A Note on the Mohr–Coulomb and Drucker–Prager Strength Criteria

Mechanics Research Communications 64 (2015) 57 Contents lists available at ScienceDirect Mechanics Research Communications journal h om epa ge: www.elsevier.com/locate/mechrescom Corrigendum Corrigendum to “A note on the Mohr–Coulomb and Drucker–Prager strength criteria” [Mech. Res. Commun. 38 (2011) 309–314] Hua Jiang ∗ , Yongli Xie Key Laboratory for Bridge and Tunnel of Shaanxi Province, Chang’an University, Xi’an, PR China a r t i c l e i n f o Article history: Received 11 December 2014 Accepted 4 January 2015 Available online 17 January 2015 Required corrections: The paper entitled “A note on the Mohr–Coulomb and Drucker–Prager strength criteria” [1] contains various expression of the Mohr–Coulomb criterion, but Eq. (12b) contains an error. The correct form of that equation is ( 1 − 3 ) 2 ( 1 tan ϕ − c)( 3 tan ϕ − c) = 4 (12b) It can be obtained as follows: The length of the tangent line AB of the Mohr circle (see Fig. 1), which passes though point A( 0 , 0) can be expressed as |AB| = 1 2 ( 1 − 3 ) × cot ϕ (A1) According to Tangent–Secant Power Theorem [2] |AB| 2 = |AC||AD| (A2) and |AC||AD| = ( 1 − 0 )( 3 − 0 ) with 0 = c cot ϕ (A3) Substituting Eqs. (A3) and (A1) into Eq. (A2), we have 1 4 ( 1 − 3 ) 2 cot 2 ϕ = ( 1 − c cot ϕ)( 3 − c cot ϕ) (A4) After mathematical transformation, gives ( 1 − 3 ) 2 ( 1 − c cot ϕ)( 3 − c cot ϕ) = 4 tan 2 ϕ (A5) DOI of original article: http://dx.doi.org/10.1016/j.mechrescom.2011.04.001. ∗ Corresponding author. Tel.: +3892882659. E-mail address: [email protected] (H. Jiang). Fig. 1. The M–C criterion on n − plane. Or in alternative form ( 1 − 3 ) 2 ( 1 tan ϕ − c)( 3 tan ϕ − c) = 4 (A6) Acknowledgment The authors thank Liu Nian from China University of Mining and Technology, Beijing for pointing out the error. The ﬁrst author is grateful for the support from the National Science Foundation of China (Grant 51308054). References [1] H. Jiang, Y.L. Xie, A note on the Mohr–Coulomb and Drucker–Prager strength criteria, Mech. Res. Commun. 38 (2011) 309–314. [2] H.S.M. Coxeter, Introduction to Geometry, 2nd ed., Wiley, New York, 1969. http://dx.doi.org/10.1016/j.mechrescom.2015.01.001 0093-6413/© 2015 Elsevier Ltd. All rights reserved.

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Transcript of A Note on the Mohr–Coulomb and Drucker–Prager Strength Criteria

Mechanics Research Communications 64 (2015) 57

Contents lists available at ScienceDirect

Mechanics Research Communications

journa l h om epa ge: www.elsev ier .com/ locate /mechrescom

Corrigendum

Corrige b and DruckerPragerstrengt 11) 309314]

Hua JianKey Laboratory

a r t i c l

Article history:Received 11 DAccepted 4 JanAvailable onlin

RequireThe pap

DruckerProf the Mohrcorrect form

((1 tan

It can beThe leng

which passes though point A(0, 0) can be expressed as

|AB| = 12 (1 3) cot (A1)

According to TangentSecant Power Theorem [2]

|AB|2 = |AC||AD| (A2)

and

|AC||AD| = (

Substitu

14 (1 3)

2

After ma

(1(1 c cot

DOI of orig Correspon

E-mail add

Fig. 1. The MC criterion on n plane.

Or in alternative form

(1 3)2(1 tan c)(3 tan c)

= 4 (A6)

Acknowledgment

http://dx.doi.o0093-6413/ 1 0)(3 0) with 0 = c cot (A3)

ting Eqs. (A3) and (A1) into Eq. (A2), we have

cot2 = (1 c cot )(3 c cot ) (A4)

thematical transformation, gives

3)2)(3 c cot )

= 4 tan2 (A5)

inal article: http://dx.doi.org/10.1016/j.mechrescom.2011.04.001.ding author. Tel.: +3892882659.ress: [email protected] (H. Jiang).

The authors thank Liu Nian from China University of Mining andTechnology, Beijing for pointing out the error. The rst author isgrateful for the support from the National Science Foundation ofChina (Grant 51308054).

References

[1] H. Jiang, Y.L. Xie, A note on the MohrCoulomb and DruckerPrager strengthcriteria, Mech. Res. Commun. 38 (2011) 309314.

[2] H.S.M. Coxeter, Introduction to Geometry, 2nd ed., Wiley, New York, 1969.

rg/10.1016/j.mechrescom.2015.01.0012015 Elsevier Ltd. All rights reserved.ndum to A note on the MohrCoulomh criteria [Mech. Res. Commun. 38 (20

g , Yongli Xie for Bridge and Tunnel of Shaanxi Province, Changan University, Xian, PR China

e i n f o

ecember 2014uary 2015e 17 January 2015

d corrections:er entitled A note on the MohrCoulomb andager strength criteria [1] contains various expressionCoulomb criterion, but Eq. (12b) contains an error. The

of that equation is

1 3)2 c)(3 tan c)

= 4 (12b)

obtained as follows:th of the tangent line AB of the Mohr circle (see Fig. 1),

Corrigendum to A note on the MohrCoulomb and DruckerPrager strength criteria [Mech. Res. Commun. 38 (2011) 309314]AcknowledgmentReferences