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1 Lehigh University Lehigh Preserve Fritz Laboratory Reports Civil and Environmental Engineering 1980 Lrfd, a comparison with allowable stress design and plastic design, "Visuals," Presented at American Petroleum nst. Conf. Lehigh University, September 1980, 34p. L. S. Beedle Follow this and additional works at: Recommended Citation Beedle, L. S., "Lrfd, a comparison with allowable stress design and plastic design, "Visuals," Presented at American Petroleum nst. Conf. Lehigh University, September 1980, 34p." (1980). Fritz Laboratory Reports. Paper This Technical Report is brought to you for free and open access by the Civil and Environmental Engineering at Lehigh Preserve. t has been accepted for inclusion in Fritz Laboratory Reports by an authorized administrator of Lehigh Preserve. For more information, please contact preserve@lehigh.edu.

2 D A Com pari.son with. ' ~ Allowlible Stress Des1qn li, i and ~ ~ ; Pla.st, c De.si~r:> ~~; :!. i. i. StZpt 1980 ftitl: E V)q V) q (fv~ la..bdf't.dory. Le~t:~ U~'ltreS ily i : Report b v ' ' i.

3 FUNCTONAL RE.QUREME.NTS support LOAD J PROVDE STFFNESS ECONOMCAL REQUREMENTS Fig. 1. Structurql Design Objectives. The main objectives of Structural Design do not change with the design method.

4 ""'' 3'71.1 n:::: Steps. in Destqn 1. Function Z.. Structure and Loadinq 3. Loadinq Conditions 4. Preliminary Desiqn 5. Analysis 6. Selection of Section :! 7. Secondary Deslqn Check. ; ' Fig. 2.. ~ ~ ~ The steps in design are also independent of the method that is used..

5 Allowable Stress Design Working Stress Design Elastic Design Plastic Design Ultimate Strength Design Limit Design Load and Resistance Factor Design Load Factor Design Limit States Design ' Fig. 3. There are three groups of design concepts: The "allowable stress" group, the "plastic design" group, and the "load and resistance factor" gr oup.

6 ',. :: ;:. :.;. :::.. ~ :.i :.... ::,. '.::... ' < frr <~Q.....,<.!.,l.. :' ::. ' :: ; ~ ::) : ~. : :... : : ; :.. [ : ~. :, Fig. 4. The LRFD formulation is simple: The load factor times the load effect must be less than the resistance factor times the resistance of the member. (The format shown in the second line of the formulation :l.s typical of that which appears in research papers.)

7 DEAD LOAD LVE LOAD Long Term Short Term Extraordinary COMBNATONS P PLASTC LMT STABLTY LMT ELASTC LMT FATGUE. FRACTURE DEFLECTON (VBRATON) Fig. 5. LRFD involves the examination of the loading function (left) and the resistance function (right). Design is equating the two through analytical'techniques and the use of the basic LRFD equation.

8 p / /,LR ~ a y!!lllli!!j p, Fig. 6. LRFD is compared with allowable stress design at the left. At the right it is compared with a form of load factor design, first with single load.factors and then with multiple load factors. The comparison is, in fact, with a plastic design, except that the use of multipleload factors can lead to lighter members.

9 p Fig. 7. The load deflection curves and load bars of Fig. 6 are simplistic. Actually there is uncertainty. This figure shows an example of uncertainty in the loading function fl.

10 p Fig. 8. The uncertainty in response is shown (fr). Comparing with Fig. 7, there ~s less variation in response or resistance than there is in load...

11 pp ~R T p FD L R fe L ~ ~R. (yq~cpr) Fig. 9. Failure is defined according to the following criterion: The maximum load, fl is less than the minimum possible resistance (f x R). r.

12 .; :: LOAD psf ~:....:..... _...., ~ i : ~ ; ~ ;. : : ~ : : :..::: t'...~"'..,. ~! ~.... ~~ ~,...J.. ~ :: ~ j : : :: :1 p Per j. NO. :. i Fig. 10. Actual measured load and resistance data. To the left is shown the variation in floor load. ro the right, the variation in resistan~e of continuous beams. These observations illustrate the greater scatter in load as compared to that of resistance. =,

13 Load,, ' '.,!.Po. R s.! R s Ps ASD PD LRFD D.ef lection Fig. 11. How safety is achieved in the three design methods. Allowable Stress Design: Start with yield and come down to allowable. Plastic Design: Start with the service load and factor up to design ultimate load. LRFD: Factor up from service load and factor down 'from nominal resistance of the structure. The arrows show where design attention is focussed in each of the three methods.

14 . APPROXMATONS N ANALYSS APPROXMATONS N DESGN, STREss CONCENTRATONS AND RESDUALS VARATON VARATON WORKMANSHP LOCATON VARATON N c omb NATON OF NTENDED N PROPERTES N DMENSONS USE LOAD TYPE. LOADS Fig. 12. Tabulation of the approximations and uncertainties in design, workmanship, and loading. These factors must be accommodated in any design method......

15 :'. :: '::.~ ~ : :!: ::. 3 '7 3 }\ ' load Factor Tension Ft :: 0. 60fy 1.67 Bending Fb = 0. 66Fy 1.70 z r,_ (Kh) c 2 c: Y. Compresslon Fa = a _2_ + 3 (Kf;r). (Kf!r) 3 o c, B c; L67 l.9z, Fig. 13. How safety is achieved in Allowable Stress Design for three types of loading. 'To the right is shown the corresponding load factors

16 GRAVTY PLUS LATERAL LOAD TENSON MEMBERS SHORT COLUMNS BEAMS PLASTC DESGN LONG COLUMNS RVETS BOLTS WELDS SHEAR CONNECTORS Fig. 14. Uncertainty in Plastic Design is accommodated by load factors. Note the'rational progression of load factors depending on the importariceof member or uncertainty of loading or response.

17 ALLOWABLE STRESS DESGN PLASTC DESGN P. u FY NHERENT MARGN OF SAFETY P. u,,,,,,,,,,,,,,,,, CTmax =20 ksi R'""tj'" o~ Deflection Deflection Fig. 15. The philosophy behind selection of load factor F in Plastic Design is this: The same safety in continuous beams as inherent in the past ASD of simple beams. r

18 : '~,(!": '1 '7/ t/ ::: ::: _) F = Pp Mp ~l Pa Ma Q'"d s y a., (J"'i z. f!!... S. LZ Fig. 16. The ~a1cu1ation of F based on concept of Fig. 15.

19 :::.!~n: =? l ~~; : Q.R ~ Q 0 " Fig. 17. Examining safety in LRFD. Variations of load and resistance indicated in Fig. 9 are shown. Resistance at top, load at bottom. What is failure? When Q is greater than R. Area under. curves (see shaded at left) is related to robabilit of failure.

20 Tj[:.) / lr Pn < P.Q. Pfz Fig. 18. Safety depends upon two things: The difference in Q and R and the variability of Q and R. This figure illustrates the first..... ::: = :

21 1m11m l.l\~mmm1 Pfl < Pfz Variability Fig. 19. An illustration of how an increase in the variability (in this case variability of load) increases the probability of failure.

22 klormal Event En Mean Nomina\ (hand book) Uo~ ol Occurrences Fig. 20. Some of the terms and functions associated with measuring and evaluating variability: Normal and skew distributions. Standard deviations a. Mean and nominal (handbook) events (E m and E n, respectively).

23 :: Q R. Rm Fig. 21. Functions shown are the mean value of load, Q standard deviation m of load a, meanvalue of resistance R, and standard deviation of resist2nce ar. Coefficient of vari~tion is ratio of standard deviat_ion to mean value.

24 R Rm ftr T Rm Gm Qrn.. (JQ. l Q Saf~ty Marqin: R.& 0 Fig. 22. Failure can now be defined more specifically. is R Q, so safety will depend on two things: Area under curve ~s probability of.failure. The safety margin R Q and on a. m m f!

25 . :3,..,,. Q R ' RQ R 0 Fig. 23. f safety depends on R Q it can be plotted that way. See on right.

26 ; "~. :. ::::.~. '''T 3/1 _,?J ::: RQ "'J + UQ 0 Fig. 24. B is defined as the "safety index" or "reliability index". The relationship shown is only true for normal distributions.

27 ol:, ::,.. R ln Q 0 Fig. 25. The relationship of S to R, Q, and standard deviation can also m m be express~d in terms of logar1thmic functions of R and Q.

28 .: ':. Beams Connections f3 = 3. 0 f: cr 4.5 cr 0,~~ Fig. 26. "Calibration" is achieved by comparing the 8v<~lues with what would be obtained in the design of a beam by Allowable Stress Design. Two cases are shown.

29 Rm Rn "Related" to t5 0 Fig. 27. Although the specific comparison is not indicated, this illustrates the fact that F x R and F x Q are related to 8.. r q. :. : ::: :... :~..

30 :,..,,, : i.ri:!!!hlln\l11lt!n :l:!~ill 1 :i :::1: 1 :::: : :r:m:::::! :!:! :: : ::1::.:: ~::: ::l 11::: 1: ::. : 1:1 1:! ::,.:: : : : ~,: :1,.:: T 1:: 1 :: 1: r :! 1 : r::.: m.::: : ' : : :, Fig. 28. The relationship of load and resistance factors with B is shown mathematically.

31 Yf. (t3 \,.:::: F.L t < Fig. 29. The simplification of the LRFD format shown earlier, is expanded here to show the multipleloadfactor aspect.

32 Load Combinations Load Factors _D_e_,a_d ; l i v_rz ; 1.4 l i.z.z '.2..Z ~ S_noY! '~~~~ O.Z 0.6, 3 (. 3 ~o'!h~u~ak~! t5' : t5 ; 1.5.! :,! :~' ' i~~.. ~..1~ Fig. 30. A possible ~et of load combinations and load factors for use in LRFD. ::: ; 1 rr~ r:t : :i..,',;.'~ _.'~.'~ ~ l j H1l ~

33 Element Tension Member. Beam Resistance Factor& Limit State YiQid Fracture Bendinq (Mp.M,r) Shear (Vp.Vcr.) Fr ( ) Co{umn Weld Bolt shape Stability Other Stability 6roove Fillet Fracture Shear Fracture Shear Fracture.,8.8.9.s ;. :. Fig. 31. Possible resistance factors for use in LRFD. These have been simplified and rounded off. mmml" u1 1l, r '~@ mmrm:.. : :; ;...

34 ... ' ' :: ' :, H fo Q 1> + FL QL < fr zo' lln PL 4 f 0 : L2 fl:. (.6. FR. = 0.~ Qo: Mo QL: ML Rn: t!y 'i P: Z f( 0:9 l: ll l.z M ML ( <fy'l:. 12 <CJlzol< 12.) 1,. 4 o~<1okrz) t ' 4.( 0.9(36) c Fig. 32. Some of the. essentials of the LRFD method are shown in this design example.

35 Z. z , Save cost zo 0 0 L Ot\. All Dead Load All liv~ load Fig. 33. The required plastic modulus according to three ASD (59.9 in. 3 ), PD (59.6 in. 3 ). LRFD (46.7 to depending on ratib of dead load to live load). multiple load factor aspect of LRFD has a great ~hether material will be saved or not. different designs: in., Evidently the deal to do with