William John Macquorn Rankine, (born July 5, 1820, Edinburgh, Scot.—died Dec. 24, 1872, Glasgow), Scottish engineer and physicist and one of the founders of the science of thermodynamics, particularly in reference to steam-engine theory. Trained as a civil engineer under Sir John Benjamin MacNeill, Rankine was appointed to the Queen Victoria chair of civil engineering and mechanics at the University of Glasgow (1855). One of Rankine’s first scientific works, a paper on fatigue in metals of railway axles (1843), led to new methods of construction. His Manual of Applied Mechanics (1858) was of considerable help to designing engineers and architects. His classic Manual of the Steam Engine and Other Prime Movers (1859) was the first attempt at a systematic treatment of steam-engine theory. Rankine worked out a thermodynamic cycle of events (the so-called Rankine cycle) used as a standard for the performance of steam-power installations in which a condensable vapour provides the working fluid.

2.  Rankine - best known for his accomplishments in
thermodynamics (description of the operational
cycle of an ideal engine using steam or another
vapor) & soil mechanics (earth pressure theory).
 Born- in Edinburgh, Scotland, on July 5, 1820.
(1820 - 1872)

3. CAREER
 primary education - taught mostly by his father &
private tutors,
 two extraordinary years -schooling at the University
of Edinburgh.
 Leaving without a degree, Rankine set out to become a
civil engineer.
 Apprenticed under -Sir John Benjamin
MacNeill(Thomas Telford’s chief assistant).
(1820 - 1872)

4.  practiced the civil engineering profession until the late
1840’s.
 From 1848 to 1855, Rankine spent a great amount of
his time in researches on theoretical physics,
thermodynamics and applied mechanics.
 On December 3, 1855 - was appointed by the Queen’s
Commission to the Chair of Civil Engineering and
Mechanics at Glasgow - a Regius Chair established by
royal decree.
 His ensuing years, leading up to the time of his death,
were spent- as a professor and author.
(1820 - 1872)

5. CIVIL ENGINEER
Rankine spent a year assisting his father
David Rankine .
Then left for Ireland -worked on railroad,
hydraulic, and various other projects.
After four years in Ireland, he returned to
Scotland and worked with railway companies
and consultants until about 1848.
(1820 - 1872)

6. EDUCATOR
 Rankine first pushed for an award of Diploma in
Engineering Science.
 secondly, Rankine endeavored for the award and
got approval.
 Lastly to Rankine’s effort were his success at
establishing a BSc in science.
 Again, Rankine’s incessant efforts aside from his
respected knowledge gained him praise
throughout the world for pioneering the
engineering education.
(1820 - 1872)

7. AUTHOR
 Authoring 111 papers & writing numerous textbooks,
his respective scientific findings remain a foundation
in soil mechanics and thermodynamics today.
 One of the first scientific works- a paper on fatigue in
metals of railway axles (1843), led to new methods of
construction.
 His Manual of Applied Mechanics (1858) was of
considerable help to designing engineers and
architects.
(1820 - 1872)

8.  His classic Manual of the Steam Engine and Other
Prime Movers (1859) was the first attempt at a
systematic treatment of steam-engine theory.
 Rankine worked out a thermodynamic cycle of
events (the so-called Rankine cycle) used as a
standard for the performance of steam-power
installations in which a condensable vapour provides
the working fluid.
 In soil mechanics his work on earth pressures and
the stability of retaining walls was a notable
advance.
(1820 - 1872)

9. CONTRIBUTION TO SOIL
MECHANICS
 Rankine's theory (maximum-normal stress theory),
developed in 1857 - is a stress field solution that
predicts active and passive earth pressure.
 It assumes that the soil - cohesionless, the wall is
frictionless, the soil-wall interface is vertical, the
failure surface on which the soil moves is planar, and
the resultant force is angled parallel to the backfill
surface.
(1820 - 1872)

10.  The pressure exerted by soil against the wall is
referred to as active pressure. The resistance offered by
the soil to an object pushing against it is referred to as
passive pressure.
 Rankine's theory is applicable to incompressible soils.
 The equation for cohesionless active earth pressure is
expressed as
𝑃𝑎 = 𝐾 𝑎 𝑤ℎ
where:
𝐾 𝑎 =
cos 𝛽 − (cos 𝛽2 − cos ∅2)
1
2
cos 𝛽+ (cos 𝛽2 − cos ∅2)
1
2
* cos 𝛽
(1820 - 1872)

11. where:
Ka = Coefficient of active pressure
w = weight density of soil
h = depth of the section (below top soil) where the
pressure is being evaluated.
β = angle that the top surface of soil makes with the
horizontal.
φ = angle of internal friction of soil.
(1820 - 1872)

12.  The expression for passive pressure is:
𝑃𝑝 = 𝐾 𝑝 𝑤ℎ
where:
𝐾 𝑝 =
cos 𝛽+ (cos 𝛽2 − cos ∅2)
1
2
cos 𝛽− (cos 𝛽2 − cos ∅2)
1
2
* cos 𝛽
where:
Kp = Coefficient of active pressure
(1820 - 1872)

13. LIMITATIONS OF RANKINE’S THERY
(i) As the retaining walls are usually constructed of
masonry or cement concrete, the back of the wall is
never smooth, and hence friction develops.
(ii)due to assumption that wall back is smooth, the
resultant pressure must act parallel to the surface but
due to frictional forces, the active earth pressure gets
inclined in the wall at an angle equal to angle of
friction.
(1820 - 1872)

14. (iii) The wall back may not always be vertical. In
practice a batter is given to the wall back.
(iv) The retained soil may not be always cohesion-
less.
(1820 - 1872)

15. RANKINE VERSUS COULOMB EARTH
PRESSURE THEORIES
The primary difference between Rankine and Coulomb
earth pressure theories is that Coulomb's considers a
frictional retaining wall. In other words, the interface
between the soil and the retaining wall is not assumed
frictionless (as it is in Rankine theory).
(1820 - 1872)

16.  Rankine underpredicts the true orientation of
the failure surface, whereas Coulomb
overpredicts the orientation. In that sense, you
could use both methods, and use the two
solutions to bound what will likely occur.
(1820 - 1872)

17. REFERENCES
1. htt[ps://www.britanica.comwww.ejge.com
2. www.icsandfoundationengineering.blogspot.com
3. https://en.Wikipedia.org/wiki/Rankine_Theory