Stress Analysis of Stiffener Plate at the Base of the Overhanging Traffic Sign Post under

Effect of Vehicle-Induced Gusts

Luangsod Somchai1, Tempiam Anan1, Fongsamootr Thongchai2 and Chartpuk Prakorb1

1Department of Mechanical Engineering, Rajamangala University of Technology Phra Nakhon, Thailand 2Department of Mechanical Engineering, Chiang Mai University, Thailand

prakorb.c@rmutp.ac.th

Abstract — This research is an analysis of stiffener plate dimensions at the column base of the overhanging traffic sign post under effect on vehicle-induced gusts. The finite element analysis (FEA) result is compared with the result form computation using mathematical equation and an experimental result which cited from Fongsamootr T. and Chartpuk P. [2006]. It is found that the FEA result has deviation about 1% and 8% respectively. Traffic sign post structure is exerted by three forces in the same time; body force, Vehicle-Induced Gusts and wind load. The higher stiffener plate leads to decrease of maximum stress at the column base. Height extension of stiffener plate from 250 to 350 mm with fixed thickness and base width leads to increase in the safety factor of column and stiffener plate. Rectangular stiffener plate with cut off a corner (type C) is the best type for supporting the base of traffic sign post column. Cutting of a corner of rectangular stiffener plate results increase of stress in itself but less than maximum stress in traffic sign post column.

Keywords-overhanging traffic sign post; stiffener plate; vehicle-induced gusts

I. INTRODUCTION Traffic sign is a component for traffic symbol. Traffic sign

is installed on highway area or roadside [1]. It controls and introduces for the traffic route. Fig. 1 shows the overhanging traffic sign, stiffener plate and steel column. The structure of overhanging traffic sign is complex structure particular stiffener plate which cannot be analyzed by using mathematics equation. Finite element method is suitable ways to solve this problem.

According to Fongsamootr T. and Chartpuk P. [2, 3] analyzed the strength of traffic sign post under wind effect but theirs in formations still lack of analyzing of strength at stiffener plate. A.Sanz Andres, J. Santiago Prowald, C. Baker and A. Quinn [4] presented a mathematical model for the vehicle-induced load on a flat sign panel, simple enough to give analytical results, but able to explain the main characteristics of the phenomenon. Phillip M. Cali and Eugene E. Covert [5] investigated the induced horizontal loads by vehicle-induced gusts on an overhead highway sign structure. The experiment was designed to measure unsteady loads on a

model highway sign (1:30 scale) produced by a model vehicle passing underneath. Osman Hag Elsafi, Sreenivas Alampalli and Frank Owens [6] described a computer-aided, spreadsheet implementation of a new procedure for design of end-plates and base-plates of sign, signal, and light cantilevered traffic support-structures and also for base-plates of span-wire-mounted traffic-signal structures. However, in previous study have no researcher analysis stiffener plate stress at the base of the overhanging traffic sign post for large structure. Thus, the aim of this study is analysis of stiffener plate stress at the base of the overhanging traffic sign post under effect on vehicle-induced gusts, equivalent static wind load and its body force.

(a) Overhanging traffic sign (b) Stiffener plate and steel column

Figure 1. Overhanging traffic sign post

II. STRESS AND STRAIN ANALYSIS OF TRAFFIC SIGN COLUMN ON A MODEL 1:6

In this study there are three methods for analyzing of stress and strain of traffic sign column; a) Experiment b) Finite element method c) Mathematical equation.

A. Experimental Setup Experimental model was fabricated column from stainless

steel 304 (scale factor 1:6). The length of column traffic sign is 123.33 mm with diameter 44.56 mm and thickness 4.7 mm and size of base steel plate is: width 96.7 mm, length 96.7 mm and thickness 4.7 mm. There are eight triangular stiffness plates. Size of stiffness plate size is: width 25 mm, height 43.4 mm and thickness 2 mm.

978-1-4673-1773-3/12/$31.00 ©2013 IEEE

Strain gauges KYOWA type KFG-5-120-C1-11L3M2R with resistance 120.0−120.8 Ω at ambient temperature 24 °C and 50 %RH was used. Six strain gauges were installed on the surface of traffic sign column which installed in pair opposite at 3 points along the length of column. First point of strain gauge is higher from column base 75 mm, second point is 370 mm and third point is 815 mm. Strain gauge indicator model SM-60D and switching balance box SS 24 were used. Stiffener plate and location of strain gauge are shown in the Fig. 2.

Figure 2. Experimental setup

B. Finite Element Method Analyses. SolidWorks program is implement which have been

designed finite element model (scale 1:6) and CosmosWorks program is used for analysis stress and strain in the column.

Pre-Processing, material properties of stainless steel 304 are followed; Young’s modulus 193 GPa, Poisson’s ratio 0.3, tensile stress 520 MPa, compressive stress 210 MPa, density 8,000 kg/m3 and body force is taken into account. In this study, ten nodes tetrahedral element type is used all parts of structures and six nodes tetrahedral element type is used for traffic sign plate.

Solve-Processing, computer-aid engineering analyzes stress and strain.

Post-Processing, the results are displayed in form of numerical value of stress and strain in spreadsheet.

C. Mathematical Equations Stress and strain in the column of traffic sign is calculated

based on beam equations with respected body force as load. Parameters of traffic sign column are defined and shown in Fig. 3 body force as load which exerts on each cross section of column is determined by SolidWorks. Given density of column material is 8,000 kg/m3.

Figure 3. Parameters of traffic sign post

Where x is x-axis coordinate z is z-axis coordinate xi is center of mass of structure traffic sign zi is center of mass of structure traffic sign ri is displacement of center of mass

θi is angle of center of mass respect x-axis D is outside diameter of traffic column d is inside diameter of traffic sign column ai is position of strain gauge (Outer side) bi is position of strain gauge (Inner side)

Data reduction: Compressive stresses occur in column at focused point (ai) can be calculated by (1) as follows.

,ii

pi

PA

σ = − (1)

Bending moment can be calculated by (2)

i

im

M CI

σ = ± (2)

Combine stress is calculated by (3)

i

i i

i

P M CA I

σ = − ± (3)

Where 4 4( ) / 64I D dπ= − and 2 2 ( ) / 4A D dπ −= Strain is calculated by (4)

i

iEσε = (4)

Where E is Young’s Modulus

D. Comparision of the Results Obtained stress occurs in column of traffic sign was shown

in Fig. 4-5. This figure shows the results which obtain from three methods; experiment, finite element method and mathematical equation. It can be seen that the stress occurs in column of traffic sign on range of 75–815 mm agree with each other. When compared to the result from finite element method, the obtained result from mathematical equation and the result from experimental have deviation about 1% and 8% respectively. However, when considered result as shown in Fig. 4-5, it can be seen that to solve the problem like this by experiment and mathematical equation has a limit because they cannot analysis stress occur throughout the length of column but finite element method can analyze. The result from finite element method shows highest stress concentration at 890 mm from base of column.

Figure 4. Stress distribution along the length of column at outer side

Figure 5. Stress distribution along the length of column at inner side

III. MODELING AND SIMULATION OF REAL SIZE TRAFFIC SIGN POST

Finite element model scale 1:1 is developed and analyzed stress concentration in by using SolidWorks program combine with CosmosWorks program.

A. Model of Overhanging Traffic Sign Post Size of traffic sign post refer to standard size which

defined by office of transport and traffic policy and planning, ministry of transport Thailand [1]. The length of traffic sign column is 8,750 mm with diameter 318.5 mm and thickness 6 mm, size of base steel plate is: width 620 mm length 620 mm thickness 28 mm and size of traffic sign plate is: width 3,500 mm height 2,400 mm thickness 2 mm.

B. Material Properties The traffic sign post is made from steel JIS G3444 grade

STK41 and traffic sign plate ASTM A36. The boundary condition is assumed to be isotropic and linear elastic material. An element type of tetrahedral 10 nodes has been adopted for the analysis. The properties of traffic sign post material including elasticity modulus E, Poison’s ratio υ, and density ρ are given in Table I.

TABLE I. STYLES MATERIAL PROPERTY FOR COLUMN TRAFFIC SIGN

Material Type

Tensile Strength

Poisson’s Ratio

Yield Strength

Mass Density

Elastic Modulus

(MPa) (MPa) (kg/m3) (GPa) JIS G3444

Grade STK41

402 0.3 235.4 7850 200

ASTM A 36 Steel 400 0.26 250.0 7850 200

C. Apply Forces There are three forces exert on the traffic sign post; body

force, equivalent static wind load and force due to vehicle-induced gusts. Equivalent static wind load [7] can be calculated by (5,6) and force due to vehicle-induced gusts is calculated by (7) which proposed by A.Sanz Andres, J. Santiago Prowald, C. Baker and A. Quinn in 2003 [4].

1) Body Force Body force is a weight of traffic sign post structure which

calculate by using SolidWorks program. Volume and density are properties of material that use for this calculation process, also gravity force.

2) Equivalent Static Wind Load Equivalent static wind load equation [7] is

212

q Vρ= (5)

A w e g pF I qC C C= (6) Where Ce is exposure factor, (1) Iw is significant factor of the wind force, (1) CP is external pressure coefficient, (1.52) Cg is gust effect factor, (2.35) ρ is air density, (1.2 kg/m3) V is reference wind speed, (15 m/s) A is area of traffic sign plate, (3.5×2.4 m2) q is reference velocity pressure, (135 N/m2) FA is equivalent static wind pressure, (482 N/m2)

3) Vehicle-Induced Gusts Force due to vehicle-induced gusts can be calculated by, (7)

2 2 2 2 2

2 2 5/ 22

4 [( ) ]b

Ch B U A U t dF

U t dρ ∞ ∞

∞

−=+

(7)

Where ρ is air density, (1.2 kg/m3) h is traffic sign plate height, (2.4 m) B is half of width of traffic sign, (3.5 m) U∞ is highest velocity of truck, (90 km/hr) d is distance between center of truck projection area to center of traffic sign plate in vertical direction, (4.5 m) Ab is twofold of projection area of truck, (18.75 m2) t is time (start -1 to 1 second) FC is vehicle-induced gusts, (N)

Fig. 6 shows magnitude of force due to vehicle-induced gusts which exert on traffic sign post by (6)

Figure 6. Relation between vehicle-induced gusts and time from (7)

IV. ANALYTICAL RESULTS OF REAL SIZE TRAFFIC SIGN POST

Three types, i.e. type (A) rectangle, type (B) triangle and type (C) rectangle with cut off a corner have been considered for stiffener plate. The type of stiffener can be found in Table II. The height of stiffener plate are vary about 250, 300 and 350 mm with fixed thickness and base width, maximum stress in stiffener plate and maximum stress in traffic sign post column have been determined. Safety factor of structure has been determined. Results have been shown in the Table II.

Since, it has biggest volume of material, stiffener plate type A is the most strength when it compared with stiffener plate type B and C.

Fig. 7−11 show distribution of stress which occurs in stiffener plate. Extension in height of stiffener plate with fixed thickness and base width results decreasing of maximum stress in column for all type stiffener plates. Considering Fig. 8, in area A has lowest stress about 2.3 MPa, thus this area is redundant part thus it can be cut off and it becomes C type like shown in Fig. 9 and 10.

For these reasons, stiffener plate C type is the most suitable for supporting of overhanging traffic sign post. However, the maximum stress in stiffener plat is less than maximum stress in column.

TABLE II. TYPE OF STIFFENER PLATE AND RESULTS

Type of stiffener

plate

Dimensions

(mm)

Max. Stress at stiffener

plate

(MPa)

Max. Stress at column

(MPa)

Safety factor

stiffener

plate at

column

(A) rectangle

w =140 h =250 t =12

81

94

2.90 2.50

w =140 h =300 t =12

80 92 2.94 2.55

w =140 h =350 t =12

78

90 3.01 2.61

(B) triangle

w =140 h =250 t =12

91

92 2.58 2.55

w =140 h =300 t =12

90

92 2.61 2.55

w =140 h =350 t =12

84

88 2.80 2.67

(C) rectangle with cut off a corner

w =140 h =250 t =12 b= 10 c= 10

86

90

2.73 2.61

w =140 h =300 t =12 b= 10 c= 10

84 90 2.80 2.61

w =140 h =350 t =12 b= 10 c= 10

80 87 2.94 2.70

Figure 7. Maximum stress in the column of traffic sign post for type A rectangle with w =140 mm, h =250 mm and t =12 mm

Figure 8. Stress distribution in stiffener plate of type A rectangle with w =140 mm, h =250 mm and t =12 mm

Figure 9. Stress distribution in stiffener plate of type B triangle with w =140 mm, h =250 mm and t =12 mm

Figure 10. Stress distribution in stiffener plate of type C rectangle with cut off a corner with w =140 mm, h =250 mm, t =12 mm b =10 mm and c =10 mm

t

w

h

w

h

w

h

b

c

Deformed shape

Figure 11. Stress distribution in stiffener plate of type 3 rectangle with cut off a corner with w =140 mm, h =350 mm, t =12 mm b =10 mm and c =10 mm

V. CONCLUSIONS The aim of this study is investigation the aspect

(configuration) of stiffener plate which suitable for traffic sign post structure is exerted by three forces in the same time: body force, Vehicle-Induced Gusts and wind load. The shape and size of stiffener plate are designed using SolidWorks program. Finite element method (CosmosWorks program) has been used to analyze the stress. The height of stiffener plate has an effect on stress concentration at the base of column, the higher stiffener plate results decrease of stress concentration in column. Rectangular stiffener plate with cut off a corner (Type C) is the best type for supporting the base of traffic sign post column. Cutting of a corner of rectangular stiffener plate results increase of stress in its self but less than maximum stress in traffic sign post column.

ACKNOWLEDGMENT The authors would like to thank the University of Chiang

Mai and Rajamangala University of Technology Phra Nakhon Thailand, Mechanical engineering department for facility and financial support.

REFERENCES [1] Manual of the support structures for traffic control devices. Office of

transport and traffic policy and planning, Ministry of Transport. Thailand. 2004.

[2] Fongsamootr T. and Chartpuk P. Analyses of Stress Distribution in Overhanging Traffic Sign Pole Using Finite Element Method, KKU Engineering Journal. ISSN 0125-8273. Published on behalf of Faculty of Engineering, KHON KAEN University, Thailand. Volume33, Number6, November−December, 2006.

[3] Fongsamootr T. and Chartpuk P. Analysis of Vehicle−Induced Gusts Effect on Stress Distribution and Natural Frequency of Traffic Sign Post Using Finite Element Method, Conference of Mechanical Engineering Network of Thailand. 20th 18−20 October 2006 at Mandarin Golden Valley Resort Khao Yai Hotel. Organize by Suranaree University of Technology, Thailand.

[4] A.Sanz Andres, J. Santiago Prowald, C. Baker and A Quinn. 2003. Vehicle induced loads on traffic sign panels. Journal of Wind Engineering and Industrial Aerodynamics. Volume 91, Issue 7 (June 2003): pp 925−942.

[5] Philip M. Cali and Eugene E. Covert. 2000. Experimental measurements of the loads induced on an overhead highway sign structure by vehicle-induced gusts. Journal of Wind Engineering and Industrial Aerodynamics. Volume84, Issue1 (January 2000): pp 87−100.

[6] Osman Hag Elsafi, Sreenivas Alampalli and Frank Owens. 2001. Computer-aided implementation of a new procedure for design of end-plates and base-plates for traffic support structures. Journal of Engineering Structures. Volume23, Issue11 (November 2001): pp 1503−1511.

[7] The calculation standard of wind load and response of the building. Department of Public Works and Town & Country Planning. Ministry of Interior. 2007.

[8] A.D.Quinn, C.J.Baker, N.G.Wright. 2001. Wind and Vehicle induced Forces on Flat Plates-Part 2: Vehicle Induced Force. Journal of Wind Engineering and Industrial Aerodynamics. Volume 89, Issue 9 (July 2001): pp 831−847.

[9] Robert D.Cook, David S. Malkus and Michael E. Plesha. Concept and applications of Finite Element Analysis. 3 rd Edition. New York: John Wiley & Son. 1989.