4,5 1,2,3,5,71,6,7,9,13,
15, 16
1,2,3,4,5,8,1
11,2,3,5,7,9,13
1,6,7,9,13,
15, 16
1,2,3,4,5,8,
111,2,3,5,7,9,13
M(KN.m) 7668.9 -48857.5 -44172.3 32879.7 -49169.9 -41198.1 32879.7 -49169.9 -41198.1
N(KN) 3608.3 -4796.6 -5056.6 5102.8 -4294.4 -5107.2 5102.8 -4294.4 -5107.2
V(KN) -1720.6 9312.4 9062.2 -6043.3 9089.2 8580.4 -6043.3 9089.2 8580.4
1, 16 1,2,3,4,5 1,2,4,5,71,6,7,8,11,14
, 16
1,2,3,4,5,9,1
31,2,4,5,7,9,13
1,6,7,8,11,1
4, 161,2,3,4,5 1,2,4,5,7,9,13
M(KN.m) 9420.4 -53305.3 -50032.3 32460.2 -51518.5 -48572.9 32460.2 -53305.3 -48572.9
N(KN) 3732.4 -5540.0 -5923.2 3306.1 -6262.4 -6607.4 3306.1 -5540.0 -6607.4
V(KN) 1944.1 -9779.6 -9584.2 4481.1 -9364.1 -9188.2 4481.1 -9779.6 -9188.2
1,14 1,2,3,5,7 1,2,4,5,71,4,6,8,11,14
, 16
1,2,3,5,7,9,1
3, 151,2,4,5,7,9,13
1,4,6,8,11,1
4, 16
1,2,3,5,7,9,
13, 151,2,4,5,7,9,13
M(KN.m) 5612.5 -7899.6 -3287.1 11735.4 -9580.2 -3756.4 11735.4 -9580.2 -3756.4
N(KN) -1658.3 -4487.9 -5556.9 2903.3 -4142.4 -6256.2 2903.3 -4142.4 -6256.2
V(KN) -1053.2 -4353.0 -5920.3 1558.1 -1956.8 -5676.4 1558.1 -1956.8 -5676.4
1,14 1,2,3,5,7 1,2,4,5,71,4,6,8,11,14
, 16
1,2,3,5,7,9,1
3, 151,2,4,5,7,9,13
1,4,6,8,11,1
4, 16
1,2,3,5,7,9,
13, 151,2,4,5,7,9,13
M(KN.m) 5612.5 -7899.6 -3287.1 11735.4 -9580.2 -3756.4 11735.4 -9580.2 -3756.4
N(KN) -1658.3 -4487.9 -5556.9 2903.3 -4142.4 -6256.2 2903.3 -4142.4 -6256.2
V(KN) -1053.2 -4353.0 -5920.3 1558.1 -1956.8 -5676.4 1558.1 -1956.8 -5676.4
1,4,5 1, 16 1,2,4,5,7 1,4,5,8,111,2,3,6,7,9,1
3, 15, 161,2,4,5,7,9,13 1,4,5,8,11
1,2,3,6,7,9,
13, 15, 161,2,4,5,7,9,13
M(KN.m) 26738.6 -3115.4 25355.7 26936.7 -12654.5 23717.9 26936.7 -12654.5 23717.9
N(KN) -4349.2 4321.6 -4915.7 -5113.0 3521.9 -5641.6 -5113.0 3521.9 -5641.6
V(KN) 434.9 -432.2 491.6 606.3 -1405.7 469.2 606.3 -1405.7 469.2
INTERNAL FORCE DESIGN
ELEMENT SECTIONINTERNAL
FORCE
LOAD COMBINATION 1 LOAD COMBINATION 2
B1
START
0m
END
6,03m
B2
START
0m
END
9,04m
B3
START
0m
END
9,04m
B4
START
0m
END
6,03m
B5
START
0m
END
6,03m
B6
START
0m
END
10,55m
LOAD COMBINATION OF RAFTER
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 28
CHAPTER 5. PURLINS DESIGN.
TOLE DESIGN.
Properties.
This product is taken from Ngo Long Cor. catalogue
Sectional drawing:
Properties:
2
tolef = 2100 daN/cm và 3ρ = 7850 daN/m
Table below:
Total
coated
thickness
Single
span
Coating
weight
Rib
height
Moment
of inertia
x-x
Moment
of inertia
y-y
Section
modulus
x-x
Section
modulus
y-y
t (mm) L
(mm)
P
(daN/m2) h (mm)
Jx
(104 mm4)
Jy
(104 mm4)
Wx
(103 mm3)
Wy
(103 mm3)
0.3 1000 2,65 21 2,117 25000 1,623 500
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 29
Define load.
Self weight of tole is devided into 2 part gx and gy:
Normal load: tole
tc 2g = 2,65 (daN/m ) tc tc 2
y(tole)= g cosα = 2,65×0,995 = 2,64 (daN/m )
toleg
tc tc 2
x(tole)= p sinα = 2,65×0,1 = 0,27 (daN/m )
toleg
Design load:
tt tc 2( ) ( )g = ng =1,1×2,64 = 2,904 (daN/m )
y ytole tole
tt tc 2
( ) ( )g = ng = 1,1×0,27 = 0,3 (daN/m )
x xtole tole
Wind load: the most dangerous load case for tole is negative wind (c = -0.6):
gió
gió gió
tc 2
tt tc 2
q = W .c.k = 85×(-0,6)×1,09 = -55,59 (daN/m )
q =nq = 1,2 -55,59 = -66,71 (daN/m )
C
Live load:
Short-term load tc 2p = 30 daN/mroof is devided into 2 part px and py:
tc tc 2
y máip = p cosα = 30×0,995 = 29,85 (daN/m )
tc tc 2
x máip = p sinα = 30×0,1 = 3 (daN/m )
tt tc 2
y yp = np = 1,3×29,85 = 38,81 (daN/m )
tt tc 2
x xp = np = 1,3×3 = 3,9 (daN/m )
Design tole section.
Purlins spacing a = 1,1 m
Model of calculation: width of the section is supposed to be 1m to design:
These are the most dangerous load case is given below:
a) Load combination 1: Dead load and Wind load:
Check for allowable stress:
tt ttgió ( )q = q + g ×1 = -66,71 + 2,904 1= -69,61(daN/m)tt
y y tole
( )q = g 1= 0,3 1=0,3(daN/m)tt tt
x x tole
The value q 0,3 /tt
xdaN m is too small. Thus, it is neglected.
2 2q a -69,61×1,1M = = = -10,53 (daN.m)
8 8
tt
y
Section modulus at least:
3 3
yc x
c tole
M 10,53×100W = = = 0,55 (cm ) < W = 1,623 cm
γ f 0,9×2100
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 30
Allowable stress:
2 2
c
x
M 10,53×100σ = = =648,8(daN/cm ) < fγ = 0,9 2100=1890 daN/cm
W 1,623
This section is OK.
Check for displacement:
tc tc
gió ( )q = q + g ×1 = -55,59 + 2,64 1= -52,95(daN/m)tc
y y tole
( )q = g 1= 0,27 1=0,27(daN/m)tc tc
x x tole
The value q 0,27 /tt
xdaN m is too small. Thus it is neglected.
3 3
6
x
q aΔ 5 5 (52,95/100)×(1,1×100) 1 Δ 1= = × = < =
a 384 EI 384 2,1×10 ×2,117 484 a 150
tc
y
This section is OK.
b) Load combination 2: Dead load and Wind load:
Check for allowable stress:
tt tt
( )q = g + p ×1 = 2,904 38,81 1= 41,71(daN/m)tt
y y tole y
tt tt
( )q = g + p ×1 = 0,3 3,9 1= 4,2(daN/m)tt
x x tole x
Moment: 2 2q a 41,71×1,1
M = = = 6,31 (daN.m)8 8
tt
y
x
2 2q a 4,2×1,1M = = = 5,08 (daN.m)
8 8
tt
xy
Allowable stress:
y 2x
max x y
x y
2
c
MM 6,31 100 5,08 100σ = σ + σ = + = + =389,8 (daN/cm )
W W 1,623 500
< fγ =1890 daN/cm
This section is OK.
Check for displacement:
tc tc
( )q = g + p ×1 = 3 29,85 1= 32,85(daN/m)tc
y y tole y
tc tc
(t )q = g + p ×1 = 0,27 2,64 1= 2,91(daN/m)tc
x x ole x
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 31
2222 tc 3 tc 3y yx x
x
2 23 3
6 6
Δ q aΔ q aΔ 5 5 = + = +
a a a 384 EI 384 EI
32,85 /100 1,1 100 2,91/100 1,1 1005 5 1 Δ 1= + =
384 2,1×10 ×2,117 384 2,1×10 ×25000 781 a 150
y
This section is OK.
PURLINS DESIGN.
Properties. According to vvvTra co Cor. catalogue
Chose steel C15015
4 3
4 3
4,44 /
353 ; 34,7
39,6 ; 7,17
xg
x x
y y
g daN m
I cm W cm
I cm W cm
Load impact.
Purlins self weight: tc
y(xg) xgg = g cosα = 4,44×0,995 = 4,42 (daN/m)
tc
x(xg) xgg = g sinα = 4,44×0,1 = 0,444 (daN/m)
tt tc
y(xg) yg = ng = 1,1×4,42= 4,86(daN/m)
tt tc
x(xg) xg = ng = 1,1×0,444 = 0,488(daN/m)
Tole self weight:
tc tc
tole toleq = ag = 1,1×2,65 = 2,92 (daN/m) tc tc
y(tole)= q cosα = 2,92×0,995 = 2,91 (daN/m)
toleq
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 32
tc tc
x(tole)= q sinα = 2,92×0,1 = 0,29(daN/m)
toleq
tt tc
( ) ( )= nq = 1,1×2,91 = 3,2 (daN/m)y ytole toleq
tt tc
( ) ( )= nq = 1,1×0,29 = 0,32 (daN/m)
x tole x toleq
Wind load: the most dangerous load case for tole is negative wind (c = -0.6).
gió
gió gió
tc
tt tc
q = W .c.k.a = 85×(-0,6)×1,09 1,1 = -61,15 (daN/m)
q =nq = 1,2 -61,15 = -73,38 (daN/m)
C
Short-term load tc 2p = 30 daN/mroof is devided into 2 part px and py:
tc tc
y máip = p .a.cosα = 30 1,1 0,995 = 32,84(daN/m)
tc tc
x máip = p .a.sinα = 30 1,1 0,1 = 3,3(daN/m)
tt tc
y yp = np = 1,3×32,84 = 42,69(daN/m)
tt tc
x xp = np = 1,3×3,3 = 4,29(daN/m)
Purlins design.
Model of calculation: pinned beam.
These are the most dangerous load case is given below:
a) Load combination 1: Dead load and Wind load:
Check for allowable stress: tt tt tt tt
y y(tole) y(xg) gióq = (q + g ) + q = 4,86 + 3,87 +(-73,38) = -64,65 (daN/m)
tt tt tt
x(tole) x(xg)q = (q + g ) = 0,32 + 0,488 = 0,81 (daN/m)
x
Moment: 2 2q -64,65×6,5
M = = = -341,4 (daN.m)8 8
tt
y
x
B
2 2q 0,81×6,5M = = = 4,28 (daN.m)
8 8
tt
xy
B
Allowable stress:
y 2x
max x y
x y
2
c
MM 341,4 100 4,28 100σ = σ + σ = + = + =1042,4 (daN/cm )
W W 34,7 7,17
< fγ =1890 daN/cm
This section is OK
Check for displacement: tc tc tc tc
y y(tole) y(xg) gióq = (q + g ) + q = 2,91 + 4,42 +(-61,15) = -53,82 (daN/m)
tc tc tc
x(tole) x(xg)q = q + g = 0,29 + 0,444 = 0,734 (daN/m)
x
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 33
2 22 tc 3 tc 32
y xyx
x
2 23 3
6 6
q qΔΔ Δ 5 5 = + = +
384 EI 384 EI
53,82 /100 6,5 100 0,734 /100 6,5 1005 5 1= +
384 2,1×10 ×353 384 2,1×10 ×39,6 382
Δ 1 =
a 150
y
B B
B B B
This section is OK.
b) Load combination 2: Dead load and Wind load:
Checking for allowable stress: tt tt tt tt
y y(tole) y(xg)q = (q + g ) + p = 3,2 + 4,86 +42,69 = 50,75 (daN/m)
y
tt tt tt
x(tole) x(xg)q = (q + g ) + p = 0,32 + 0,488 + 4,29 = 5,098 (daN/m)tt
x x
Moment: 2 2q 50,75×6,5
M = = =268,02 (daN.m)8 8
tt
y
x
B
2 2q 5,098×6,5M = = = 26,92 (daN.m)
8 8
tt
xy
B
Allowable stress:
y 2x
max x y
x y
2
c
MM 268,02 100 26,92 100σ = σ + σ = + = + =1147,85 (daN/cm )
W W 34,7 7,17
< fγ =1890 daN/cm
This section is OK.
Check for displacement: tc tc tc tc
y y(tole) y(xg)q = (q + g ) + p = 2,91 + 4,42 + 32,84 = 40,17(daN/m)
y
tc tc tc
x(tole) x(xg)q = q + g + p = 0,29 + 0,444 + 3,3 = 4,034 (daN/m)tc
x x
2222 tc 3 tc 3y yx x
x
2 23 3
6 6
Δ qΔ Δ 5 5 q = + = +
384 EI 384 EI
40,17 /100 6,5 100 4,034 /100 6,5 1005 5 1= +
384 2,1×10 ×353 384 2,1×10 ×39,6 384
Δ 1 =
a 150
y
B B
B B B
This section is OK.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 34
DESIGN CONECTION BETWEEN TOLE AND PURLINS.
Spacing screw, bđv = 500 mm.
Chose screw has properties is as follow: d = 5.5 mm; ftb = 1700 (daN/cm2),
fvb = 1500 (daN/cm2), fcb = 3950 (daN/cm2).
Area force pressure impact on screw: 21,1 0,5 0,55đvA ab m
Load combination 1: Dead load and Wind load:
Tension force:
tt tt
gió y(tole)q 0,55 66,71 2,904 35,09tN A g daN
2 23,14 0,55
35,09 1700 403,694 4
t t bn tb tb
dN daN N A f f daN
This screw is OK.
Load combination 2: Dead load and Wind load:
Load ( )
tt tt
x tole xg p cause shear and bearing failure
tt
x(tole) ( ) 0,55 0,3 0,3 0,33tt
x htN A g p daN
Shear strength and bearing strength of screw:
2
min
3,14 0,551 0,9 1500 320,57
4
0,55 0,03 3950 0,9 58,66
v b vbvb
cb bcb
N n f A daN
N d t f daN
min
58.66N daN
So min
0,33 58,66N daN N daN
This screw is OK.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 35
DESIGN CONECTION BETWEEN PURLINS AND RAFTER:
Figure is as follow:
a) Load combination 1: Dead load and Wind load: tt tt tt tt
y y(tole) y(xg) gióq = (g + g ) + q = 2,904 + 4,86 + (-73,38) = -65,62 (daN/m)
tt tt tt
x(tole) x(xg)q = (g + g ) = 0,3 + 0,488 = 0,788 (daN/m)
x
b) Load combination 2: Dead load and Wind load: tt tt tt tt
y y(tole) y(xg)q = (q + g ) + p = 2,094 + 4,86 +42,69 = 49,64 (daN/m)
y
tt tt tt
x(tole) x(xg)q = (g + g ) + p = 0,3 + 0,488 + 4,29 = 5,08 (daN/m)tt
x x
tt
xq causing shear and moment for fillet weld conected plate purlin and rafter is
neglected.
tt
yq causing shear and bearing to bolts. Load combination 1 is more dangerous
than 2 one.
6,5 65,62 426,53tt
yN B q daN
Properties of bolt 4.6 ftb = 1700 (daN/cm2), fvb = 1500 (daN/cm2), fcb = 3950
(daN/cm2) - steel CCT34. Chose bolt’s diameter d = 14mm.
Shear strength and bearing strength of bolt:
2
min
3,14 1,41 0,9 1500 2077,11
4
1,4 0,49 3950 0,9 2438,73
v b vbvb
cb bcb
N n f A daN
N d t f daN
min
2077,11N daN
So min
426,53 2077,11N daN N daN . According to geometry
requirement, bolts are located as figure below.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 36
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 37
CHAPTER 6. RAFTER DESIGN
DESIGN THE START SECTION OF RAFTER B1.
Section dimention.
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof:
M(daN.m) -34735.6
N(daN) -4986.7
VdaN) -8443.5
This force is at section (4) is caused by these load cases 1, 2, 3, 5, 6,7.
Section molulus is given as follow :
334735,6 100
1837,9 ( )0,9 2100
yc
x
c
MW cm
f
Preliminary height:
335,5 W 5,5 1837,9 67,37yc
xh cm
The smallest rafter height (model of calculation: pinned restraint):
min 6
5 5 2100 1500250 67,9
24 24 2,1 10 1,15tb
f l lh cm
E
Limit deflection: 1
250l
, take γtb = 1,15
Preliminary thickness of web: assume w minh h
maxw
3 3 8443,50,16
2 2 67,9 1200w v
Vt cm
h f
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 38
tw is too small if using this formula. tw should be calculated follow shear
buckling of plate girder web: 6
w
w
2,1 103,2 3,2 101,19
2100
h E
t f
w
67,90,67
101,19t cm .
Chose tw = 1 (cm)
The effective height:
w
W 1837,91,2 51,44
1
yc
xkth k cm
t
k = 1,2 – coefficient factor.
Chose: h = 70 (cm) > hmin = 67,9 (cm)
Define flange dimention (bf và tf)
Flange area:
2W3 3 1873,920,08
4 4 70
yc
xfA cm
h
From local and over all buckling, formula is given below:
w
6
; 12 24
2,1 1031,62
2100
1 1 1 1700 140 350 ; 180
2 5 2 5
f f
f
f
f f
t t t mm
b E
t f
b h mm b mm
Chose tf = 1,4 (cm), bf = 35 (cm)
Checking section.
a) Properties of section.
Section area: 2 2 2 1 67,2 2 35 1,4 165,2( )n w f w w f fA A A t h b t cm
Moment of inertia relative to axis x-x:
3 2 3 3 2 3
w ww
4
. 35 1,4 68,6 1 67,22 2 . 2 35 1,4
12 4 12 12 4 12
140600,73
f f f
x x f f
b t h t hI I I b t
cm
Modulus of section:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 39
32 2 140600,73 4017,16 ( )
70
xx
IW cm
h
Statical moment of flange area:
368,6. . 1,4 35 1680,7
2 2
f
f f f
hS t b cm
Statical moment of ½ area:
w w wx
3
68,6 1 67,2 67,21,4 35
2 2 4 2 2 4
2245,18
f
f w f f
h t h hS S S t b
cm
b) Checking for allowable stress:
2
2
4986,7 34735,6 100 894,87 /
165,2 4017,16
2100 0.9 1890 /
x
n x
c
N MdaN cm
A W
f daN cm
This section is OK.
Checking for allowable shear stress:
20,9 1200 1080 /x
c v
x w
VSf daN cm
I t
2 28443,5 2245,18134,83( / ) 1080 /
140600,73 1
x
x w
VSdaN cm daN cm
I t
This section is OK.
The start rafter section is concurrent impacted by shear and moment. Thus,
allowable stress need to be stratified this formula below: 2 2 2
1 1 3 1,15 1,15 0,9 2100 2173,5 ( / )
td cf daN cm
Where:
2w
1
x
M h 34735,6 100 67,2σ = = × = 830,1(daN/cm )
W h 4017,16 70
2
1
8443,5 1680,7100,93( / )
140600,73 1
f
x w
VSdaN cm
I t
2 2 2 2 2 2
td 1 1σ = σ + 3τ = 830,1 + 3×100,93 = 848,3 (daN/cm ) < 2173.5 (daN/cm )
This section is OK
Because of impacting of purlin so rafter need to be checked by local buckling
limit:
2
cb
cb w z
F Fσ = = 0,9 2100 1890 /
A t lcf daN cm
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 40
Where:
F – impact of purlin on rafter.
c) Load combination 1: Dead load and Wind load: tt tt tt tt
y y(tole) y(xg) gióq = (q + g ) + q = 4,86 + 3,87 +(-73,38) = -64,65 (daN/m)
tt tt tt
x(tole) x(xg)q = (q + g ) = 0,32 + 0,488 = 0,81 (daN/m)
x
d) Load combination 2: Dead load and Live load: tt tt tt tt
y y(tole) y(xg)q = (q + g ) + p = 3,2 + 4,86 +42,69 = 50,75 (daN/m)
y
tt tt tt
x(tole) x(xg)q = (q + g ) + p = 0,32 + 0,488 + 4,29 = 5,098 (daN/m)tt
x x Load combination 2 cause local web buckling in rafter (neglect qx
tt).
. 50,75 6,5 329,88( )tt
yF q B daN
lz – is fictitious length of load distribution determined depending on condition
of leaning.
2 8 2 1,4 10,8z f
l b t cm
2 2329,88 30,54 / 1890 /
1 10,8cb
w z
FdaN cm daN cm
t l
This section is OK
Checking for normal stress, shear stress and local buckling of web.
2 2 2 2
1 1 1 - 3 1,15 1,15 0,9 2100 2173,5 ( / )
td cb cb cf daN cm
2
1
2
1
2
830,1( / )
100,93( / )
30,54 /cb
daN cm
daN cm
daN cm
2 2 2 2
2
830,1 30,54 -830,1 30,54 3 100,93 833,79 /
< 2173,5 ( / )
td
td
daN cm
daN cm
This section is OK.
e) Checking for over all buckling:
Top flange connect to purlins, with purlins spacing is 1,1 (m).
So:
0 11003,143
350f
l
b
Maximum value of 0
f
l
b:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 41
6
0,41 0,0032 0,73 0,016
35 35 35 2,1 100,41 0,0032 0,73 0,016 20,82
1,4 1,4 68,6 2100
f f fo
f f f fk
b b bl E
b t t h f
o o
f f
l l
b b
so non checking.
f) Checking for local buckling of flange and web:
Flange: 635 1 2,1 10
12,14 0,5 0,5 15,812 1,4 2100
of
f
b E
t f
This section is OK.
Web:
Slender ratio of web
ww 6
w
67,2 21002,125
1 2,1 10
h f
t E
w w2,125 3.2 web without stiffeners is not buckling by shear.
Acctually, there is local buckling occur in top flange of rafter but it is doesn’t
mean so it is necglected. According to section 5.6.1.3 TCVN 5575 – 2012,
local buckling web do not need to check.
g) Calculating fillet weld connected between flange and web:
As rafter bending, flange slip on web and fillet weld is created to prevent
sliping.
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
2
w wmin
. 0,7 2000 1400 /
. 1 1530 1530 /
. 1400 /
f f
s
f f
f daN cm
f daN cm
f f daN cm
The height of the fillet weld:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 42
w min
.S 8443,5 1680,70,04
2 . . 2 1400 140600,73 0,9
f
f
x c
Vh cm
f I
The height of the fillet weld follow above formula is too small so it should be
calculated by following formula:
min
min
1.2 1,2 10 12
5
f
f f
h t mm
h h mm
Chosse hf = 6 (mm) along longitudinal rafter.
DESIGN SECTION AT THE END OF D1 – BEGIN OF D2.
Section dimension.
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof:
M(daN.m) -8023,6
N(daN) -3083,0
V(daN) -3672,2
This force is at section (5) is caused by these load cases 1, 2, 4, 6, 8, 11.
Section molulus is given as follow:
38023,6 100424,53( )
0,9 2100
yc
x
c
MW cm
f
Section varies by the height so other values should be constant:
tw = 1 (cm)
tf = 1,4 (cm)
bf = 35 (cm)
The effective height:
w
W 424,531,2 24,72
1
yc
xkth k cm
t
k = 1,2 – coefficient factor.
Chose h = 40 (cm)
Check tw:
maxw
6
w
w
3 3 3672,21 0,12
2 2 37,2 1200
37,2 2,1 1037,2 3,2 3,2 101,19
1 2100
w v
Vt cm cm
h f
h E
t f
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 43
This section is OK
Checking section.
a) Properties of section.
Section area: 2 2 1 37,2 2 35 1,4 135,2( )w f w w f fA A A t h b t cm
Moment of inertia relative to axis x-x:
3 2 3 3 2 3
w ww
4
. 35 1,4 38,6 1 37,22 2 . 2 35 1,4
12 4 12 12 4 12
40809,93
f f f
x x f f
b t h t hI I I b t
cm
Modulus of section:
32 2 40809,93 2040,50 ( )
40
xx
IW cm
h
Statical moment of flange area:
338,6. . 1,4 35 945,7
2 2
f
f f f
hS t b cm
Statical moment of ½ area:
w w wx
3
38,6 1 37,2 37,21,4 35
2 2 4 2 2 4
1118,68
f
f x f f
h t h hS S S t b
cm
b) Checking for allowable stress.
2
2
3083 8023,6 100 416,02 /
135,2 2040,50
2100 0,9 1890 /
x
n x
c
N MdaN cm
A W
f daN cm
This section is OK.
Checking for allowable shear stress:
20,9 1200 1080 /x
c v
x w
VSf daN cm
I t
2 22672,2 1118,6873,25( / ) 1080 /
40809,93 1
x
x w
VSdaN cm daN cm
I t
This section is OK.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 44
The start rafter section is concurrent impacted by shear and moment. Thus,
allowable stress need to be stratified this formula below: 2 2 2
1 1 3 1,15 1,15 0,9 2100 2173,5 ( / )
td cf daN cm
Where:
2w
1
x
M h 8023,6 100 37,2σ = = × = 365,69 (daN/cm )
W h 2040,50 40
2
1
3672,2 945,785,1( / )
40809,93 1
f
x w
VSdaN cm
I t
2 2 2 2 2 2
td 1 1σ = σ + 3τ = 365,69 +3×85,1 = 394,28 (daN/cm ) < 2173,5 (daN/cm )
This section is OK.
Because of impacting of purlin so rafter need to be checked by local buckling
limit:
2
cb
cb w z
F Fσ = = 0,9 2100 1890 /
A t lcf daN cm
Where:
F – impact of purlin on rafter.
c) Load combination 1: Dead load and Wind load: tt tt tt tt
y y(tole) y(xg) gióq = (q + g ) + q = 4,86 + 3,87 +(-73,38) = -64,65 (daN/m)
tt tt tt
x(tole) x(xg)q = (q + g ) = 0,32 + 0,488 = 0,81 (daN/m)
x
d) Load combination 2: Dead load and Live load: tt tt tt tt
y y(tole) y(xg)q = (q + g ) + p = 3,2 + 4,86 +42,69 = 50,75 (daN/m)
y
tt tt tt
x(tole) x(xg)q = (q + g ) + p = 0,32 + 0,488 + 4,29 = 5,098 (daN/m)tt
x x Load combination 2 cause local web buckling in rafter (neglect qx
tt).
. 50,75 6,5 329,88( )tt
yF q B daN
lz – is fictitious length of load distribution determined depending on condition
of leaning.
2 8 2 1,4 10,8z f
l b t cm
2 2329,88 30,54 / 1890 /
1 10,8cb
w z
FdaN cm daN cm
t l
This section is OK.
Checking for normal stress, shear stress and local buckling of web.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 45
2 2 2 2
1 1 1 - 3 1,15 1,15 0,9 2100 2173,5 ( / )
td cb cb cf daN cm
2
1
2
1
2
365,69( / )
85,1( / )
30,54 /cb
daN cm
daN cm
daN cm
2 2 2 2
2
365,69 30,54 -365,69 30,54 3 85,1 381,08 /
< 2173,5 ( / )
td
td
daN cm
daN cm
This section is OK.
e) Checking for over all buckling:
Top flange connect to purlins, with purlins spacing is 1,1 (m).
So:
0 11003,143
350f
l
b
Maximum value of 0
f
l
b:
6
0,41 0,0032 0,73 0,016
35 35 35 2,1 100,41 0,0032 0,73 0,016 24,96
1,4 1,4 38,6 2100
f f fo
f f f fk
b b bl E
b t t h f
o o
f f
l l
b b
so non checking.
f) Checking for local buckling of flange and web:
Flange: 617 2,1 10
12,14 0,5 0,5 15,811,4 2100
of
f
b E
t f
This section is OK.
Web:
Slender ratio of web
ww 6
w
37,2 21001,18
1 2,1 10
h f
t E
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 46
w w1,18 3,2 web without stiffeners is not buckling by shear.
Acctually, there is local buckling occur in top flange of rafter but it is doesn’t
mean so it is necglected. According to section 5.6.1.3 TCVN 5575 – 2012,
local buckling web do not need to check.
g) Calculating fillet weld connected between flange and web:
As rafter bending, flange slip on web and fillet weld is created to prevent
sliping.
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
2
w wmin
. 0,7 2000 1400 /
. 1 1530 1530 /
. 1400 /
f f
s
f f
f daN cm
f daN cm
f f daN cm
The height of the fillet weld:
w min
.S 3672,2 945,70,034
2 . . 2 1400 40809,93 0,9
f
f
x c
Vh cm
f I
The height of the fillet weld follow above formula is too small so it should be
calculated by following formula:
min
min
1.2 1,2 10 12
5
f
f f
h t mm
h h mm
Chosse hf = 6 (mm) along longitudinal rafter.
DESIGN SECTION AT THE END OF D2 – SECTION (6).
Section dimension.
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof:
M(daN.m) 24311.4
N(daN) -3838.0
V(daN) 718.6
This force is at section (6) is caused by these load cases 1, 2, 3, 6.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 47
Section molulus is given as follow:
324311,4 100
1286,32( )0,9 2100
yc
x
c
MW cm
f
Section varies by the height so other values should be constant:
tw = 1 (cm)
tf = 1,4 (cm)
bf = 35 (cm)
The effective height:
w
W 1286,321,2 43,04
1
yc
xkth k cm
t
k = 1,2 – coefficient factor.
Chose h = 50 (cm)
Check tw:
maxw
6
w
w
3 3 718,61 0,02
2 2 47,2 1200
47,2 2,1 1047,2 3,2 3,2 101,19
1 2100
w v
Vt cm cm
h f
h E
t f
This section is OK.
Checking section.
a) Properties of section.
Section area: 2 2 1 47,2 2 35 1,4 145,2( )w f w w f fA A A t h b t cm
Moment of inertia relative to axis x-x:
3 2 3 3 2 3
w ww
4
. 35 1,4 48,6 1 47,22 2 . 2 35 1,4
12 4 12 12 4 12
66646,86
f f f
x x f f
b t h t hI I I b t
cm
Modulus of section:
32 2 66646,862665,87 ( )
50
xx
IW cm
h
Statical moment of flange area:
348,6. . 1,4 35 1190,70
2 2
f
f f f
hS t b cm
Statical moment of ½ area:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 48
w w wx
3
48,6 1 47,2 47,21,4 35
2 2 4 2 2 4
1469,18
f
f x f f
h t h hS S S t b
cm
b) Checking for allowable stress.
2
2
3838 24311,4 100 938,4 /
145,2 2665,87
2100 0,9 1890 /
x
n x
c
N MdaN cm
A W
f daN cm
This section is OK.
Checking for allowable shear stress:
20,9 1200 1080 /x
c v
x w
VSf daN cm
I t
2 2718,6 469,185,06( / ) 1080 /
66646,86 1
x
x w
VSdaN cm daN cm
I t
This section is OK.
The start rafter section is concurrent impacted by shear and moment. Thus,
allowable stress need to be stratified this formula below: 2 2 2
1 1 3 1,15 1,15 0,9 2100 2173,5 ( / )
td cf daN cm
Where:
2w
1
x
hM 24311,4 100 47,2σ = = × = 860,88 (daN/cm )
W h 2665,87 50
2
1
718,6 1190,712,84( / )
66646,86 1
f
x w
VSdaN cm
I t
2 2 2 2
td 1 1
2
σ = σ + 3τ = 860,88 +3×12,84 = 1547,37 (daN/cm )
< 2173,5 (daN/cm )
This section is OK.
Because of impacting of purlin so rafter need to be checked by local buckling
limit:
2
cb
cb w z
F Fσ = = 0,9 2100 1890 /
A t lcf daN cm
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 49
Where:
F – impact of purlin on rafter.
c) Load combination 1: Dead load and Wind load tt tt tt tt
y y(tole) y(xg) gióq = (q + g ) + q = 4,86 + 3,87 +(-73,38) = -64,65 (daN/m)
tt tt tt
x(tole) x(xg)q = (q + g ) = 0,32 + 0,488 = 0,81 (daN/m)
x
d) Load combination 2: Dead load and Live load tt tt tt tt
y y(tole) y(xg)q = (q + g ) + p = 3,2 + 4,86 +42,69 = 50,75 (daN/m)
y
tt tt tt
x(tole) x(xg)q = (q + g ) + p = 0,32 + 0,488 + 4,29 = 5,098 (daN/m)tt
x x
Load combination 2 cause local web buckling in rafter (neglect qxtt).
. 50,75 6,5 329,88( )tt
yF q B daN
lz – is fictitious length of load distribution determined depending on condition
of leaning.
2 8 2 1,4 10,8z f
l b t cm
2 2329,88 30,54 / 1890 /
1 10,8cb
w z
FdaN cm daN cm
t l
This section is OK.
Checking for normal stress, shear stress and local buckling of web. 2 2 2 2
1 1 1 - 3 1,15 1,15 0,9 2100 2173,5 ( / )
td cb cb cf daN cm
2
1
2
1
2
860,88( / )
12,84( / )
30,54 /cb
daN cm
daN cm
daN cm
2 2 2 2
2
860,88 30,54 -860,88 30,54 3 12,84 846,32 /
< 2173,5 ( / )
td
td
daN cm
daN cm
This section is OK.
e) Checking for over all buckling.
Top flange connect to purlins, with purlins spacing is 1,1 (m).
So:
0 11003,143
350f
l
b
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 50
Maximum value of 0
f
l
b:
6
0,41 0,0032 0,73 0,016
35 35 35 2,1 100,41 0,0032 0,73 0,016 23,01
1,4 1,4 48,6 2100
f f fo
f f f fk
b b bl E
b t t h f
o o
f f
l l
b b
so non checking.
f) Checking for local buckling of flange and web.
Flange: 617 2,1 10
12,14 0,5 0,5 15,811,4 2100
of
f
b E
t f
This section is OK.
Web:
Slender ratio of web
ww 6
w
47,2 21001,49
1 2,1 10
h f
t E
w w1,49 3,2 web without stiffeners is not buckling by shear.
Acctually, there is local buckling occur in top flange of rafter but it is doesn’t
mean so it is necglected. According to section 5.6.1.3 TCVN 5575 – 2012,
local buckling web do not need to check.
g) Calculating fillet weld connection:
As rafter bending, flange slip on web and fillet weld is created to prevent
sliping.
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
2
w wmin
. 0,7 2000 1400 /
. 1 1530 1530 /
. 1400 /
f f
s
f f
f daN cm
f daN cm
f f daN cm
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 51
The height of the fillet weld:
w min
.S 718,6 1190,70,0051
2 . . 2 1400 66646,86 0,9
f
f
x c
Vh cm
f I
The height of the fillet weld follow above formula is too small so it should be
calculated by following formula:
min
min
1,2 1,2 10 12
5
f
f f
h t mm
h h mm
Chosse hf = 6 (mm) along longitudinal rafter.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 52
8 9 10
M (daN.m) -53305.25 11735.427 26936.689
N (daN) -5539.99 2903.313 -5113.026
V (daN) -9779.56 1558.077 606.26
Pcb (daN) 329.88 329.88 329.88
h (cm) 80 40 50
hw (cm) 77.2 37.2 47.2
tw (cm) 1 1 1
tf (cm) 1.4 1.4 1.4
bf (cm) 35 35 35
hfk (cm) 78.6 38.6 48.6
bof (cm) 17 17 17
A (cm2) 175.2 135.2 145.2
Ix (cm4) 189717.66 40809.93 66646.86
Wx (cm3) 4742.94 2040.50 2665.87
Sf (cm3) 1925.70 945.70 1190.70
Sx (cm3) 2670.68 1118.68 1469.18
σxmax (daN/cm2) 1155.51 596.60 1045.64
γcf = 1890 (daN/cm2) OK OK OK
Τmax (daN/cm2) 137.67 42.71 13.36
γcfv = 1080(daN/cm2) OK OK OK
σ1 (daN/cm2) 1084.55 534.87 953.84
τ1 (daN/cm2) 99.27 36.11 10.83
σtd (σ1, τ1) (daN/cm2) 1098.09 538.51 954.03
1.15γcf = 2173.5 (daN/cm2) OK OK OK
σcb (daN/cm2) 42.29 42.29 42.29
γcf = 1890 (daN/cm2) OK OK OK
σtd (σ1, τ1, σcb) (daN/cm2) 1077.84 518.81 933.60
1.15γcf = 2173.5 (daN/cm2) OK OK OK
3.14 3.14 3.14
19.24 23.85 21.99
Condition OK OK OK
12.14 12.14 12.14
Condition OK OK OK
2.55 1.23 1.56
3.2 3.2 3.2
Non checking Non checking Non checking
hf (design) (mm) 0.39 0.14 0.04
hf (preliminary) (mm) 5 ≤ hf ≤ 12 5 ≤ hf ≤ 12 5 ≤ hf ≤ 12
hf (optimize) (mm) 6 6 6
CHECK FOR FLANGE
STABIITY
CHECK FOR WEB
STABILITY
CONECTION BETWEEN
FLANGE AND WEB
SECTION
INTERIAL FORCE
DIMENSION
SECTION PROPERTIES
CHECK FOR ULTIMATE
STRESS
CHECK FOR OVER ALL
STABILITY
o
f
l
b
o
f
l
b
of
f
b
t
ww
w
h f
t E
w
DESIGN SECTION OF RAFTER D5 AND D6.
The design process is the same to D1 and D2 rafter, the table below:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 53
CHAPTER 7. COLUMN DESIGN
DESIGN STRAIGHT COLUMN C1.
Design length:
Length H = 14,2 m
Side span L1 = L3 = 30m.
a) In the plane frame:
Factors of design length for columns with constant section in the frame
plane at stiff fixing of collar beams to columns shall be determined by formula
of Table 17a according to SNiP II – 23 – 81.
Factor for extreme column of multi – span frame shall be determined as for
single – span frame column.
Formulars for determining factor :
b
c 1
I H 14,2n = 0,29 0,14
I L 30
Where: Ib – the smallest moment of inertia of rafter.
Ic – moment of inertia of column.
The factor of design lengh is given below:
n + 0,56 0,14 0,56μ = = 1,6
n + 0,14 0,14 0,14
Design length ler of columns (posts) with constant section or of separate
portions of stepped columns shall be determined by formula:
. 1,6 14,2 22,72xl H m
b) Out of the frame plane:
Design lengths of columns in the direction along the buildings length (out of
frame planes) shall be adopted equal to distances between points fixed
fromshifting out of the frame plane (column supports, crane and eaves girders;
joints of braces' and collar beams' fixing, etc.). Design lengths may be
determined onthe basis of design schemes which consider actual type of
columns' fixing.
Setting wide – flange steel bracing system at level code +6,35 m.
Design length: yl = 7(m)
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 54
Section dimension.
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof |N|max:
M(daN.m) -22677.0
N(daN) -14001.2
VdaN) -4036.1
This force is at base column section is caused by these load cases 1, 2, 3, 6, 7.
The height of column section:
1 1 1 114200 (568 947)mm
15 25 15 25h H
Chose h = 700 mm
The width of flange of column section is chosen follow geometry:
350
1 1 1 1 7000 350 250
20 30 20 30
0,3 0,5 0,3 0,5 700 210 350
f
f y
f
b mm
b l mm
b h mm
Chose bf = 350 mm.
According to formula of Iasinky xc
x
N M + fγ
φA W , area section requirement
shall be conducted as follow:
x xyc
c x c x
M A MN 1 N 1A = + = +
fγ φ NW fγ φ ρ N
Preliminary φ = 0,8 and xρ = (0,35 ÷ 0,45)h :
2
14001,2 22677 1001,25 2,2 2,8 1,25 (2,2 2,8)
2100 0,9 70 14001,2
46,97 57,25
x
yc
c
MNA
f h N
cm
The thickness of flange and web column is chosen follow geometry:
1 1 1 1 2100
= 35 1,25 1 ( )28 35 2100 28 35 2100
f f
ft b cm
Chose tf = 1,4 (cm)
w
1 1 1 170 0,58 1,17
120 60 120 60
8
w
f
t h cm
cm t t
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 55
Chose tw = 1 (cm)
Checking section.
a) Properties of section.
Section area: 22 1 67,2 2 35 1,4 165,2 ( )w w f fA t h b t cm
Moment of inertia relative to axis x-x, y-y:
3 2 3 3 2 3
w ww
4
. 35 1,4 68,6 1 67,22 2 . 2 35 1,4
12 4 12 12 4 12
140600,73
f f f
x x f f
b t h t hI I I b t
cm
33 3 3
467,2 1 352 2 1,4 10009,77 ( )
12 12 12 12
fw wy f
bh tI t cm
Inertia radius of cross section relative to axes x-x, y-y:
xx
I 140600,73i = = = 29,17 (cm) ;
A 165,2
y
y
I 10009,77i = = = 7,78 (cm)
A 165,2
Modulus of section:
3xx
2I 2×140600,73W = = = 4017,16(cm )
h 70
Design flexibility in planes perpendicular to axes x-x and y-y:
xx
x
l 22,72 100λ = = = 77,89
i 29,17
x x 6
f 2100λ = λ =77,89× = 2,46
E 2,1×10
y
y
y
l 7,5×100λ = = = 96,4;
i 7,78
y y 6
f 2100λ = λ = 96,4 × = 3,05
E 2,1×10
max yλ = λ = 96,4 < λ = 165
Design flexibility [λ] of column is satisfied.
Relative eccentricity m and reduced relative eccentricity me:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 56
x
x
e A 22677 100 165,2m = = × = 6,7
W 14001,2 4017,16
M
N
According to Table 73 SNiP II-23-81, with f
w
A 2×1,4×35 = = 1,46 > 1
A 1×67,2;
x0 λ = 2,46 < 5 and 5 < m = 6,7 < 20 , factor of influence of cross section form
η is given as:
1,4 0,2 1,4 0,2 2,46 0,91x
e m = ηm = 0,91×6,7 =6,1
Coefficient e at reduced relative eccentricity 6,1em and fictitious flexibility
2,46x : 0,178e
Ultimate flexibility compression components:
180 60 180 60 0,25 165
where 14001,2
0,250,178 165,2 2100 0,9e c
N
Af
b) Checking for strength of eccentric compression.
According to Section 5.24 SNiP II-23-81: The strength analysis of
eccentrically compressed and compressed-and-bent components according to
formula (49) is not necessary when the value of reduced eccentricity
6,1 20em , the section weakening does not occur and the values of bending
moments used for strength and stability are equal.
c) Checking for stability in the plane of moment action.
The stability analysis of eccentric compression and compression-and-bending
components with constant section (with regard to requirements of Sections
5.28 and 5.33 of this Code) in the plane of the moment's action which
coincides with the symmetry plane, shall be conducted by formula:
x c
e
Nσ = fγ
φ A
Factor eφ in formula (51) shall be determined.
The internal force are calculating is at base section of column Mc = -22677
(daN.m), causing by load case 1, 2, 3, 6, 7.
2 2
x c
e
N 14001,2σ = = = 476,14 (daN/cm ) < γ f = 0,9 2100 =1890 daN/cm
φ A 0,178×165,2
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 57
This column is OK.
d) Checking for stability out of the moment action.
According to Section 5.30 SNiP II-23-81, The stability analysis of eccentric
compression components with constant section out of the moment action plane
at bending thereof in the plane of maximum stiffness (Jx > Jy ) coinciding with
the symmetry plane shall be executed by formula:
y c
y
Nσ = fγ
cφ A
Where:
yφ
is factor calculated according to requirements of Section 5.3 on this Code,
when 2,5 3,05 4,5y then yφ is given below:
2
2
1,47 13 (0,371 27,3 ) (0,0275 5,53 )
1,47 13 0,001 (0,371 27,3 0,001) 3,05 (0,0275 5,53 0,001) 3,05 0,61
y y y
f f f
E E E
c is factor calculated as required by Section 5.31.
When determining the relative eccentricity mx it is necessary to adopt as the
design moment Mx:
The maximum moment within the middle third of bar length (but not less than
the haft of the maximum moment along the bar length) for bars with hinged
bearing ends which are prevented from shifting perpendiculally to the plane of
moment’s action.
The internal force are calculating is at base section of column Mc = -22677
(daN.m), causing by load case 1, 2, 3, 6, 7, moment value at head column is
Md = 34635,9 (daN.m).
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 58
So:
1/3
34635,9 22677max ; ; max 15531,1; ; 17317,9 daN.m
2 2 2 2
d cx
M MM M
Relative eccentricity mx is defined by adopted moment Mx:
x
x
e A 17317,9 100 165,2m = = × = 5,09
W 14001,2 4017,16
x
x
M
N
For relative eccentricity 5 < mx = 5,09 < 10, by formula:
5 102 0,2 0,2 1x xc c m c m
c5 is determined at mx = 5:
51 x
cm
α and β are factors adopted according to Table 10:
When mx = 5 the factor 0,65 0,05 0,65 0,05 5 0,9xm
When 62,1 10
96,4 3,14 3,14 99,32100
y c
E
f
the factor β = 1.
So 5
10,181
1 1 0,9 5x
cm
c10 is determined at mx = 10:
10
1
1x y
b
cm
0,61y (as calculated)
bφ is factor determined as required by Section 5.15 and Appendix 7 as for a
beam with two or more fixings of compression chord; bφ = 1.0 for closed
sections.
For welded double-T sections composed of three sheets as well as for double-
T sections with chord joints on high strength bolts: 2 23 3
o f w
3
fk f f f
l t at 700 1,4 68,6 1α = 8 1 + = 8 1 1,81
h b b t 68,6 35 2 35 1,4
According to Table 77 formulas for at 0.1 1,81 40 :
2,25 0,07 2,25 0,07 1,81 2,4
1φ is given as follow:
2 2 6
1
10009,77 70 2,1 10 2,4 1,49
140600,73 700 2100
y
x o
I h E
I l f
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 59
φ1 > 0,851
1
0,68 0,21 0,68 0,21 1,49 0,99
b
b
Take φb = 0,99.
10
1 10,14
10 0,6111
0,99x y
b
cm
5 102 0.2 0,2 1 0,181 2 0,2 5,09 0,14 0,2 5,09 1 0,18x xc c m c m
So:
2 2
y c
y
N 14001,2σ = = = 771,89 / γ f = 0,9 2100 =1890 daN/cm
cφ A 0,18 0,61 165,2daN cm
This column is OK.
e) Checking for stability of flange and web.
For flange:
When analyzing centric and eccentric compression and compression - and
bending components with the fictitious flexibility equal to 0.8 to 4, the ratio
of design width of an overhang of chord sheets (flanges) be to thickness t shall
not exceed values determined by formulas of Table 29*:
62,1 10
0,36 0,1 0,36 0,1 2,46 19,22100
ob E
t f
Ratio:
0,5 (35 1)12,14
1,4
o
f
b
t
So:
12,14 19,2o o
f
b b
t t
This section is OK.
For web:
Checking by: w w
w w
h h
t t
.
In checking for stability:
2 2476,14 / 771,89 /x ydaN cm daN cm so the strength of this column
is mostly depend on moment’s action in the plane. Thus the slenderness ratio
[hw/tw] is given by Section 7.16 SNiP II-23-81 Code.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 60
14001,2 22677,1 100 67,2
550,42 165,2 140600,73 2
x w
x
M hN
A I
1
14001,2 22677,1 100 67,2533,44
2 165,2 140600,73 2
x w
x
M hN
A I
1
2 2
550,4 533,44 (2 1)1,97 1 4,35
550,4 2 4
w
w
h E
t
4036,11,4 (2 1) 1,4 (2 1) 1,4 (2 1,68 1) 0,36
67,2 1 550,4w w
V
h t
2 22 2
(2 1) (2 1,68 1) 21000004,35 4,35 281,66
550,4 2 1,68 1,68 4 0,362 4
21000003,8 3,8 120,17
2100
120.17
w
w
w
w
w
w
h E
t
h E
t f
h
t
Check:
w w
w w
h h67,2 = = 67,2 < = 120,17
t 1 t
This section is OK. In addition:
6
w
w
h 67,2 E 2,1×10 = = 67,2 < 2,3 = 2,3× = 72,73
t 1 f 2100
Web of this column need not be strengthend by lateral stiffening ribs.
Checking column at |M|max.
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof |M|max:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 61
M(daN.m) 34735.6
N(daN) -8897.8
VdaN) -4121.8
This force is at top of column section is caused by these load cases 1, 2, 3, 5,
6, 7.
Using dimension of calculated section.
But:
Relative eccentricity m and reduced relative eccentricity me:
x
x
e A 34735,6 100 165,2m = = × = 16,05
W 8897,8 4017,16
M
N
According to Table 73 SNiP II-23-81, with f
w
A 2×1,4×35 = = 1,46 > 1
A 1×67,2;
x0 λ = 2,46 < 5 and 5 < m = 6,7 < 20 , factor of influence of cross section form
η is given as:
1,4 0,2 1,4 0,2 2,64 0,87x
e m = ηm = 0,87×16,05 = 13,96
Coefficient e at reduced relative eccentricity 13.96em and fictitious
flexibility 2,64x : 0,098e
Ultimate flexibility compression components:
180 60 180 60 0,25 162.6
where 8897.8
0,290,098 165,2 2100 0,9e c
N
Af
max yλ = λ = 96.4< λ = 162.6
a) Checking for strength of eccentric compression.
According to Section 5.24 SNiP II-23-81: The strength analysis of
eccentrically compressed and compressed-and-bent components according to
formula (49) is not necessary when the value of reduced eccentricity
13.96 20em , the section weakening does not occur and the values of
bending moments used for strength and stability are equal.
b) Checking for stability in the plane of moment action.
The stability analysis of eccentric compression and compression-and-bending
components with constant section (with regard to requirements of Sections
5.28 and 5.33 of this Code) in the plane of the moment's action which
coincides with the symmetry plane, shall be conducted by formula:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 62
x c
e
Nσ = fγ
φ A
Factor eφ in formula (51) shall be determined.
The internal force are calculating is at top section of column Md = 34735,6
(daN.m), causing by load case 1, 2, 3, 5, 6, 7.
2 2
x c
e
N 8897,8σ = = = 549,6 (daN/cm ) < γ f = 0,9 2100 =1890 daN/cm
φ A 0,098×165,2
This section is OK.
c) Checking for stability out of the moment action.
According to Section 5.30 SNiP II-23-81, The stability analysis of eccentric
compression components with constant section out of the moment action plane
at bending thereof in the plane of maximum stiffness (Jx > Jy ) coinciding with
the symmetry plane shall be executed by formula:
y c
y
Nσ = fγ
cφ A
Where:
yφ
is factor calculated according to requirements of Section 5.3 on this Code,
when 2,5 3,05 4,5y then yφ is given below:
2
2
1,47 13 (0,371 27,3 ) (0,0275 5,53 )
1,47 13 0,001 (0,371 27,3 0,001) 3.05 (0,0275 5,53 0,001) 3,05 0,61
y y y
f f f
E E E
c is factor calculated as required by Section 5.31.
When determining the relative eccentricity mx it is necessary to adopt as the
design moment Mx:
The maximum moment within the middle third of bar length (but not less than
the haft of the maximum moment along the bar length) for bars with hinged
bearing ends which are prevented from shifting perpendiculally to the plane of
moment’s action.
The internal force are calculating is at top section of column Md = 34735,6
(daN.m) , causing by load case 1, 2, 3, 6, 7, 9, 13, moment value at base of
column is Mc = 29613,1 (daN.m).
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 63
So:
1/3
34735,6 29613,1max ; ; max 33028,1; ; 33028,1 daN.m
2 2 2 2
d cx
M MM M
Relative eccentricity mx is defined by adopted moment Mx:
x
x
e A 34735,1 100 165,2m = = × =16,05
W 8897,8 4017,16
x
x
M
N
For relative eccentricity mx = 16.05 > 10, by formula:
1
1x y
b
cm
Where:
bφ is factor determined as required by Section 5.15 and Appendix 7 as for a
beam with two or more fixings of compression chord; bφ = 1.0 for closed
sections.
For welded double-T sections composed of three sheets as well as for double-
T sections with chord joints on high strength bolts: 2 23 3
o f w
3
fk f f f
l t at 700 1,4 68,6 1α = 8 1 + = 8 1 1,81
h b b t 68,6 35 2 35 1,4
According to Table 77 formulas for at 0.1 1,81 40 :
2,25 0,07 2,25 0,07 1,81 2,4
1φ is given as follow:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 64
2 2 6
1
10009,77 70 2,1 10 2,4 1,49
140600,73 700 2100
y
x o
I h E
I l f
φ1 > 0,851
1
0,68 0,21 0,68 0,21 1,49 0,99
b
b
Take φb = 0,99.
So:
1 1
0 0916 05 0 61
110 99
.. .
.x y
b
cm
So:
2 2
y c
y
N 8897,8σ = = = 981,07 / γ f = 0,9 2100 =1890 daN/cm
cφ A 0,09 0,61 165,2daN cm
This column is OK.
d) Checking for stability of flange and web.
For flange:
When analyzing centric and eccentric compression and compression - and
bending components with the fictitious flexibility equal to 0.8 to 4, the ratio
of design width of an overhang of chord sheets (flanges) be to thickness t shall
not exceed values determined by formulas of Table 29*:
62,1 10
0,36 0,1 0,36 0,1 2,46 19,22100
ob E
t f
Ratio:
0,5 (35 1)12,14
1,4
o
f
b
t
So:
12,14 19,2o o
f
b b
t t
This section is OK.
For web:
Checking by: w w
w w
h h
t t
In checking for stability:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 65
2 2549,6 / 981,07 /x ydaN cm daN cm so the strength of this column
is mostly depend on moment’s action in the plane. Thus the slenderness ratio
[hw/tw] is given by Section 7.16 SNiP II-23-81 Code:
8897,8 34735,6 100 67,2883,95
2 165,2 140600,73 2
x w
x
M hN
A I
1
8897,8 34735,6 100 67,2776,23
2 165,2 140600,73 2
x w
x
M hN
A I
1
2 2
883,95 776,23 (2 1)1,88 1 4,35
883,95 2 4
w
w
h E
t
4121,81,4 (2 1) 1,4 (2 1) 1,4 (2 1,88 1) 0,27
67,2 1 883,95w w
V
h t
2 22 2
(2 1) (2 1,88 1) 21000004,35 4,35 77,3
883,95 2 1,88 1,88 4 0,272 4
21000003,8 3,8 120,17
2100
77,3
w
w
w
w
w
w
h E
t
h E
t f
h
t
Check:
w w
w w
h h67,2 = = 67,2 < = 77,3
t 1 t
This section is OK. In addition:
6
w
w
h 67,2 E 2,1×10 = = 67,2 < 2,3 = 2,3× = 72,73
t 1 f 2100
Web of this column need not be strengthend by lateral stiffening ribs.
DESIGN STRAIGHT COLUMN C2-C3.
Design length.
Length H = 14,2 m
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 66
Side span L1 = L3 = 30 (m), centre span L2 = 33 (m)
a) In the plane frame:
Factors of design length for columns with constant section in the frame
plane at stiff fixing of collar beams to columns shall be determined by formula
of Table 17a according to SNiP II – 23 – 81.
Factor for extreme column of multi – span frame shall be determined as for
single – span frame column.
Formulars for determining factor :
1 2( )
1
k n nn
k
Where:
k – the number of span, k = 3.
Side span L1 = 30 (m)
b
1
c 1
I H 15n = 0,29 0,15
I L 30
Centre span L2 = 33 (m)
b
2
c 2
I H 15n = 0,29 0,13
I L 33
Ib – the smallest moment of inertia of rafter.
Ic – moment of inertia of column.
1 2
2 0,15 0,13( )0,21
1 3 1
k n nn
k
The factor of design lengh is given below:
n + 0,56 0,21 0,56μ = = 1,49
n + 0,14 0,21 0,14
Design length ler of columns (posts) with constant section or of separate
portions of stepped columns shall be determined by formula:
. 1,49 14,2 21,16xl H m
b) Out of the frame plane:
Design lengths of columns in the direction along the buildings length (out of
frame planes) shall be adopted equal to distances between points fixed
fromshifting out of the frame plane (column supports, crane and eaves girders;
joints of braces' and collar beams' fixing, etc.). Design lengths may be
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 67
determined onthe basis of design schemes which consider actual type of
columns' fixing.
Setting wide – flange steel bracing system at level code +6,35 m.
Design length: yl = 7(m)
Section dimension.
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof |N|max:
M(daN.m) -4953.8
N(daN) -40638.8
VdaN) -1232.8
This force is at base column section is caused by these load cases trọng 1, 2, 3,
4, 5, 8, 11.
The height of column section:
1 1 1 114200 (947 568)mm
15 25 15 25h H
Chose h = 700 mm
The width of flange of column section is chosen follow geometry:
350
1 1 1 1 7000 350 230
20 30 20 30
0.3 0.5 0,3 0,5 700 210 350
f
f y
f
b mm
b l mm
b h mm
Chose bf = 350 mm.
According to formula of Iasinky xc
x
N M + fγ
φA W , area section requirement
shall be conducted as follow:
x xyc
c x c x
M A MN 1 N 1A = + = +
fγ φ NW fγ φ ρ N
Preliminary φ = 0,8 and xρ = (0,35 ÷ 0,45)h :
2
40638,8 4953,8 1001,25 2,2 2,8 1,25 (2,2 2,8)
2100 0,9 70 40638,8
35,11 37,36
x
yc
c
MNA
f h N
cm
The thickness of flange and web column is chosen follow geometry:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 68
1 1 1 1 2100
= 35 1,25 1 ( )28 35 2100 28 35 2100
f f
ft b cm
Chose tf = 1.4 (cm)
w
1 1 1 170 0,58 1,17
120 60 120 60
8
w
f
t h cm
cm t t
Chose tw = 1 (cm)
Checking section.
a) Properties of section.
Section area: 22 1 67.2 2 35 1.4 165.2 ( )w w f fA t h b t cm
Moment of inertia relative to axis x-x, y-y:
3 2 3 3 2 3
w ww
4
. 35 1.4 68.6 1 67.22 2 . 2 35 1.4
12 4 12 12 4 12
140600.73
f f f
x x f f
b t h t hI I I b t
cm
33 3 3
467.2 1 352 2 1.4 10009.17 ( )
12 12 12 12
fw wy f
bh tI t cm
Inertia radius of cross section relative to axes x-x, y-y:
xx
I 140600.73i = = = 29.17 (cm) ;
A 165.2
y
y
I 10009.77i = = = 7.78 (cm)
A 165.2
Modulus of section:
3xx
2I 2×140600.73W = = = 4017.16(cm )
h 70
Design flexibility in planes perpendicular to axes x-x and y-y:
xx
x
l 21.16 100λ = = = 72.54
i 29.17
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 69
x x 6
f 2100λ = λ =72.54× =2.29
E 2.1×10
y
y
y
l 7×100λ = = = 89.97 ;
i 7.78
y y 6
f 2100λ = λ = 89.97× = 2.85
E 2.1×10
max yλ = λ = 88.97< λ = 165.54
Design flexibility [λ] of column is satisfied
Relative eccentricity m and reduced relative eccentricity me:
x
x
e A 4953.8 100 165.2m = = × = 0.5
W 40638.8 4017.16
M
N
According to Table 73 SNiP II-23-81, with f
w
A 2×1,4×35 = = 1,46 > 1
A 1×67,2;
x0 λ = 2,46 < 5 and 5 < m = 6,7 < 20 , factor of influence of cross section form
η is given as:
1.90 0.1 0.02 6 1.90 0.1 0.5 0.02 (6 0.5) 2.29 1.59xm m
e m = ηm = 1.59 0.5=0.795
Coefficient e at reduced relative eccentricity 0.795em and fictitious
flexibility 2.29x : 0.539e
Ultimate flexibility compression components:
180 60 180 60 0.241 165.54
where 40638.8
0.2410.539 165.2 2100 0.9e c
N
Af
b) Checking for strength of eccentric compression.
According to Section 5.24 SNiP II-23-81: The strength analysis of
eccentrically compressed and compressed-and-bent components according to
formula (49) is not necessary when the value of reduced eccentricity
0.795 20em , the section weakening does not occur and the values of
bending moments used for strength and stability are equal.
c) Checking for stability in the plane of moment action.
The stability analysis of eccentric compression and compression-and-bending
components with constant section (with regard to requirements of Sections
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 70
5.28 and 5.33 of this Code) in the plane of the moment's action which
coincides with the symmetry plane, shall be conducted by formula:
x c
e
Nσ = fγ
φ A
Factor eφ in formula (51) shall be determined.
The internal force are calculating is at base section of column Mc = -4953.8
(daN.m), causing by load case 1, 2, 3, 4, 5, 8, 11.
2 2
x c
e
N 40638.8σ = = = 456.4 (daN/cm ) < γ f = 0.9 2100 =1890 daN/cm
φ A 0.539×165.2
This column is OK.
d) Checking for stability out of the moment action.
According to Section 5.30 SNiP II-23-81, The stability analysis of eccentric
compression components with constant section out of the moment action plane
at bending thereof in the plane of maximum stiffness (Jx > Jy ) coinciding with
the symmetry plane shall be executed by formula:`
y c
y
Nσ = fγ
cφ A
Where:
yφ
is factor calculated according to requirements of Section 5.3 on this Code,
when 2,5 3,05 4,5y then yφ is given below:
2
2
1.47 13 (0.371 27.3 ) (0.0275 5.53 )
1.47 13 0.001 (0.371 27.3 0.001) 2.85 (0.0275 5.53 0.001) 2.85 0.66
y y y
f f f
E E E
c is factor calculated as required by Section 5.31.
When determining the relative eccentricity mx it is necessary to adopt as the
design moment Mx:
The maximum moment within the middle third of bar length (but not less than
the haft of the maximum moment along the bar length) for bars with hinged
bearing ends which are prevented from shifting perpendiculally to the plane of
moment’s action.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 71
The internal force are calculating is at base section of column Mc = -4953.8
(daN.m) , causing by load case 1, 2, 3, 4, 5, 8, 11, moment value at head
column is Md = 9407.8(daN.m).
So:
1/3
9407.8 4953.8max ; ; max 4588.3; ; 4703.9 daN.m
2 2 2 2
d cx
M MM M
Relative eccentricity mx is defined by adopted moment Mx:
x
x
e A 4703.9 100 165.2m = = × = 0.47
W 40638.8 4017.16
x
x
M
N
For relative eccentricity mx = 0.47 < 5, by formula:
1 x
cm
α and β are factors adopted according to Table 10:
When mx = 0.47 <1 the factor 0.7
When 62.1 10
89.97 3.14 3.14 99.32100
y c
E
f
the factor β = 1.
So: 1
0.751 1 0.7 0.47x
cm
So:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 72
2
y
y
2
c
N 40638.8σ = = = 573,42 /
cφ A 0.65 0.66 165.2
γ f = 0.9 2100 =1890 daN/cm
daN cm
This column is OK.
e) Checking for stability of flange and web.
For flange:
When analyzing centric and eccentric compression and compression - and
bending components with the fictitious flexibility equal to 0.8 to 4, the ratio
of design width of an overhang of chord sheets (flanges) be to thickness t shall
not exceed values determined by formulas of Table 29*:
62.1 10
0.36 0.1 0.36 0.1 2.29 18.632100
ob E
t f
Ratio: 0.5 (35 1)
12.141.4
o
f
b
t
So:
12.14 18.63o o
f
b b
t t
This section is OK.
For web:
Checking by: w w
w w
h h
t t
In checking for stability:
2 2456.4 / 573.42 /x ydaN cm daN cm so the strength of this
column is mostly depend on moment’s action in the plane. Thus the
slenderness ratio [hw/tw] is given by Section 7.16 SNiP II-23-81 Code.
40638.8 4953.8 100 67.2364.38
2 165.2 140600.73 2
x w
x
M hN
A I
1
40638.8 4953.8 100 67.2127.61
2 165.2 140600.73 2
x w
x
M hN
A I
1 364.38 127.610.65
364.38
Accoding to Section 7.16:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 73
α is determined by linear interpolation between values calculated for α = 0.5
and α = 1 when 0.5 < α < 1.
When 0.5 this ratio [hw/tw] is determined by Section 7.14 of this Codes
when m = 0.5 < 1 and xλ = 2.29 :
6
w
w w
6w
w
w
2.1 101.2 0.35 1.2 0.35 2.29 63.29
210063.29
2.1 103.1 3.1 98.03
2100
x
h E
t f h
th E
t f
When 1 this ratio [hw/tw] is determined as follow:
1232.81.4 (2 1) 1.4 (2 1) 1.4 (2 0.65 1) 0.02
67.2 1 364.38w w
V
h t
2 22 2
(2 1) (2 0.65 1) 21000004.35 4.35 127.86
364.38 2 0.65 0.65 4 0.022 4
21000003.8 3.8 120.17
2100
w
w
w
w
h E
t
h E
t f
120.17w
w
h
t
This ratio [hw/tw]= 100.26 is determined by linear interpolation between values
calculated for 0.5 and 1
Check:
w w
w w
h h67.2 = = 67.2 < = 100.26
t 1 t
This section is OK.
In addition: 6
w
w
h 67.2 E 2.1×10 = = 67.2 < 2.3 = 2.3× = 72.73
t 1 f 2100
Web of this column need not be strengthend by lateral stiffening ribs.
Checking column at |M|max
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof |M|max:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 74
M(daN.m) -27186.3
N(daN) -27482.7
VdaN) -4511.2
This force is at top of column section is caused by these load cases 1, 4, 5, 7,
8, 10, 15.
Using dimension of calculated section.
But:
Relative eccentricity m and reduced relative eccentricity me:
x
x
e A 27186.3 100 165.2m = = × = 4.07
W 27482.7 4017.16
M
N
According to Table 73 SNiP II-23-81, with f
w
A 2×1,4×35 = = 1,46 > 1
A 1×67,2;
x0 λ = 2,46 < 5 and 5 < m = 6,7 < 20 , factor of influence of cross section form
η is given as:
1.90 0.1 0.02 6 1.90 0.1 4.07 0.02 (6 4.07) 2.29 1.4xm m
e m = ηm = 1.4 4.07= 5.7
Coefficient e at reduced relative eccentricity 4.07em and fictitious
flexibility 2.29x : 0.192e
Độ mảnh giới hạn của thanh chịu nén là cột chính:
180 60 180 60 0.458 152.52
Where 27482.7
0.4580.192 165.2 2100 0.9e c
N
Af
max y
λ = λ = 89.87< λ = 152.52
a) Checking for strength of eccentric compression.
According to Section 5.24 SNiP II-23-81: The strength analysis of
eccentrically compressed and compressed-and-bent components according to
formula (49) is not necessary when the value of reduced eccentricity
5.7 20em , the section weakening does not occur and the values of bending
moments used for strength and stability are equal.
b) Checking for stability in the plane of moment action.
The stability analysis of eccentric compression and compression-and-bending
components with constant section (with regard to requirements of Sections
5.28 and 5.33 of this Code) in the plane of the moment's action which
coincides with the symmetry plane, shall be conducted by formula:
x c
e
Nσ = fγ
φ A
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 75
Factor eφ in formula (51) shall be determined.
This force is at top of column section is caused by these load cases Md = -
27186.3 (daN.m), causing by load case 1, 4, 5, 7, 8, 10, 15.
2 2
x c
e
N 27482.8σ = = = 866.46 (daN/cm ) < γ f = 0,9 2100 =1890 daN/cm
φ A 0,192×165,2
This section is OK.
c) Checking for stability out of the moment action.
According to Section 5.30 SNiP II-23-81, The stability analysis of eccentric
compression components with constant section out of the moment action plane
at bending thereof in the plane of maximum stiffness (Jx > Jy ) coinciding with
the symmetry plane shall be executed by formula:
y c
y
Nσ = fγ
cφ A
Where:
yφ
is factor calculated according to requirements of Section 5.3 on this Code,
when 2,5 3,05 4,5y then yφ is given below:
2
2
1.47 13 (0.371 27.3 ) (0.0275 5,53 )
1.47 13 0.001 (0.371 27.3 0.001) 2.85 (0.0275 5.53 0.001) 2.85 0.66
y y y
f f f
E E E
c is factor calculated as required by Section 5.31.
When determining the relative eccentricity mx it is necessary to adopt as the
design moment Mx:
The maximum moment within the middle third of bar length (but not less than
the haft of the maximum moment along the bar length) for bars with hinged
bearing ends which are prevented from shifting perpendiculally to the plane of
moment’s action.
The internal force are calculating is at base section of column Mc = -27186.3
(daN.m) , causing by load case 1, 4, 5, 7, 8, 10, 15, moment value at base of
column is Md = -8729.9(daN.m).
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 76
So:
1/3
8729.9 27186.3max ; ; max 20884.2; ; 20884.2 daN.m
2 2 2 2
d cx
M MM M
Relative eccentricity mx is defined by adopted moment Mx:
x
x
e A 20884.2 100 165.2m = = × = 3.12
W 27482.7 4017.16
x
x
M
N
For relative eccentricity mx = 3.12 < 5, by formula:
1 x
cm
α and β are factors adopted according to Table 10:
When mx = 3.12 <1 the factor 0.65 0.05 0.65 0.05 3.12 0.81xm
When 62.1 10
89.97 3.14 3.14 99.32100
y c
E
f
the factor β = 1.
So 1
0.281 1 0.81 3.12x
cm
So:
2 2
y c
y
N 27482.7σ = = = 900.22 / γ f = 0.9 2100 =1890 daN/cm
cφ A 0.28 0.66 165.2daN cm
This sec tion is OK.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 77
d) Checking for stability of flange and web.
For flange:
When analyzing centric and eccentric compression and compression - and
bending components with the fictitious flexibility equal to 0.8 to 4, the ratio
of design width of an overhang of chord sheets (flanges) be to thickness t shall
not exceed values determined by formulas of Table 29*:
62,1 100,36 0,1 0,36 0,1 2,46 19,2
2100
ob E
t f
Ratio:
0.5 (35 1)12.14
1.4
o
f
b
t
So:
12,14 19,2o o
f
b b
t t
This section is OK.
For web:
Slenderness ratio of web:
ww 6
w
67.2 21002.13
1 2.1 10
h f
t E
w w2.13 3.2
Web of this column need not be strengthend by lateral stiffening ribs.
DESIGN COLUMN BRACING.
Chose steel-pipe with diameter d90 and thickness 1.5 mm. These are some
properties:
Section area:
2 2 2 2 2( ) (9 8.7 ) 4.17( )4 4
A D d cm
Moment of inertia relative to axis x-x, y-y:
4 4 4 4( ) (9 8.7 ) 40.864 64
x yI I D d
Inertia radius of cross section relative to axes x-x:
xx
I 40.8i = = = 3.13(cm) ;
A 4.17
Section modulus:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 78
3xx
2I 2×40.8W = = = 9.07(cm )
h 9 Bracing slenderness ratio:
xx
x
l 6.5 100λ = = = 207.7
i 3.13y
According to Section 6.16 flexibility of tension components shall not exeed
values specified in Table 20:
Component of
structure
Ultimate flexibility of tension components subject to impact of
Dynamic loads Static loads Crane load
Brace components 400 400 300
max y minλ = λ = 207.7 < λ = 300
Design flexibility [λ] of column is satisfied
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 79
DEAD LIVE1 LIVE2 LIVE3 LIVE4 LIVE5 LIVE6DMAX
LEFT
DMAX
RIGHTT LEFT - T LEFT T RIGHT - T RIGHT
LEFT
WIND
RIGHT
WIND
LONGITUDINAL
WIND
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
6 U3 -43.3 -20.8 -21.1 6.1 3.4 -0.6 0.3 0.9 1.0 0.9 -0.9 -0.3 0.3 58.9 40.9 55.3
10 U3 -50.3 3.5 5.3 -27.6 -27.6 5.3 3.5 -1.3 -1.3 -1.2 1.2 -1.2 1.2 30.9 30.9 68.1
JOINT DISPLACEMENT
LOAD PATTERN
MAX MIN MAX MIN
1, 14 1, 2, 3, 6 1, 4, 5, 7, 9, 10,
14, 161, 2, 3, 6, 11
15.6 -85.8 70.1 -82.4
1, 16 1 4 51, 2, 3, 6, 7, 11,
14, 161, 4, 5, 8, 10
17.9 -105.4 55.6 -102.2
6 85.8 30 350
10 105.4 33 313
JOINTLOAD COMBINATION 1 LOAD COMBINATION 2 CHOSE
(mm)
SPAN L
(m)L/Δ
CHAPTER 8. CHECKING DISPLACEMENT. Using software SAP2000 to analyze the structure and export the most
unfavourable displacement point.
CHECKING VERTICAL DISPLACEMENT.
Export vertical displacement at (6) and (10) point of structure:
Limit deflection:
max
1 1
350 250L L
OK
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 80
MAX MIN MAX MIN
1, 14 1, 3, 5, 71, 2, 4, 6, 8, 11,
14, 16
1, 3, 5, 7, 9, 10,
13
23.8 -26.4 44.4 -41.3
1, 14 1, 151, 2, 4, 6, 8, 11,
14, 16
1, 3, 5, 7, 9, 10,
15
21.7 -24.2 38.9 -38.4
1, 14 1, 151, 2, 4, 6, 8, 11,
14, 16
1, 3, 5, 7, 9, 10,
15
21.0 -24.4 36.0 -37.4
1, 14 1, 151, 2, 4, 6, 8, 11,
14
1, 3, 5, 7, 9, 10,
15
21.8 21.8 31.9 -31.9
4
8 37.4 14.2 320
10 31.9 14.85 334
H/Δ
44.4 14.2 320
JOINT
LOAD COMBINATION 1 LOAD COMBINATION 2CHOSE
(mm)
HEIGHT H
(m)
6 38.9 15.7 354
DEAD LIVE1 LIVE2 LIVE3 LIVE4 LIVE5 LIVE6DMAX
LEFT
DMAX
RIGHTT LEFT - T LEFT T RIGHT - T RIGHT
LEFT
WIND
RIGHT
WIND
LONGITUDINAL
WIND
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
4 U1 -13.5 0.3 -4.6 1.0 -4.8 1.3 -3.5 4.1 -3.8 -2.8 2.8 2.6 -2.6 37.3 -11.4 17.3
6 U1 -9.5 2.0 -2.3 0.3 -5.1 1.3 -3.4 3.9 -3.8 -2.8 2.8 2.6 -2.6 31.2 -14.7 12.2
8 U1 -5.1 4.2 -0.7 0.2 -5.3 1.4 -3.6 4.0 -4.0 -3.0 3.0 2.7 -2.7 26.1 -19.3 6.7
10 U1 0.0 3.9 -0.8 2.4 -2.4 0.8 -3.9 3.8 -3.8 -2.8 2.8 2.8 -2.8 21.8 -21.8 0.0
JOINT DISPLACEMENT
LOAD PATTERN
CHECKING HORIZONTAL DISPLACEMENT.
Export vertical displacement at (4), (6), (8) AND (10) of structure:
Limit deflection:
max
1 1
354 300H L
OK
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 81
CHAPTER 9. BRACKET COLUMN DESIGN
SECTION DIMENSION.
Using wide – flange cold – form steel product.
Model of calculation: console, with spacing Z = 0.4 m.
Load combination is used to design: Dmax and self weight runway beam Gdct.
Internal force at column’s bracket section:
max
max
19955.48 1430 0.4 8554.19 .
19955.48 1430 21385.48
dct
dct
M D G Z daN m
V D G daN
Preliminary for rib width of bracket colum bdct = 35 (cm)
Preliminary for width of bracket colum 35dvb cm
Preliminary for the flange thickness of bracket colum: dv
ft 1.2 cm
Beam web is defined base on load application to upper beam chord which are
not strengthened by stiffening ribs:
21385.48
0.302( 2 ) (35 2 1.2) 0.9 2100
dv
w dv
dct f c
Vt cm
b t f
Chose dv
wt 1 cm
Beam height is defined base on strength of web under shear application:
3 3 21385.48
29.72 2 1 0.9 1200
dv
w dv
w v c
Vh cm
t f
Chose dv
w 37.6h cm
So w 2 37.6 2 1.2 40dv dv
fh h t cm
SECTION PROPERTIES.
Section area: 2 2 2 37.6 2 35 1.2 159.2( )w f w w f fA A A t h b t cm
Moment of inertia relative to axis x-x:
3 2 3 3 2 3
w ww
4
. 35 1.2 38.8 1 37.62 2 . 2 35 1.2
12 4 12 12 4 12
36054.1
f f f
x x f f
b t h t hI I I b t
cm
Modulus of section:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 82
32 2 36054.11802.7( )
40
xx
IW cm
h
Statical moment of flange area:
338.8. . 1.2 35 814.8
2 2
f
f f f
hS t b cm
Statical moment of ½ area:
3w w wx
38.8 1 37.6 37.61.2 35 991.5
2 2 4 2 2 4
f
f x f f
h t h hS S S t b cm
CHECKING FOR ALLOWABLE STRESS:
2 28554.19 100
474.52 / 2100 0.9 1890 /1802.7
x c
x
MdaN cm f daN cm
W
This section is OK
Checking for allowable shear stress:
20.9 1200 1080 /x
c v
x w
VSf daN cm
I t
2 221385.48 991.5588.1( / ) 1080 /
36054.1 1
x
x w
VSdaN cm daN cm
I t
This section is OK
The start rafter section is concurrent impacted by shear and moment. Thus,
allowable stress need to be stratified this formula below: 2 2 2
1 1 3 1.15 1.15 0.9 2100 2173.5 ( / )
td cf daN cm
Where:
2w
1
x
hM 8554.19 100 37.6σ = = × = 446.05(daN/cm )
W h 1802.7 40
221385.48 814.8
483.3( / )36054.1 1
f
x w
VSdaN cm
I t
2 2 2 2 2 2
td 1 1σ = σ + 3τ = 446.05 + 3×483.3 = 948.52 (daN/cm ) < 2173.5 (daN/cm )
This section is OK.
CHECKING FOR OVER ALL BUCKLING.
Model of calculation: console, lo = 0.4(m)
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 83
Ratio:
0 4001.14
350f
l
b
Maximum value of 0
f
l
b:
6
0.41 0.0032 0.73 0.016
35 35 35 2.1 100.41 0.0032 0.73 0.016 23.43
1.2 1.2 38.8 2100
f f fo
f f f fk
b b bl E
b t t h f
o o
f f
l l
b b
so non checking.
CHECKING FOR LOCAL BUCKLING OF FLANGE AND WEB.
Flange: 617 2.1 10
14.17 0.5 0.5 15.811.2 2100
of
f
b E
t f
This section is OK.
Web:
Slender ratio of web
ww 6
w
37.6 21001.19
1 2.1 10
h f
t E
w w1.19 2.2 web without stiffeners is not buckling by shear.
Acctually, there is local buckling occur in top flange of rafter but it is
doesn’t mean so it is necglected. According to section 5.6.1.3 TCVN 5575 –
2012, local buckling web do not need to check.
CALCULATING FILLET WELD CONNECTION.
As rafter bending, flange slip on web and fillet weld is created to prevent
sliping.
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 84
2
w
2
ws
. 0.7 2000 1400 /
. 1 1530 1530 /
f f
s
f daN cm
f daN cm
2
w wmin. 1400 /f ff f daN cm
The height of the fillet weld:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 6 (mm)
The length design of fillet weld:
Upper flange (2 lines): w 35 1 34l cm
Lower flange (4 lines): w 17 1 16l cm
Web (2 lines): w 36.4 1 35.4l cm
Properties of fillet weld:
Section area:
2 0.7 0.6 34 2 16 4 35.4 2 85.18wf f f w
A h l cm
Moment of inertia:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 85
3 3 32 2
w
4
34 0.6 0.6 35.4 16 0.60.7 2 34 0.6 20.3 4 16 0.6 18.3
12 12 12
23878.13
fI
cm
Section modulus:
32 2 23878.13
1159.1341.2
wf
wf
IW cm
h
Checking allowable stress:
22 2 2
2 2 28554.19 100 21385.48 779.52 /
1159.13 85.18w M Q
w wf
M VdaN cm
W A
2 2
w779.52 / 0.9 2000 1800 /
w c fdaN cm f daN cm
This fillet weld is OK.
STIFFENING RIB DIMENSION.
At the location connecting between bracket and column and impact of runway
beam, web bracket column shall be strengthened by stiffening ribs.
The height: w 376dv
sh h mm
Width and thickness:
w
6
37640 40 52.53
30 30
21002 2 52.53 3.32
2.1 10
s
s s
hb mm
ft b mm
E
Chose bs = 100 (mm), ts = 6 (mm)
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 86
CHAPTER 10. DESIGN JOINTS.
DESIGN BOLT JOINT BETWEEN C1 AND D1.
The internal force are used to calculate which is causing the most unfavourable
tension to bolts.
Column head
C1 1, 2, 3, 5, 6, 7
M(daN.m) 34735.6
N(daN) -8897.8
V(KN) -4121.8
Design bolts conection.
Chose high strength bolta, class 8.8, diameter d = 27 (mm).
Outside flange of column is strengthend by stiffener with some properties:
Thickness: s wt t = 1cm. Chose ts = 1 cm
Width (depend on stiffener’s dimension), chose bs = 12 cm
Height s1.5 1.5 12 18sh b cm
Chose hs = 20 (cm)
MV
N
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 87
Tensile strength of single bolt:
4000 4.59 18360tb bntb
N f A daN
Where:
ftb: tensile strength of bolt class 8.8, ftb = 4000 daN/cm2
Abn : is the net area of bolt’s cross section, the value of Abn for bolts with
metric thread shall be adopted in accordance with Appendix 1, d = 27 mm
Abn = 4.59 cm2.
Shear strength of single bolt:
1
2
0.257700 4.59 1 1 5197.5
1.7hb bn b fb
b
N f A n daN
Where:
fhb : shear strength of bolt.
20.7 0.7 11000 7700 /hb ubf f daN cm
fub: ultimate resitance of steel. Steel grade 40Cr: fub= 11000 daN/cm2
138
80
35
0
17
01
01
70
1467214
25700120
9913813813813460
80
19
0
138
276
414
552
686
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 88
b1γ woking condition factor of joint; the number of bolts in joint is na =
12 > 10 b1γ 1
b2μ, γ is coefficient of friction and reliability factor to be adopted
according to Table 39, SNiP II-23-81. Without treatment so μ = 0.25; b2γ
=1.7.
nf: is number of friction surfaces of joined component, nf = 1.
In case, joined component is applied simultaneously by shear and moment, it
should be checked separately by shear and moment respectively.
1
max 2 2 2 2 2 2
34735.6 100 68.6 8897.810693.52
2 2 13.8 27.6 41.4 55.2 68.6 12b
i
Mh NN daN
h n
See: ,max 10693.52 18360 0.95 17442b ctbN daN N daN
This joint component is OK.
Checking for shear strength:
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof Vmax.
Column head
C1 1, 2, 3, 6, 7
Mtư (daN.m) 34735.6
Ntư (daN) -8897.8
Vmax (daN) -4121.8
Shear force impact on single bolt:
4121.8
343.512
V
VN daN
n
See: 343,5 5197.5 0.95 4938V cbN KN N daN
This joint component is OK.
Design joint flange.
Thickness of joint flange:
1
1
19 10693.52 (13.8 27.6 41.4 55.2 68.6)1.1 1.1 1.84
( ) 68.6 35 68.6 2100
ib Nt cm
b h f
Where:
b1 – distance of 2 bolts’s line, b1 = 19 cm.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 89
b – width of joint flange, b = 35 cm.
Chose t = 2 cm
Design fillet welded between joint flange and column.
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
. 0.7 2000 1400 /
. 1 1530 1530 /
f f
s
f daN cm
f daN cm
2
w wmin. 1400 /f ff f daN cm
Fillet weld at flange:
The length design of fillet weld:
wl =4 17 1 2 12 1 86 cm
Tensile force impact on upper flange:
34735.6 100 8897.8
45173.392 70 2
k
d
M NN daN
h
The requirement height of fillet weld:
80
35
0
17
01
01
70
1467214
25700120
845
9913813813813813460
80
19
0
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 90
45173.39
0.42( ) 86 1400 0.9
yc k
f
w w c
Nh cm
l f
The preliminary height:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
Fillet weld at web:
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof Vmax.
Column head
C1 1, 2, 3, 6, 7
Mtư (daN.m) 34735.6
Ntư (daN) -8897.8
Vmax (daN) -4121.8
The length design of fillet weld:
wl =2 67.2 1 132.4 cm
The requirement height of fillet weld:
4121.8
0.023( ) 142.4 1400 0.9
yc
f
w w c
Vh cm
l f
Chose hf = 10 mm.
DESIGN BOLT JOINT BETWEEN C3 AND DẦM D4, D5.
The internal force are used to calculate which is causing the most unfavourable
tension to bolts:
Beam D4 and
Column C3
Beam D5 and
Column C3
Load
combination 1,2,3,4,5,8,11 1,2,3,4,5
M (daN.m) -49169.9 -53305.3
N (daN) -4294.4 -5540.0
V (daN) 9089.2 -9779.6
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 91
Internal force is calculated:
Beam D5 and
Column C3 1,2,3,4,5
M (daN.m) -53305.3
N (daN) -5540.0
V (daN) -9779.6
Design bolts conection.
Chose high strength bolta, class 8.8, diameter d = 27 (mm).
Lower flange of rafter is strengthened by stiffener with some properties:
Thickness: s wt t = 1cm. Chose ts = 1 cm
Width (depend on stiffener’s dimension), chose bs = 12 cm
Height s1.5 1.5 12 18sh b cm
Chose hs = 20 (cm)
Web of rafter is strengthened by stiffener with some properties:
Thickness: s wt t = 1cm. Chose ts = 1 cm
Width (depend on stiffener’s dimension), chose bs1 = 17 cm
Height s1.5 1.5 17 25.5sh b cm
Chose hs = 25 (cm)
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 92
Tensile strength of single bolt:
4000 4.59 18360tb bntb
N f A daN
Where:
ftb: tensile strength of bolt class 8.8, ftb = 4000 daN/cm2
Abn : is the net area of bolt’s cross section, the value of Abn for bolts with
metric thread shall be adopted in accordance with Appendix 1, d = 27 mm
Abn = 4.59 cm2.
Shear strength of single bolt:
1
2
0.257700 4.59 1 1 5197.5
1.7hb bn b fb
b
N f A n daN
Where:
80 190 80
350
17
4
27
4
37
4
54
6
64
6
74
6
92
0
17010
170
14
38
11
03
81
14
12
08
00
12
0
10
40
60
17
41
00
10
01
72
10
01
00
17
46
0
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 93
fhb : shear strength of bolt.
20.7 0.7 11000 7700 /hb ubf f daN cm
fub: ultimate resitance of steel. Steel grade 40Cr: fub= 11000 daN/cm2
b1γ woking condition factor of joint; the number of bolts in joint is na =
16 > 10 b1γ 1
b2μ, γ is coefficient of friction and reliability factor to be adopted
according to Table 39, SNiP II-23-81. Without treatment so μ = 0.25; b2γ
=1.7.
nf: is number of friction surfaces of joined component, nf = 1.
In case, joined component is applied simultaneously by shear and moment, it
should be checked separately by shear and moment respectively.
1
max 2
2 2 2 2 2 2 2
cos sin
2
53305.3 100 92 5540.0 0.995 9779.6 0.1
2 17.4 27.4 37.4 54.6 64.6 74.6 92 16 16
9968.6
b
i
Mh N VN
h n n
daN
See: ,max 9968.6 18360 0.95 17442b ctbN daN N daN
This joint component is OK.
Checking for shear strength:
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof Vmax.
Beam D5 and
Column C3 1,2,4,5,7,9,13
M (daN.m) -48572.9
N (daN) -6607.4
V (daN) -9188.2
Shear force impact on single bolt:
sin cos 6607.4 0.1 9188.2 0.995
530.0916 16
v
N VN daN
n n
See: 530.09 5197.5 0.95 4937.63blV cbN daN N daN
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 94
This joint component is OK.
Design joint flange.
Thickness of joint flange:
1
1
19 9968.6 (17.4 27.4 37.4 54.6 64.6 74.6 92)1.1 1.1 1.85
( ) 92 35 92 2100
ib N
t cmb h f
Where:
b1 – distance of 2 bolts’s line, b1 = 19 cm.
b – width of joint flange, b = 35 cm
Chose t = 2.5 cm.
Design fillet welded between joint flange and column.
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
. 0.7 2000 1400 /
. 1 1530 1530 /
f f
s
f daN cm
f daN cm
2
w wmin. 1400 /f ff f daN cm .
Fillet weld at flange:
The length design of fillet weld:
wl =4 17 1 2 12 1 86 cm
Tensile force impact on upper flange:
80
19
08
0
35
0
17
01
01
70
14 381 10 381 14
120 800 120
1040
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 95
cos sin 53305.3 100 5540 0.995 9779.6 0.1
2 2 80 2 2
63386.5
k
d
M N VN
h
daN
The requirement height of fillet weld:
63386.5
0.585( ) 86 1400 0.9
yc k
f
w w c
Nh cm
l f
The preliminary height:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
Fillet weld at web:
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof Vmax.
Beam D5 and
Column C3 1,2,4,5,7,9,13
M (daN.m) -48572.9
N (daN) -6607.4
V (daN) -9188.2
The length design of fillet weld:
wl =4 38.1 1 4 17 1 212.4 cm
The requirement height of fillet weld:
sin Vcos 6607.4 0.1 9188.2 0.995
0.03( ) 212.4 1400 0.9
yc
f
w w c
Nh cm
l f
Chose hf = 10 mm
DESIGN BOLT JOINT BETWEEN D1-D2, D3-D4 AND D5-D6.
Section are the same at 3 point so chose 1 for calculating.
The internal force are used to calculate which is causing the most unfavourable
tension to bolts.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 96
D1-D2 D3-D4 D5-D6
1,2,4,6,8,11 1,2,4,5,8,11,14 1,4,6,8,11,14, 16
M (daN.m) 8023.6 -11070.4 11735.4
N (daN) -3083.0 -2366.2 2903.3
V (daN) -3672.2 1312.7 1558.1
Internal force is calculated:
Design Check Check
D5-D6 D1-D2 D3-D4
1,4,6,8,11,14, 16 1,2,4,6,8,11 1,2,4,5,8,11,14
M (daN.m) 11735.4 8023.6 -11070.4
N (daN) 2903.3 -3083.0 -2366.2
V (daN) 1558.1 -3672.2 1312.7
Design bolt joint between D5 – D6.
a) Design bolts conection.
D5-D6 Design
1,4,6,8,11,14, 16
M (daN.m) 11735.4
N (daN) 2903.3
V (daN) 1558.1
Chose high strength bolta, class 8.8, diameter d = 27 (mm).
Lower flange of rafter is strengthened by stiffener with some properties:
Thickness: s wt t = 1cm. Chose ts = 1 cm
Width (depend on stiffener’s dimension), chose bs = 12 cm
Height s1.5 1.5 12 18sh b cm
Chose hs = 20 (cm)
Tensile strength of single bolt:
4000 4.59 18360tb bntb
N f A daN
Where:
ftb: tensile strength of bolt class 8.8, ftb = 4000 daN/cm2
Abn : is the net area of bolt’s cross section, the value of Abn for bolts with
metric thread shall be adopted in accordance with Appendix 1, d = 27 mm
Abn = 4.59 cm2.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 97
80
19
08
0
35
0
60 174 172 174 60
174
346
520
17
01
01
70
14 372 14
120 400 120
640
Shear strength of single bolt:
1
2
0.257700 4.59 0.9 1 4677.75
1.7hb bn b fb
b
N f A n daN
Where:
fhb : shear strength of bolt.
20.7 0.7 11000 7700 /hb ubf f daN cm
fub: ultimate resitance of steel. Steel grade 40Cr: fub= 11000 daN/cm2
b1γ woking condition factor of joint; the number of bolts in joint is na = 8
< 10 b1γ 0.9
b2μ, γ is coefficient of friction and reliability factor to be adopted
according to Table 39, SNiP II-23-81. Without treatment so μ = 0.25; b2γ
=1.7.
nf: is number of friction surfaces of joined component, nf = 1.
In case, joined component is applied simultaneously by shear and moment, it
should be checked separately by shear and moment respectively.
1
max 2 2 2 2
11735.4 100 52 2903.37620.9
2 2 17.4 34.6 52 8b
i
Mh NN daN
h n
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 98
See: ,max 7620.9 18360 0.95 17442b ctbN daN N daN
This joint component is OK.
Checking for shear strength:
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof Vmax.
D5-D6 1,2,4,5,7,9,13
M (daN.m) -3756.4
N (daN) -6256.2
V (daN) -5676.4
Shear force impact on single bolt:
5676.4
709.68
V
VN daN
n
See: 709.6 4677.75 0.95 4443.86blV cbN daN N daN
This joint component is OK.
b) Design joint flange.
Thickness of joint flange:
1
1
19 7620.9 (17.4 34.6 52)1.1 1.1 1.38
( ) 52 35 52 2100
ib N
t cmb h f
Where:
b1 – distance of 2 bolts’s line, b1 = 19 cm.
b – width of joint flange, b = 35 cm.
Chose t = 2 cm.
c) Design fillet welded between joint flange and rafter.
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
. 0.7 2000 1400 /
. 1 1530 1530 /
f f
s
f daN cm
f daN cm
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 99
80
19
08
0
35
0
60 174 172 174 60
17
01
01
70
14 372 14
120 400 120
640
2
w wmin. 1400 /f ff f daN cm .
Fillet weld at flange:
The length design of fillet weld:
wl =4 17 1 2 12 1 86 cm
Tensile force impact on upper flange:
11735.4 100 2903.3
30790.152 40 2
k
d
M NN daN
h
The requirement height of fillet weld:
30790.15
0.28( ) 86 1400 0.9
yc k
f
w w c
Nh cm
l f
The preliminary height:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
Fillet weld at web:
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof Vmax.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 100
D5-D6 1,2,4,5,7,9,13
M (daN.m) -3756.4
N (daN) -6256.2
V (daN) -5676.4
The length design of fillet weld:
wl =2 37.2 1 72.4 cm
The requirement height of fillet weld:
5676.4
0.06( ) 72.4 1400 0.9
yc
f
w w c
Vh cm
l f
Chose hf = 10 mm.
Checking joint bolt at D1-D2
The same arrangement between D1-D2 and D5-D6.
Internal force design
1,2,4,6,8,11
Mmax (daN.m) 8023.6
Ntư (daN) -3083.0
1,2,3,5,7,9,13
Vmax (daN) 3961.8
Strength of one bolt [N]tb (daN) 18360
[N]b (daN) 4677.75
Max tensile force Nb max (daN) 4577 < γc.[N]tb = 17442
THỎA
Max shear force NV (daN) 495.23 < γc.[N]tb =
4443.86 THỎA
Calculating joint flange 1
1
1.1( )
ib Nt cm
b h f
1.07 < tchọn = 2
Chord fillet weld
lw (tính toán) (cm) 86
Nk (daN) 18517.5
hfyc (cm) 0.17 < hf chọn = 1
Web fillet weld
lw (tính toán) (cm) 72.4
V(KN) 3961.8
hfyc (cm) 0.04 < hf chọn = 1
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 101
Checking joint bolt at D3-D4
Internal force design
1, 2, 4, 5, 8, 11, 14
Mmax (daN.m) -11070.4
Ntư (daN) -2366.2
1,2,3,5,7,9,13
Vmax (daN) -4756.0
Strength of one bolt [N]tb (daN) 18360
[N]b (daN) 4677.75
Max tensile force Nb max (daN) 7142.49 < γc.[N]tb =
17442 THỎA
Max shear force NV (daN) 594.5 < γc.[N]tb =
4443.86 THỎA
Calculating joint flange 1
1
1.1( )
ib Nt cm
b h f
1.34 < tchọn = 2
Chord fillet weld
lw (tính toán) (cm) 86
Nk (daN) 28859.1
hfyc (cm) 0.27 < hf chọn = 1
Web fillet weld
lw (tính toán) (cm) 72.4
V(KN) -4756.0
hfyc (cm) 0.05 < hf chọn = 1
DESIGN BOLT JOINT BETWEEN D2-D3 AND D6-D7.
Section are the same at 3 point so chose 1 for calculating.
The internal force are used to calculate which is causing the most
unfavourable tension to bolts:
D2-D3 D6-D7
1,2,3,6 1,4,5,8,11
M (daN.m) 24311.4 26936.7
N (daN) -3838.0 -5113.0
V (daN) 718.6 606.3
Internal force is calculated:
Check Design
D2-D3 D6-D7
1,2,3,6 1,4,5,8,11
M (daN.m) 24311.4 26936.7
N (daN) -3838.0 -5113.0
V (daN) 718.6 606.3
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 102
Design bolt joint between D6-D7.
a) Design bolts conection.
D6-D7 Design
1,4,5,8,11
M (daN.m) 26936.7
N (daN) -5113.0
V (daN) 606.3
Chose high strength bolta, class 8.8, diameter d = 27 (mm).
Lower flange of rafter is strengthened by stiffener with some properties:
Thickness: s wt t = 1cm. Chose ts = 1 cm
Width (depend on stiffener’s dimension), chose bs = 12 cm
Height s1.5 1.5 12 18sh b cm
Chose hs = 20 (cm)
Tensile strength of single bolt:
4000 4.59 18360tb bntb
N f A daN
Where:
ftb: tensile strength of bolt class 8.8, ftb = 4000 daN/cm2
Abn : is the net area of bolt’s cross section, the value of Abn for bolts with
metric thread shall be adopted in accordance with Appendix 1, d = 27 mm
Abn = 4.59 cm2.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 103
80 190 80
350
60
90
90
16
46
0
170 170
14
47
21
4
12
05
00
12
0
74
0
16
4
25
4
36
6
45
6
11
21
64
62
0
Shear strength of single bolt:
1
2
0.257700 4.59 1 1 5197.5
1.7hb bn b fb
b
N f A n daN
Where:
fhb : shear strength of bolt.
20.7 0.7 11000 7700 /hb ubf f daN cm
fub: ultimate resitance of steel. Steel grade 40Cr: fub= 11000 daN/cm2
b1γ woking condition factor of joint; the number of bolts in joint is na =
12 > 10 b1γ 1
b2μ, γ is coefficient of friction and reliability factor to be adopted
according to Table 39, SNiP II-23-81. Without treatment so μ = 0.25; b2γ
=1.7.
nf: is number of friction surfaces of joined component, nf = 1.
In case, joined component is applied simultaneously by shear and moment, it
should be checked separately by shear and moment respectively.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 104
1
max 2
2 2 2 2 2
cos sin
2
26936.7 100 62 5113 0.995 606.3 0.19838.56
12 122 16.4 25.4 36.6 45.6 62
b
i
Mh N VN
h n n
daN
See: ,max 9838.56 18360 0.95 17442b ctbN daN N daN
This joint component is OK.
Checking for shear strength:
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof Vmax.
D6-D7 1,2,4,5,7,9,13
M (daN.m) 23717.9
N (daN) -5641.6
V (daN) 469.2
Shear force impact on single bolt:
cos sin 469.2 0.995 5641.6 0.1
8.112 12
V
V NN daN
n n
See: 8.1 5197.5 0.95 4937.63blV cbN daN N daN
This joint component is OK.
b) Design joint flange.
Thickness of joint flange:
1
1
19 9838.56 16.4 25.4 36.6 45.6 621.1 1.1 1.83
( ) 62 35 62 2100
ib N
t cmb h f
Where:
b1 – distance of 2 bolts’s line, b1 = 19 cm.
b – width of joint flange, b = 35 cm.
Chose t = 2 cm.
c) Design fillet welded between joint flange and column.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 105
80 190 80
3506
09
09
01
64
60
17010
170
14
47
21
4
12
05
00
12
0
74
0
11
21
64
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
. 0.7 2000 1400 /
. 1 1530 1530 /
f f
s
f daN cm
f daN cm
2
w wmin. 1400 /f ff f daN cm .
Fillet weld at flange:
The length design of fillet weld::
wl =4 17 1 2 12 1 86 cm
Tensile force impact on upper flange:
26936.7 100 5113
51316.92 50 2
k
d
M NN daN
h
The requirement height of fillet weld:
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 106
51316.9
0.47( ) 86 1400 0.9
yc k
f
w w c
Nh cm
l f
The preliminary height:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
Fillet weld at web:
From internal force table, chose N, Mx and My are absolute values of lateral
force and bending moments respectively at the most unfavourable
combination thereof Vmax:
D6-D7 1,2,4,5,7,9,13
M (daN.m) 23717.9
N (daN) -5641.6
V (daN) 469.2
The length design of fillet weld:
wl =2 47.2 1 92.4 cm
The requirement height of fillet weld:
cos sin 469.2 0.995 5641.6 0.1
0.001( ) 92.4 1400 0.9
yc
f
w w c
V Nh cm
l f
Chose hf = 10 mm.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 107
Checking joint bolt at D2-D3
The same arrangement between D2-D3 and D6-D7.
Internal force design
1,2,3,6
Mmax (daN.m) 24311.4
Ntư (daN) -3838.0
1,2,3,5,7,9,13
Vmax (daN) -4184.9
Strength of one bolt [N]tb (daN) 18360
[N]b (daN) 5197.5
Max tensile force Nb max (daN) 8863.6< γc.[N]tb = 17442
THỎA
Max shear force NV (daN) 315.01 < γc.[N]tb =
4443.86 THỎA
Calculating joint flange 1
1
1.1( )
ib Nt cm
b h f
1.73 < tchọn = 2
Chord fillet weld
lw (tính toán) (cm) 86
Nk (daN) 46703.8
hfyc (cm) 0.43 < hf chọn = 1
Web fillet weld
lw (tính toán) (cm) 92.4
V(KN) -4184.9
hfyc (cm) 0.032 < hf chọn = 1
DESIGN BASE OF COLUMN.
Base column C1.
a) Design joint flange.
The internal force are used to calculate which is causing the most
unfavourable combination |M|max and Nmax:
1,2,3,5,7,9,1
3, 15
1,2,3,6,7
Mmax -30490.9 Mtư -22677.0
Ntư -10104.9 Nmax -14001.2
Vtư -5511.1 Vtư -4036.1
The premilinary width:
cot 12 35 2 10 55
bdB b c cm
Where:
bcot = 35 cm – column width
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 108
c1 = 10 cm
The length of joint flange is defined from concrete’s located pressure
condition: 2
, , ,
6
2 2bd
bd b loc bd b loc bd b loc
N N ML
B R B R B R
Where:
ψ = 0.75 for nonuniform load
2
,0.98 1.1 145 155.93 /
b loc b bR R daN cm
Using concrete class B25: Rb =145 daN/cm2; Rbt= 10.5 daN/cm2.
10.5
13.5 13.5 0.98145
bt
b
R
R .
3 1.5 m
b
bd
A
A Chose 1.1.b
The length of joint flange with Mmax and Nmax :
In case of |M|max
2
max
, , ,
6
2 2
tu tu
bd
bd b loc bd b loc bd b loc
N N ML
B R B R B R
2
d
10104.9 10104.9 6 30490.9 10054.1
2 55 0.75 155.93 2 55 0.75 155.93 55 0.75 155.93b
L cm
In case of Nmax
2
max max
, , ,
6
2 2
tu
bd
bd b loc bd b loc bd b loc
N N ML
B R B R B R
2
d
14001.2 14001.2 6 22677 10047.09
2 55 0.75 155.93 2 55 0.75 155.93 55 0.75 155.93bL cm
Base on geometry, the length of joint flange with c2 = 14 (cm) and the
thickness is 1 (cm)
dd dd 22 2 70 2 1 2 14 100L h t c cm
Chose Ldd = 100 (cm)
Stress reaction of concrete causing by Mmax:
2max
max 2 2
6 10104.9 6 30490.9 10035.1 /
55 100 55 100
tu
bd bd bd bd
N MdaN cm
B L B L
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NAME: NGUYỄN TRÍ THIỆN Page 109
2max
min 2 2
6 10104.9 6 30490.9 10031.43 /
55 100 55 100
tu
bd bd bd bd
N MdaN cm
B L B L
2
max min ,, 0.75 155.93 116.94 /b locR daN cm
Stress reaction of concrete causing by Nmax:
2max
max 2 2
6 14001.2 6 22677 10027.28 /
55 100 55 100
tu
bd bd bd bd
N MdaN cm
B L B L
2max
min 2 2
6 14001.2 6 22677 10022.19 /
55 100 55 100
tu
bd bd bd bd
N MdaN cm
B L B L
2
max min ,, 0.75 155.93 116.94 /b locR daN cm
According to stress results, using unfavourable focre |M|max to determine
the thickness of joint flange.
The thickness of joint flange is determined base on moment resistence
condition under the stress reaction of concrete, chosing maximum stress for
safe.
max6
bd
c
Mt
f
Where:
Mmax – maximum moment in cellular
Moment is defined as: 2
b i iM = α σ d i
di – calculating span in cellular i
iσ - is stress reaction of concrete
bα - is taken according to, Table 4.12, 4.13 (Structural steel book – Pham
Van Hoi).
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 110
Cellular viewing:
O1 (3 edge soported slab)
1 2 234.5 ; 27d a cm b cm
Ratio: 2 2/ 0.783b a . Table 2.4 (book), using interpolation method: 0.095b
2 2
1 1 1 0.095 25.12 34.5 2840.41 .bM d daN cm
O2 (2 edge soported slab)
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2 2 230.414 ; 12.429d a cm b cm
Ratio: 2 2/ 0.409b a . Table 2.4 (book), using interpolation method: 0.06b
2 2
2 1 1 0.06 35.1 30.414 1948.07 .bM d daN cm
max 1 2max( , ) 2840.41 . M M M daN cm
So the requirement thickness: max6 6 2840.41
2.852100
bd
c
Mt cm
f
Chose tbd= 3 cm.
b) Design stiffening rib.
Dimension:
Thickness: tdd = 1 (cm)
Width: bdd = Bbd = 55 (cm)
Height: hdd depend on the strength capacity of weld line transmitting load
to column form concrete’s stress reaction.
Concrete’s stress reaction force:
dd 15 35.1 17.5 25.12 55 53135.5N daN
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
. 0.7 2000 1400 /
. 1 1530 1530 /
f f
s
f daN cm
f daN cm
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NAME: NGUYỄN TRÍ THIỆN Page 112
2
w wmin. 1400 /f ff f daN cm .
The preliminary height:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
The length fillet weld design:
w
53135.521.09
2 ( ) 2 1 1400 0.9
yc dd
f w c
Nl cm
h f
Executed length weld:
w w 1 21.09 1 22.09ycl l cm
The height of stiffening rib hdd = 25 (cm)
c) Design stiffening rib A.
Model of combination: console.
13.48 2 17.5 471.8 /sq daN cm
2 2471.8 27
171971.1 .2 2
s ss
q lM daN cm
471.8 27 12738.6s s sV q l daN
Preliminary thickness ts = 1 (cm).
The height of stiffening rib is determined base on moment resistence condition
under the stress reaction of concrete:
6 6 171971.1
22.171 2100 1
s
s
s c
Mh cm
t f
ls
Ms
Vs
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NAME: NGUYỄN TRÍ THIỆN Page 113
Chose hs = 25 (cm)
Checking for allowable stress:
2 2
2 2 2
1 1 2
6 171971.1 12738.6 3 3 1872( / )
1 25 1 25td
daN cm
2 21872( / ) 1.15 1.15 2100 0.9 2173.5( / )td cdaN cm f daN cm
The preliminary height:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
Section area and section modulus:
2
w
2
3
w
2 1 25 1 48
1 25 1W 2 192
6
A cm
cm
The strength of fillet weld is checked as follow:
2 2 2 2
2 2 2171971.1 12738.6 934.17 /
192 48
s s
w M Q
w w
M VdaN cm
W A
2 2
w min934.17 / 0.9 1400 1260 /
w cdaN cm f daN cm
d) Design stiffening rib B.
It is the same to stiffenng rib A, the width of area pressure:
1.5 1.5 14 21s sa l cm
35.1 21 737.1 /sq daN cm
2 2737.1 14
72235.8 .2 2
s ss
q lM daN cm
737.1 14 10319.4s s sV q l daN
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 114
ls
Ms
Vs
Preliminary thickness ts = 1 (cm).
The height of stiffening rib is determined base on moment resistence condition
under the stress reaction of concrete:
6 6 72235.8
14.371 2100 1
s
s
s c
Mh cm
t f
Chose hs = 25 (cm)
Checking for allowable stress:
2 2
2 2 2
1 1 2
6 72235.8 10319.4 3 3 996.01( / )
1 25 1 25td
daN cm
2 2996.01( / ) 1.15 1.15 2100 0.9 2173.5( / )td cdaN cm f daN cm
The preliminary height:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
Section area and section modulus:
2
w
2
3
w
2 1 25 1 48
1 25 1W 2 192
6
A cm
cm
The strength of fillet weld is checked as follow:
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NAME: NGUYỄN TRÍ THIỆN Page 115
2 2 2 2
2 2 272235.8 10319.4 433.32 /
192 48
s s
w M Q
w w
M VdaN cm
W A
2 2
w min433.32 / 0.9 1400 1260 /
w cdaN cm f daN cm
e) Design anchored bolt.
The internal force are used to calculate which is causing the most
unfavourable tension to bolts:
1,2,3,5,7,9,1
3, 15
Mmax -30490.9
Ntư -10104.9
Vtư -5511.1
The length area is under compression c = 52.76 (cm).
Distance between centre bolt and the edge of column 7 (cm), is defined as:
d
d
100 52.7632.41
2 3 2 3
52.767 100 7 75.41
3 3
b
b
L ca cm
cy L cm
Where:
a – distance between compression area’s centre and column centre.
y – distance between compression area’s centre and opposite tension bolts
centre.
Tensile force apply to bolts:
1
30490.9 100 10104.9 32.4136090.57
75.41
M NaT daN
y
Using anchored bolts class 09Mn2Si: fba = 1900 daN/cm2.
Net cross section area requirement of single bolt:
21
1
36090.574.75
. 4 1900
yc
ba
ba
TA cm
n f
Chose bolt Φ30: Abn = 5.6 (cm2)
Tensile force apply to bolts reviewing:
2
30490.9 100 10104.930402.1
2 86 2b
M NT daN
L
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Where:
Lb – spacing of 2 line outside bolt.
Because T2 < T1 so chosing bolt class follow T1 is satisfied.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 117
f) Design fillet welded between joint flange and column.
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
. 0.7 2000 1400 /
. 1 1530 1530 /
f f
s
f daN cm
f daN cm
2
w wmin. 1400 /f ff f daN cm .
The internal force are used to calculate is the same to anchored bolt’s.
Fillet weld at flange:
The total length design of fillet weld:
wl =2 27 1 2 17 1 2 10 1 102 cm
Tensile force impact on upper flange:
30490.4 100 10104.9
38505.262 70 2
k
c
M NN daN
h
The requirement height of fillet weld:
38505.26
0.3( ) 102 1400 0.9
yc k
f
w w c
Nh cm
l f
The preliminary height:
140103451034510140
1000
170
10
170
500500
280
135
550
70 180 500 180 70
100
100
135
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 118
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
Fillet weld at web:
The total length design of fillet weld:
wl =4 33.1 1 128.4 cm
The requirement height of fillet weld:
5511.1
0.034( ) 128.4 1400 0.9
yc
f
w w c
Vh cm
l f
Chose hf = 10 mm.
Base column C2.
a) Design joint flange.
The internal force are used to calculate which is causing the most
unfavourable combination |M|max and Nmax:
1,4,5,7,8,10, 15
1,2,3,4,5,8,11
Mmax -27186.3 Mtư -4953.8
Ntư -27482.7 Nmax -40638.8
Vtư -4511.2 Vtư -1232.8
The premilinary width:
cot 12 35 2 10 55
bdB b c cm
Where:
bcot = 35 cm – column width
c1 = 10 cm
The length of joint flange is defined from concrete’s located pressure
condition: 2
, , ,
6
2 2bd
bd b loc bd b loc bd b loc
N N ML
B R B R B R
Where:
ψ = 0.75 for nonuniform load
2
,0.98 1.1 145 155.93 /
b loc b bR R daN cm
Using concrete class B25: Rb =145 daN/cm2; Rbt= 10.5 daN/cm2.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 119
10.5
13.5 13.5 0.98145
bt
b
R
R .
3 1.5 m
b
bd
A
A Chose 1.1.b
The length of joint flange with Mmax and Nmax:
In case of |M|max
2
max
, , ,
6
2 2
tu tu
bd
bd b loc bd b loc bd b loc
N N ML
B R B R B R
2
d
27482.7 27482.7 6 27186.3 10052.54
2 55 0.75 155.93 2 55 0.75 155.93 55 0.75 155.93b
L cm
In case of Nmax
2
max max
, , ,
6
2 2
tu
bd
bd b loc bd b loc bd b loc
N N ML
B R B R B R
2
d
40638.8 40638.8 6 4953.8 10024.88
2 55 0.75 155.93 2 55 0.75 155.93 55 0.75 155.93b
L cm
Base on geometry, the length of joint flange with c2 = 14 (cm) and the
thickness is 1 (cm)
dd dd 22 2 70 2 1 2 14 100L h t c cm
Chose Ldd = 100 (cm)
Stress reaction of concrete causing by Mmax:
2max
max 2 2
6 27482.7 6 27186.3 10034.65 /
55 100 55 100
tu
bd bd bd bd
N MdaN cm
B L B L
2max
min 2 2
6 27482.7 6 27186.3 10024.66 /
55 100 55 100
tu
bd bd bd bd
N MdaN cm
B L B L
2
max min ,, 0.75 155.93 116.94 /b locR daN cm
Stress reaction of concrete causing by Nmax:
2max
max 2 2
6 40638.8 6 4953.8 10012.79 /
55 100 55 100
tu
bd bd bd bd
N MdaN cm
B L B L
2max
min 2 2
6 40638.8 6 4953.8 1001.98 /
55 100 55 100
tu
bd bd bd bd
N MdaN cm
B L B L
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NAME: NGUYỄN TRÍ THIỆN Page 120
2
max min ,, 0.75 155.93 116.94 /b locR daN cm
According to stress results, using unfavourable focre |M|max to determine
the thickness of joint flange.
The thickness of joint flange is determined base on moment resistence
condition under the stress reaction of concrete, chosing maximum stress for
safe.
max6
bd
c
Mt
f
Where:
Mmax – maximum moment in cellular
Moment is defined as: 2
b i iM = α σ d i
di – calculating span in cellular i
iσ - is stress reaction of concrete
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 121
bα - is taken according to, Table 4.12, 4.13 (Structural steel book – Pham
Van Hoi)
Cellular viewing:
O1 (3 edge soported slab)
1 2 234.5 ; 27d a cm b cm
Tỉ số: 2 2/ 0.783b a . Table 2.4 (book), using interpolation method: 0.095b
2 2
1 1 1 0.095 25.75 34.5 2911.65 .bM d daN cm
O2 (2 edge soported slab)
2 2 230.414 ; 12.429d a cm b cm
Ratio: 2 2/ 0.409b a . Table 2.4 (book), using interpolation method: 0.06b
2 2
2 1 1 0.06 34.65 30.414 1923.1 .bM d daN cm
max 1 2max( , ) 2911.65 . M M M daN cm
So the requirement thickness: max6 6 2911.65
2.882100
bd
c
Mt cm
f
Chose tbd= 3 cm.
b) Design stiffening rib.
Dimension:
Thickness: tdd = 1 (cm)
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 122
Width: bdd = Bbd = 55 (cm)
Height: hdd depend on the strength capacity of weld line transmitting load
to column form concrete’s stress reaction.
Concrete’s stress reaction force:
dd 15 34.65 17.5 25.75 55 53370.63N daN
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
. 0.7 2000 1400 /
. 1 1530 1530 /
f f
s
f daN cm
f daN cm
2
w wmin. 1400 /f ff f daN cm .
The preliminary height:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
The length fillet weld design:
w
53370.6321.18
2 ( ) 2 1 1400 0.9
yc dd
f w c
Nl cm
h f
Executed length weld:
w w 1 21.18 1 22.18ycl l cm
The height of stiffening rib hdd = 25 (cm)
c) Design stiffening rib A.
Model of combination: console:
15.37 2 17.5 537.95 /sq daN cm
2 2537.95 27
196082.78 .2 2
s ss
q lM daN cm
537.95 27 14524.65s s sV q l daN
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NAME: NGUYỄN TRÍ THIỆN Page 123
Preliminary thickness ts = 1 (cm).
The height of stiffening rib is determined base on moment resistence condition
under the stress reaction of concrete:
6 6 196082.78
23.671 2100 1
s
s
s c
Mh cm
t f
Chọn hs = 25 (cm)
Checking for allowable stress: 2 2
2 2 2
1 1 2
6 196082.78 14524.65 3 3 2134.49( / )
1 25 1 25td
daN cm
2 22134.49( / ) 1.15 1.15 2100 0.9 2173.5( / )td cdaN cm f daN cm
The preliminary height:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
Section area and section modulus
2
w
2
3
w
2 1 25 1 48
1 25 1W 2 192
6
A cm
cm
The strength of fillet weld is checked as follow:
2 2 2 2
2 2 2196082.78 14524.65 1065.15 /
192 48
s s
w M Q
w w
M VdaN cm
W A
2 2
w min1065.15 / 0.9 1400 1260 /
w cdaN cm f daN cm
ls
Ms
Vs
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 124
d) Design stiffening rib B.
It is the same to stiffenng rib A, the width of area pressure:
1.5 1.5 14 21s sa l cm
34.65 21 727.65 /sq daN cm
2 2727.65 14
71309.7 .2 2
s ss
q lM daN cm
727.65 14 10187.1s s sV q l daN
Preliminary thickness ts = 1 (cm).
The height of stiffening rib is determined base on moment resistence condition
under the stress reaction of concrete:
6 6 71309.7
14.271 2100 1
s
s
s c
Mh cm
t f
Chose hs = 25 (cm)
Checking for allowable stress:
2 2
2 2 2
1 1 2
6 71309.7 10187.1 3 3 983.24( / )
1 25 1 25td
daN cm
2 2983.24( / ) 1.15 1.15 2100 0.9 2173.5( / )td cdaN cm f daN cm
The preliminary height:
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
ls
Ms
Vs
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 125
Section area and section modulus:
2
w
2
3
w
2 1 25 1 48
1 25 1W 2 192
6
A cm
cm
The strength of fillet weld is checked as follow:
2 2 2 2
2 2 271309.7 10187.1 427.77 /
192 48
s s
w M Q
w w
M VdaN cm
W A
2 2
w min427.77 / 0.9 1400 1260 /
w cdaN cm f daN cm
e) Design anchored bolt.
The internal force are used to calculate which is causing the most
unfavourable tension to bolts:
1,4,5,7,8,10, 15
Mmax -27186.3
Ntư -27482.7
Vtư -4511.2
The length area is under compression c = 58.42 (cm).
Distance between centre bolt and the edge of column 7 (cm), is defined as:
d
d
100 58.4230.53
2 3 2 3
58.427 100 7 73.53
3 3
b
b
L ca cm
cy L cm
Where:
a – distance between compression area’s centre and column centre.
y – distance between compression area’s centre and opposite tension bolts
centre
Tensile force apply to bolts:
1
27186.3 100 27482.7 30.5325562.13
73.53
M NaT daN
y
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 126
Using anchored bolts class 09Mn2Si: fba = 1900 daN/cm2.
Net cross section area requirement of single bolt:
21
1
25562.133.36
. 4 1900
yc
ba
ba
TA cm
n f
Chose bolt Φ30: Abn = 5.6 (cm2)
Tensile force apply to bolts reviewing:
2
27186.3 100 27482.117870.93
2 86 2b
M NT daN
L
Where:
Lb – spacing of 2 line outside bolt.
Because T2 < T1 so chosing bolt class follow T1 is satisfied.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 127
f) Design fillet welded between joint flange and column.
Using shielded metal arc welding, electrode N46: βf = 0.7, βs = 1, fwf = 2000
daN/cm2; fws = 0,45fu = 0,45 × 3400 = 1530 daN/cm2.
So:
2
w
2
ws
. 0.7 2000 1400 /
. 1 1530 1530 /
f f
s
f daN cm
f daN cm
2
w wmin. 1400 /f ff f daN cm .
The internal force are used to calculate is the same to anchored bolt’s.
Fillet weld at flange.
The total length design of fillet weld:
wl =2 27 1 2 17 1 2 10 1 102 cm
Tensile force impact on upper flange:
27186.3 100 27482.1
25096.522 70 2
k
c
M NN daN
h
The preliminary height:
25096.52
0.2( ) 102 1400 0.9
yc k
f
w w c
Nh cm
l f
The preliminary height:
140103451034510140
1000
170
10
170
500500
280
135
550
70 180 500 180 70
100
100
135
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 128
min
min
1.2 1.2 10 12
6
f
f f
h t mm
h h mm
Chose hf = 10 (mm)
Fillet weld at web:
The total length design of fillet weld:
wl =4 33.1 1 128.4 cm
The requirement height of fillet weld:
4511.2
0.028( ) 128.4 1400 0.9
yc
f
w w c
Vh cm
l f
Chose hf = 10 mm.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 129
REFERENCES
1. TCVN 5575 – 2012 Tiêu chuẩn thiết kế kết cấu thép.
2. SNiP II – 23 – 81 Structural Steel Design.
3. TCVN 2737 – 1997 Tải trọng và tác động.
4. SNiP 2.01.07 – 85* Loads and effects.
5. Bài giảng kết cấu thép 2 Thầy Trần Văn Phúc.
6. Phạm Văn Hội, Nguyễn Quang Viên, Phạm Văn Tư, Lưu Văn Tường. Kết cấu
thép – Cấu kiện cơ bản. NXB Khoa học và Kỹ thuật. Hà Nội – 2009.
7. Phạm Văn Hội, Nguyễn Quang Viên, Phạm Văn Tư, Đoàn Ngọc Tranh,
Hoàng Văn Quang. Kết cấu thép 2 – Công trình dân dụng và công nghiệp.
NXB Khoa học và Kỹ thuật. Hà Nội – 2010.
8. Trần Thị Thôn. Bài tập Thiết kế kết cấu thép. NXB Đại học quốc gia Tp.
HCM. Tp. HCM – 2013.
9. GS. Đoàn Định Kiến, Phạm Văn Tư, Nguyễn Quang Viên. Thiết kế Kết cấu
thép nhà công nghiệp. NXB Khoa học và Kỹ thuật. Hà Nội – 2007.
10. Tủ sách khoa học công nghệ xây dựng. Hướng dẫn thiết kế Kết cấu thép theo
TCVN 338:2005. NXB Xây dựng 338:2005. Hà Nội – 2009.
11. Dr. GooGle.
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 130
CONTENTS
SYMBOLS USED IN THIS PROJECT ............................................................................. 0
CHAPTER 1. GIVEN DATA .............................................................................................. 3
CHAPTER 2. FRAME GEOMETRY ................................................................................ 4
CHOSING CRANE. .................................................................................................... 4
DEFINE VERTICAL DIMENSION. .......................................................................... 4
Upper column length: .......................................................................................... 4
Lower column length: .......................................................................................... 4
DEFINE HORIZONTAL DIMENSION: .................................................................... 4
JACK ROOF MONITOR DIMENSION. .................................................................... 5
HORIZONTAL FRAME MODEL OF CALCULATION. ......................................... 5
CHAPTER 3. DEFINE LOAD. ........................................................................................... 7
DEAD LOAD. ............................................................................................................. 7
Self weight of structure. ....................................................................................... 7
Envelope material. ............................................................................................... 7
ROOF LIVE LOAD. .................................................................................................... 8
CRANE LOAD. ........................................................................................................... 8
Vertical impact. .................................................................................................... 8
Breaking force of trolley and lifted load: ........................................................... 10
WIND LOAD: ........................................................................................................... 10
Outside column .................................................................................................. 12
Left roof’s L1-L2 span ........................................................................................ 12
Right roof’s L1-L2 span ...................................................................................... 13
Center roof ......................................................................................................... 14
CHAPTER 4. DETERMINE INTERNAL FORCE, SHEAR AND MOMENT AT SAP
2000 V18 .............................................................................................................................. 15
DEFINE MATERIAL AND SECTION PROPERTIES. ........................................... 15
Material. ............................................................................................................. 15
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 131
Section. ............................................................................................................... 16
CREATING BUILDING MODEL. ........................................................................... 18
DEFINE LOAD. ........................................................................................................ 19
Dead load ........................................................................................................... 20
Live load. ........................................................................................................... 20
Wind load. .......................................................................................................... 22
Crane load. ......................................................................................................... 22
INTERIAL FORCE AND LOAD COMBINATION. ............................................... 24
CHAPTER 5. PURLINS DESIGN. ................................................................................... 28
TOLE DESIGN. ........................................................................................................ 28
Properties. .......................................................................................................... 28
Define load. ........................................................................................................ 29
Design tole section. ............................................................................................ 29
PURLINS DESIGN. .................................................................................................. 31
Properties. According to vvvTra co Cor. catalogue ........................................... 31
Load impact........................................................................................................ 31
Purlins design. .................................................................................................... 32
DESIGN CONECTION BETWEEN TOLE AND PURLINS. ................................ 34
Load combination 1: Dead load and Wind load: ............................................... 34
Load combination 2: Dead load and Wind load: ............................................... 34
DESIGN CONECTION BETWEEN PURLINS AND RAFTER: ........................... 35
CHAPTER 6. RAFTER DESIGN ..................................................................................... 37
DESIGN THE START SECTION OF RAFTER B1. ................................................ 37
Section dimention. ............................................................................................. 37
Checking section. ............................................................................................... 38
DESIGN SECTION AT THE END OF D1 – BEGIN OF D2. ................................... 42
Section dimension. ............................................................................................. 42
Checking section. ............................................................................................... 43
DESIGN SECTION AT THE END OF D2 – SECTION (6). .................................... 46
Section dimension. ............................................................................................. 46
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 132
Checking section. ............................................................................................... 47
DESIGN SECTION OF RAFTER D5 AND D6. ....................................................... 52
CHAPTER 7. COLUMN DESIGN ................................................................................... 53
DESIGN STRAIGHT COLUMN C1. ....................................................................... 53
Design length: .................................................................................................... 53
Section dimension. ............................................................................................. 54
Checking section. ............................................................................................... 55
Checking column at |M|max. ............................................................................. 60
DESIGN STRAIGHT COLUMN C2-C3. ................................................................. 65
Design length. .................................................................................................... 65
Section dimension. ............................................................................................. 67
Checking section. ............................................................................................... 68
Checking column at |M|max .............................................................................. 73
DESIGN COLUMN BRACING. .............................................................................. 77
CHAPTER 8. CHECKING DISPLACEMENT. ............................................................. 79
CHECKING VERTICAL DISPLACEMENT. ......................................................... 79
CHECKING HORIZONTAL DISPLACEMENT. ................................................... 80
CHAPTER 9. BRACKET COLUMN DESIGN .............................................................. 81
SECTION DIMENSION. .......................................................................................... 81
SECTION PROPERTIES. ......................................................................................... 81
CHECKING FOR ALLOWABLE STRESS: ............................................................ 82
CHECKING FOR OVER ALL BUCKLING. ........................................................... 82
CHECKING FOR LOCAL BUCKLING OF FLANGE AND WEB. ....................... 83
CALCULATING FILLET WELD CONNECTION. ................................................ 83
STIFFENING RIB DIMENSION. ............................................................................ 85
CHAPTER 10. DESIGN JOINTS. .................................................................................... 86
DESIGN BOLT JOINT BETWEEN C1 AND D1................................................... 86
Design bolts conection. .................................................................................... 86
Design joint flange. .......................................................................................... 88
STRUCTURAL STEEL PART TUTOR: DR.TRẦN VĂN PHÚC
NAME: NGUYỄN TRÍ THIỆN Page 133
Design fillet welded between joint flange and column.................................... 89
DESIGN BOLT JOINT BETWEEN C3 AND DẦM D4, D5. ................................. 90
Design bolts conection. .................................................................................... 91
Design joint flange. .......................................................................................... 94
Design fillet welded between joint flange and column.................................... 94
DESIGN BOLT JOINT BETWEEN D1-D2, D3-D4 AND D5-D6. ........................ 95
Design bolt joint between D5 – D6.................................................................. 96
Checking joint bolt at D1-D2 ......................................................................... 100
Checking joint bolt at D3-D4 ......................................................................... 101
DESIGN BOLT JOINT BETWEEN D2-D3 AND D6-D7. ................................... 101
Design bolt joint between D6-D7. ................................................................. 102
Checking joint bolt at D2-D3 ......................................................................... 107
DESIGN BASE OF COLUMN. ............................................................................ 107
Base column C1. ............................................................................................ 107
Base column C2. ............................................................................................ 118
REFERENCES ................................................................................................................. 129