1. AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF CIVIL ENGINEERING

PRESENTATION ON SOLVING STATICALLY INDETERMINATE
STRUCTUE:MOMENT CO EFFICENT METHOD
 COURSE TEACHER: Munshi Galib Muktadir
Sabreena Nasrin
 SUBMITTED BY:
 KAZI RIYADH AL SAIF AHMED
 I.D.: 10.01.03.128
 SECTION:C
4th Year 2nd Semester..

2. STATICALLY INDETERMINATE
STRUCTURE:MOMENT COEFFICIENT
METHOD

3. What is
STATICALLY INDETERMINATE STRUCTURE ?
 In statics, a structure is statically indeterminate when the static
equilibrium equations are insufficient for determining the internal forces
and reactions on that structure.
 Based on Newton’s law of motoin, the equilibrium equations available for
a two-dimensional body are the vectorial sum of the forces acting on the
body equals zero

This translates Σ H = 0: the sum of the horizontal components of the
forces equals zero; Σ V = 0: the sum of the vertical components of forces
equals zero; : the sum of the moments (about an arbitrary point) of all
forces equals zero.
Reference: http://en.wikipedia.org/wiki/Statically_indeterminate

4. In the beam construction on the right, the four unknown reactions are VA, VB, VC
and HA. The equilibrium equations are:
 Σ V = 0:
VA − Fv + VB + VC = 0 Σ H = 0:
HA − Fh = 0 Σ MA = 0:
Fv · a − VB · (a + b) - VC · (a + b + c) = 0. Since there are four
unknown forces (VA, VB, VC and HA) but only three
equilibrium equations, this system of simultaneous equations
does not have a unique solution. The structure is therefore
classified as statically indeterminate. Considerations in the
material properties and compatibility in deformations are
taken to solve statically indeterminate systems or structures.

Reference: http://en.wikipedia.org/wiki/Statically_indeterminate

5. Free Body Diagram of a statically indeterminate Beam

6. :
Moment co efficient method
 The ACI / SBC approximate method (also called coefficient
method) is used for the analysis of continuous beams, ribs and
two-way slabs.
 . It allows for various load patterns where live load is applied on
selected spans and maximum shear force and bending moment
values are obtained by the envelope curves. This simplified and
approximate method allows also for the real rotation restraint at
external supports, where the real moment is not equal to zero.

Elastic analysis gives systematic zero moment values at all
external pin supports. The coefficient method is thus more
realistic but is only valid for standard cases. It is advised to use
this method whenever its conditions of application are satisfied.
Elastic analysis should be used only if the conditions of the code
method are not satisfied.

7.  The Moment Coefficient Method included for the first
time in 1963 ACI Code is applicable to two-way slabs
supported on four sides of each slab panel by walls,
steel beams relatively deep, stiff, edge beams (h = 3hf).

 Although, not included in 1977 and later versions
of ACI code, its continued use is permissible under
the ACI 318-08 code provision (13.5.1). Visit ACI
13.5.1.


8. two way slab
moment co efficient method: cases
depending on the support conditions several case are
possible…

9.  Another typical case from moment co
efficient method:

10. The method makes use of tables of moment coefficient for a variety of conditions.
Thesecoefficients are based on elastic analysis but also account for inelastic redistribution.
.C.S = column strip; M.S = middle strip
Figure: Elements of two- way slab with beam by moment efficient method

11.  Moments:
 M aneg.= Ca neg. Wula2
 M b neg.=Cb negWl2
 M a pos.= Ca pos. * . Wula2 + Ca pos *Wulb2
 M b pos.= Cb pos. * . Wula2 + Cb pos *Wulb2
 Where Ca and Cb are tabulated moment co
efficient
 Wu= ultimate uniform load
 la and lb = lenth of clear spans in short and long directions
respectively

16. Maximum Spacing and Minimum
Reinforcement Requirement





l
Maximum spacing (ACI 13.3.2):
smax = 2 hf in each direction.
Minimum Reinforcement (ACI 7.12.2.1):
Asmin = 0.0018 b hf for grade 60.
Asmin = 0.002 b hf for grade 40 and 50

17. Advantages and Disadvantages of
moment co efficient method:
 In some respects, when estimating parameters
of a known family of probability
distributions, this method was superseded by
Fisher's method of maximum likelihood, because
maximum likelihood estimators have higher
probability of being close to the quantities to be
estimated.
 The coefficients give more exact analysis.
Significant economy can be achieved by making
a more precise analysis. There should be no
reversal of moments at the critical design
sections near midspan or at the support faces.

18. References

 CRSI Design Handbook

 ACI 318

 Design of Concrete Structures 13th Ed. by Nilson, Darwin and
Dolan.
