Steel Design

CVEN 659 BEHAVIOR AND DESIGN OF STEEL STRUCTURES

A report on

DESIGN OF A PRATT TRUSS

by

Alla, Jaya Ram Reddy, (UIN: 224002461)

Kothapalli, Akesh Varma (UIN: 423001329)

Mohammed, Azeemuddin Gulam (UIN: 223008918 )

Prodduturu, Harika Reddy (UIN: 523005004)

Spring 2015

i

Alla, Kothapalli, Mohammed, Prodduturu

Contents

Contents.................................................................................................................. i

List of Figures .......................................................................................................ii

List of tables ........................................................................................................ iii

List of symbols ...................................................................................................... iv

1. PROBLEM STATEMENT ............................................................................. 1

2. ANALYSIS OF TRUSS MEMBERS ............................................................ 2

3. DESIGN OF TRUSS MEMBERS ................................................................. 6

4. DESIGN OF BOLTED CONNECTIONS ................................................... 10

5. CHECK FOR BLOCK SHEAR FAILURE ................................................. 12

Annexure A: BILL OF QUANTITIES ............................................................... 123

Annexure B: DRAWINGS ................................................................................. 124

References ......................................................................................................... 155

ii


List of Figures

Figure 1: Side elevation of the truss...1

Figure 2: Section A-A used in method of sections.3

Figure 3: Transverse Loads on beam #72......5

Figure 4: BMD of beam #72..........5

Figure 5: Transverse Loads on beam #72..5

iii


List of tables

Table 1: Axial forces in each of denoted members4

Table 2: Bolts provided at selected joints11

Table 3: Bill of quantities for a 300 ft. long truss13

iv


List of symbols

Slenderness parameter Limiting slenderness parameter for compact element Limiting slenderness parameter for noncompact element Resistance factor Effective net area, in2 Gross cross-sectional area of member, in2. Gross area subject to shear, in2 Net area subject to tension, in2 Net area subject to shear, in2 Specified minimum tensile strength, ksi Specified minimum yield stress, ksi First-order moment using LRFD or ASD load combinations, with the structure restrained against lateral translation, kip-in

Plastic bending moment, kip-in Required axial strength in chord using LRFD load combinations, kips

1


1. PROBLEM STATEMENT

The purpose of this report is to design a 300 feet roof Pratt truss members for the given

design loads. The loads that are given are:

Dead Loads:

Decking plus clay tile roofing (on Sloping sides) =25 psf. of roof area

Decking plus built-up roofing (on center portion) =10 psf. of roof area

Purlins plus sag rods =5 psf. of roof area.

Live Loads:

Snow =25 psf. of projected area.

Roof Live load =10 psf. of projected area.

Concentrated Load =2 kips at any bottom chord panel point

Figure 1: Side elevation of the truss

The span of the truss is 300 feet with vertical members and diagonal bracings spaced 25 feet

apart as shown in Figure 1.

2


2. ANALYSIS OF TRUSS MEMBERS

2.1 Load combinations as per AISC Manual:

As per AISC Manual, following are the possible load combinations.

1 1.2 1.6 0.5 2 1.4 3 1.2 1 0.5 0.5 4 1.2 1 0.5 0.2 5 0.9 1 6 0.9 1

The critical load combination which will have a maximum effect on the truss in terms

of axial loads and moments on its individual members is:

1.2 1.6 0.5 As a first step of design, axial forces in each chord member have been calculated

using SAP 2000. The practical tributary loads on each purlin which further induces moments

in individual members of the truss have been calculated.

2.2 Calculation of axial Loads:

The purlins are assumed to be placed 5 feet apart (panel points). Transverse loads on

Panel points (P) have been applied, for calculation of axial forces in the members. The

transverse loads on the panel points have been calculated for tributary width.

Loads on panel points:

Dead loads:

Decking plus roofing = 10 40 5 2 Purlins plus sag rods = 5 40 5 1 Live Loads:

Snow Loads = 25 40 5 5 Roof Live load = 10 40 5 2 Concentrated Load = 2 on any bottom chord panel point. The axial forces in each member are deduced using these tributary loads.

3


The forces , , & are found to be 38 76 67 58

The reactions at the supports for the given loads are:

384 Method of sections has been adopted to calculate the axial forces in each member beginning

with section A-A as shown in the figure 2.

Figure 2: Section A-A used in method of sections

The truss has to be designed to take the concentrated live load of 2 kips on any bottom

panel point. Accordingly, a series of analysis were performed by using SAP 2000 and it was

found that when the concentrated load was placed at exactly center panel point, it induced

maximum axial tensile forces in lower chord panel members. So, the axial members in

tension will be designed by applying that 2 kips of load at center panel point on lower chord.

Applying Moment equilibrium about point O

125 30 125 100 75 50 25 0

Solving above equation,

875

4


Table 1: Axial forces in each of denoted members.

Beam # Pu(kips) Behaviour Beam # Pu (kips) Behaviour

25 -210.958 Compression 1 276.478 Tension 26 -151.142 Compression 2 198.427 Tension27 -90.3 Compression 3 119.421 Tension 28 -58.858 Compression 4 40.227 Tension 29 -90.3 Compression 7 197.617 Tension30 -151.142 Compression 8 275.668 Tension 31 -210.958 Compression 24 40.603 Tension 35 -717.653 Compression 32 40.603 Tension41 -717.653 Compression 55 599.904 Tension 49 -2.738 Compression 56 600.517 Tension 50 -2.738 Compression 57 540.904 Tension 53 -948.724 Compression 58 718.757 Tension 54 -948.724 Compression 59 846.475 Tension 67 -845.761 Compression 60 923.213 Tension 68 -922.794 Compression 61 923.213 Tension 69 -922.794 Compression 62 846.475 Tension 70 -845.761 Compression 63 718.757 Tension 71 -700.487 Compression 64 540.704 Tension 72 -629.844 Compression 65 600.517 Tension 73 -700.487 Compression 66 599.904 Tension 74 -629.89 Compression75 -70.21 Compression76 -70.21 Compression

The axial forces deduced and shown in table 1 are used to find the moments in

members and find the corresponding flexural demand. The assumption of allotting loads over

the panel points is only to facilitate the calculation of axial loads in the members, which

technically doesnt produce any moments in the beam. But in reality, the truss members in

the upper chords are under the influence of point loads spread evenly over the span of 25 under which there are considerable moments. Hence all the members in the upper chords act

as beam column due to presence of both lateral and transverse loadings.

Analysis of beam # 72 for flexural demands is shown. The factored loads on the beam

are shown in the figure 3. (All loads are in kips)

5


Figure 3: Transverse Loads on beam #72

For the above loading conditions the bending moment diagram is as follows in figure 4. All values are in kip-in

Figure 4: BMD of beam #72

The combined loading (including axial loads) is shown in figure 5..

Figure 5: Transverse Loads on beam#72

For this beam to be designed second order analysis has to be performed as per AISC

specification Section Appendix 8. A point of information to be mentioned is that the beams

are designed for flexure due to transverse loading about their minor axis Y-Y.

With reference to figure 5

__ 228

Assuming that dead load of member is 200 lb/ft, and is accounted for assumed self-weight of the beam and accordingly the axial loads in the members are increased by 18.75k-ft.

6


3. DESIGN OF TRUSS MEMBERS

3.1 Design of compression members

As per AISC specification Section F-1,

is found to be 1.136. Let us assume W14X120 wide flange section.

Checking the beam for following conditions:

1. Flange Local Buckling 2. Web Local Buckling 3. Lateral Torsional Buckling

1. Flange Local Buckling:

As per section F-1, AISC specifications, the criteria for flange local buckling is , 7.8

9.152 Since , Flange Local Buckling is not checked. Therefore,

382.5 . 2. Web Local Buckling

As per section F-1, AISC specifications, the criteria for web local buckling is , 19.3, 90.553

Since , Web Local Buckling is not checked. Therefore,

382.5 . 3.2 Lateral Torsional Buckling:

19.3; 300; 158.525; 623.484 Since , _ undergoes reduction and by a factor as mentioned in AISC specification F2 (eqn. F2-2) Hence _ found to be equal to be equal to 363.553 kip-ft Therefore the flexural Moment capacity of the selected member is _ 327.197 .

Checking the section in compression for following:

7


1. Flexural Local Buckling. 2. Web Local Buckling.

1. Flexural Local Buckling:

7.8; 13.487 Since , it is non-slender and Flexural Local Buckling doesnt occur. Therefore,

992.363. 2. Web Local Buckling:

19.3; 35.884 Since , it is non-slender and Web local Buckling doesnt occur. Therefore,

992.363. Based on two possible modes of failure, it is found that the capacity of the member is . kips

As per AISC specification Appendix 8, the ultimate moment and axial load demands

are increased with a factor&. Since there is no moment in X-X axis, becomes zero and is calculated as per (A-8-3) of AISC and found to be equal to 1.778

The load interaction as per section H1 in AISC specification is calculated and found

to be 1.298, which is greater than 1 and hence this member isnt suitable for the current

demands of flexure and compression. Similar procedure was adopted and it was found that

W14 X 176 was suitable with deflections in the member lesser than 1.25 in. i.e. (L/240). For

all the members acting as Beam-column, similar methodology of limit state was adopted and

to make the truss aesthetically appealing, all the members in the upper chord were assigned

W14 X 159 section.

3.2 Design of Tension Members:

It is observed, as presumed, that most of tension members were the lower chord

members. All the tension members have been designed as per AISC specification Chapter D.

There are two limit state criteria for tension member design.

1. Gross section yielding

2. Net area Rupture

8


1. Gross Section yielding:

A member with gross sectional area yields in tension when,

The capacity of the member will be , where is 0.9 as per AISC specifications. 2. Net area Rupture:

A tension member should also be checked for net area rupture as per the following equation

The capacity of the member will be , where is 0.75 as per AISC specifications. Design of beam# 60 has been shown. All the other tension members in the truss have been

design in the same manner.

For beam# 60: 913.213

5% of the ultimate load is added to accommodate the self-weight of the member. Hence

taking

988 Let us assume W 14 X 68 section for which,

20 65 50

For Gross area yielding

20 50 1000; 0.9 1000 900

which is not enough for the current demand.

9


Let us consider W14X 82, whose section and material properties are as follows.

24 65 50

For Gross area yielding

0.9 24 50 1080 For calculating Net area Rupture Capacity, net area is assumed to be 85% of the gross area.

0.75 65 0.85 24 994.5; 994.5 958.87

Hence W 14X82 is suitable member in lower chord.

All the tension members and compression members are designed in a similar manner.

Figure 6 shows the assigned sections for the truss members. (AUTO CAD PRINT)

10


4. DESIGN OF BOLTED CONNECTIONS

Connections play a very important role not only in fixing up the members but

also in terms of strength and serviceability of the member as a whole. For this design, bolted

connections have been used as per section J3 of AISC Steel specifications. Let us assume a

1in. diameter bolt and in. gusset plates. Strength of a bolt is governed by two factors.

1. Bearing capacity of the bolt

2. Shear capacity of the bolt

1. Bearing capacity of the bolt

The maximum bearing capacity of a bolt is given as:

2.4 2.4 1 0.5 58 69.6 2. Shear capacity of the bolt

The shear strength of 1 in. dia bolt as given in table 7.1 of AISC specifications is 31.8 k.

It is seen that the strength of the bolt is governed by shear. Hence taking shear

capacity of the bolt and calculating the number of bolts required for a bottom chord member

beam# 60 whose axial force is 923.213k,

923.21331.8 30

Design of connections for the joints specified has been calculated in a similar manner.

Table 2 shows the number of bolts required and number of bolts provided for critical joints.

A minimum of 3 in. center-to-center spacing, 1.25 in. edge/end distance has been

required as per AISC specifications, but the bolts are placed depending on the sections

chosen at respective joints. The number of bolts provided for each joint is specified in figure

7.

11


Table 2: Bolts provided at selected joints.

Joint Member Section Bolts

Required Bolts

Provided

1

60 W14X176 30 32 4 W14X22 2 4

28 W14X61 2 4 5 W14X22 2 4

61 W14X176 30 32

2

59 W14X176 27 283 W14X22 4 4

27 W14X61 3 4 60 W14X176 30 32

3

58 W14X176 23 24 2 W14X22 7 8

26 W14X61 5 8 59 W14X176 27 28

4

57 W14X176 18 20 1 W14X22 9 12

25 W14X61 7 8 58 W14X176 23 24

5

56 W14X176 19 2075 W14X22 3 4 24 W14X61 2 4 57 W14X176 18 20

6 55 W14X176 19 20 49 W14X22 1 4 56 W14X176 19 20

7 55 W14X176 19 20 71 W14X159 23 24

8

71 W14X159 23 24 49 W14X22 1 4 75 W14X48 3 472 W14X159 20 20

9

72 W14X159 20 20 24 W14X61 2 4

1 W14X22 9 12 35 W14X159 23 24

10

35 W14X159 23 24 25 W14X61 7 8

2 W14X22 7 8 67 W14X159 27 28

11

67 W14X159 27 28 26 W14X61 5 8

3 W14X22 4 4 68 W14X159 30 32

12

68 W14X159 30 32 27 W14X61 3 4

4 W14X22 2 4 53 W14X159 30 32

13 53 W14X159 30 32 28 W14X61 2 4 54 W14X159 30 32

12


5. CHECK FOR BLOCK SHEAR FAILURE

The tension members can fail at the connection ends doe to tear-out of the material at

the locations of connections. This is referred as block shear. Section J4.3 of AISC

specifications mentions about the block shear. It is a critical mode of failure which has to be

taken care of.

Block shear is defined as the sum of gross yielding capacity and net section fracture

strength of the tension path. It is governed mainly by the bolt pattern and the failure path

occurs along the perimeter of the entire bolt. The block shear calculated according to AISC

specifications should be greater than the ultimate tensile forces in the members. A check for

the tension members used in the design has been performed and checked against ultimate

tensile forces in the member. As an illustration, calculation of block shear capacity of

member W 14X176 having maximum tensile forces have been shown below.

, 0.6 0.6 0.6

0.6 0.6 For the section considered:

31.44; 3.93; 3.193; 30.122 207.817; 0.6 1178

0.6 1031.076; 0.6 1039.359 1031.076 923.213

which is the ultimate tensile load in the member. In a similar manner, all the steel members used are checked and found to be well within the limits.

Note that, the bottom chord members could have been built using section W14X99

for lesser weight of steel, but the section is failing in block shear after the connections are

built. Hence, it has been changed from W14X99 to W14X176. The sections assigned to

each member of the frame and details of the bolts and their center to center spacing have

been shown in figure 7.

13


ANNEXURE A: BILL OF QUANTITIES

Table 3: Bill of quantities for a 300 ft. long truss

S.No Member Section Length(ft) Weight

(#/ft)

Total Weight (Kips)

Remarks

1 1 W14X22 39 22 0.86

Only half the length is considered for the weight calculation.

2 2 W14X22 39 22 0.86 3 3 W14X22 39 22 0.86 4 4 W14X22 39 22 0.86 5 24 W14X61 30 61 1.83 6 25 W14X61 30 61 1.83 7 26 W14X61 30 61 1.83 8 27 W14X61 30 61 1.83

9 28 W14X61 15 61 0.92

10 35 W14X159 25 159 3.98 11 49 W14X22 15.9 22 0.35 12 53 W14X159 25 159 3.98 13 55 W14X176 25 176 4.40 14 56 W14X176 25 176 4.40 15 57 W14X176 25 176 4.40 16 58 W14X176 25 176 4.40 17 59 W14X176 25 176 4.40 18 60 W14X176 25 176 4.40 19 67 W14X159 25 159 3.98 20 68 W14X159 25 159 3.98 21 71 W14X159 29.15 159 4.63 22 72 W14X159 29.15 159 4.63 23 75 W14X48 29.15 48 1.40

Total Steel Weight (half of the section) 64.99 Kips Total Steel Weight: 129.97 Kips

14


ANNEXURE B: DRAWINGS

15


REFERENCES

Specification for Structural Steel Building, AMERICAN INSTITUTE OF STEEL CONSTRUCTION, Chicago, Illinois , 2010, pp 26-43, 105-108.

Steel Design

Documents

Transcript of Steel Design