Design of Sections for Flexure | Civil Engineering Optional Notes for UPSC PDF Download

 Page 1


 
Design of Sections for Flexure 
 
The design problem is taken in two steps. 
• Preliminary Design  
• Final Design for Type 1 Members  
Before moving to preliminary design the followings are needed. 
 
Page 2


 
Design of Sections for Flexure 
 
The design problem is taken in two steps. 
• Preliminary Design  
• Final Design for Type 1 Members  
Before moving to preliminary design the followings are needed. 
 
• Calculation of Moment Demand  
• For simply supported prestressed beams, the maximum moment at the span is 
given by the beam theory. For continuous prestressed beams, the analysis can be 
done by moment distribution method. The moment coefficients in Table 12 of 
IS:456 - 2000 can be used under conditions of uniform cross-section of the beams, 
uniform loads and similar lengths of span.  
• The design is done for the critical section. For a simply supported beam under 
uniform loads, the critical section is at the mid span. For a continuous beam, there 
are critical sections at the supports and at the spans.  
• For design under service loads, the following quantities are known.  
• M
DL 
= M
d
=moment due to dead load (excluding self-weight)  
• M
LL 
= moment due to live load.  
• The material properties are selected before the design.  
• The following quantities are unknown.  
• The member cross-section and its geometric properties,  
• M
SW 
= moment due to self-weight,  
• A
p 
= amount of prestressing steel,  
• P
e 
= the effective prestress,  
• e = the eccentricity.  
 
 
Page 3


 
Design of Sections for Flexure 
 
The design problem is taken in two steps. 
• Preliminary Design  
• Final Design for Type 1 Members  
Before moving to preliminary design the followings are needed. 
 
• Calculation of Moment Demand  
• For simply supported prestressed beams, the maximum moment at the span is 
given by the beam theory. For continuous prestressed beams, the analysis can be 
done by moment distribution method. The moment coefficients in Table 12 of 
IS:456 - 2000 can be used under conditions of uniform cross-section of the beams, 
uniform loads and similar lengths of span.  
• The design is done for the critical section. For a simply supported beam under 
uniform loads, the critical section is at the mid span. For a continuous beam, there 
are critical sections at the supports and at the spans.  
• For design under service loads, the following quantities are known.  
• M
DL 
= M
d
=moment due to dead load (excluding self-weight)  
• M
LL 
= moment due to live load.  
• The material properties are selected before the design.  
• The following quantities are unknown.  
• The member cross-section and its geometric properties,  
• M
SW 
= moment due to self-weight,  
• A
p 
= amount of prestressing steel,  
• P
e 
= the effective prestress,  
• e = the eccentricity.  
 
 
• There are two stages of design.  
• 1) Preliminary: In this stage the cross-section is 
defined and P
e 
and A
p 
are estimated.  
  
• 2) Final: The values of e (at the critical section), 
P
e
, A
p 
and the stresses in concrete at transfer and 
under service loads are calculated. The stresses 
are checked with the allowable values. The 
section is modified if required 
Page 4


 
Design of Sections for Flexure 
 
The design problem is taken in two steps. 
• Preliminary Design  
• Final Design for Type 1 Members  
Before moving to preliminary design the followings are needed. 
 
• Calculation of Moment Demand  
• For simply supported prestressed beams, the maximum moment at the span is 
given by the beam theory. For continuous prestressed beams, the analysis can be 
done by moment distribution method. The moment coefficients in Table 12 of 
IS:456 - 2000 can be used under conditions of uniform cross-section of the beams, 
uniform loads and similar lengths of span.  
• The design is done for the critical section. For a simply supported beam under 
uniform loads, the critical section is at the mid span. For a continuous beam, there 
are critical sections at the supports and at the spans.  
• For design under service loads, the following quantities are known.  
• M
DL 
= M
d
=moment due to dead load (excluding self-weight)  
• M
LL 
= moment due to live load.  
• The material properties are selected before the design.  
• The following quantities are unknown.  
• The member cross-section and its geometric properties,  
• M
SW 
= moment due to self-weight,  
• A
p 
= amount of prestressing steel,  
• P
e 
= the effective prestress,  
• e = the eccentricity.  
 
 
• There are two stages of design.  
• 1) Preliminary: In this stage the cross-section is 
defined and P
e 
and A
p 
are estimated.  
  
• 2) Final: The values of e (at the critical section), 
P
e
, A
p 
and the stresses in concrete at transfer and 
under service loads are calculated. The stresses 
are checked with the allowable values. The 
section is modified if required 
• Preliminary Design  
• The steps of preliminary design are as follows.  
• 1) Select the material properties f
ck 
and f
pk
.  
• 2) Determine the total depth of beam (h).  
• The total depth can be based on architectural 
requirement or, the following empirical equation can 
be used.  
• h = 0.03 vM to 0.04 vM    
• Here, h is in meters and M is in kNm. 
• M is the total moment excluding self-weight.  
• 3) Select the type of section. For a rectangular section, 
assume the breadth  
• b = h/2. 
Page 5


 
Design of Sections for Flexure 
 
The design problem is taken in two steps. 
• Preliminary Design  
• Final Design for Type 1 Members  
Before moving to preliminary design the followings are needed. 
 
• Calculation of Moment Demand  
• For simply supported prestressed beams, the maximum moment at the span is 
given by the beam theory. For continuous prestressed beams, the analysis can be 
done by moment distribution method. The moment coefficients in Table 12 of 
IS:456 - 2000 can be used under conditions of uniform cross-section of the beams, 
uniform loads and similar lengths of span.  
• The design is done for the critical section. For a simply supported beam under 
uniform loads, the critical section is at the mid span. For a continuous beam, there 
are critical sections at the supports and at the spans.  
• For design under service loads, the following quantities are known.  
• M
DL 
= M
d
=moment due to dead load (excluding self-weight)  
• M
LL 
= moment due to live load.  
• The material properties are selected before the design.  
• The following quantities are unknown.  
• The member cross-section and its geometric properties,  
• M
SW 
= moment due to self-weight,  
• A
p 
= amount of prestressing steel,  
• P
e 
= the effective prestress,  
• e = the eccentricity.  
 
 
• There are two stages of design.  
• 1) Preliminary: In this stage the cross-section is 
defined and P
e 
and A
p 
are estimated.  
  
• 2) Final: The values of e (at the critical section), 
P
e
, A
p 
and the stresses in concrete at transfer and 
under service loads are calculated. The stresses 
are checked with the allowable values. The 
section is modified if required 
• Preliminary Design  
• The steps of preliminary design are as follows.  
• 1) Select the material properties f
ck 
and f
pk
.  
• 2) Determine the total depth of beam (h).  
• The total depth can be based on architectural 
requirement or, the following empirical equation can 
be used.  
• h = 0.03 vM to 0.04 vM    
• Here, h is in meters and M is in kNm. 
• M is the total moment excluding self-weight.  
• 3) Select the type of section. For a rectangular section, 
assume the breadth  
• b = h/2. 
Preliminary Design 
• 4) Calculate the self-weight or, estimate the self-weight to be 10% to 20% of  
• the load carried.  
• 5) Calculate the total moment M
T 
including self-weight. The moment due to  
• self-weight is denoted as M
d
=M
sw
.  
• 6) Estimate the lever arm (z).  
• z ˜ 0.65h, if M
sw 
is large (M
sw 
> 0.3M
T
).  
• z ˜ 0.5h, if M
sw 
is small.  
• 7) Estimate the effective prestress (P
e
)  
• P
e 
= M
T 
/ z, if M
sw 
is large.  
• P
e 
= M
I L 
/ z, if M
sw 
is small.  
• If M
sw 
is small, the design is governed by the moment due to imposed load  
• (M
I L 
= M
T 
– M
SW
).  
• 8)  Considering f
pe 
= 0.7f
pk 
, calculate area of prestressing steel A
p 
= P
e 
/ f
pe
.  
• 9)  Check the area of the cross-section (A).  
• The average stress in concrete at service C/A (= P
e 
/A) should not be too high as compared to 50% of 
the allowable compressive stress f
cc,all 
. If it is so, increase the area of the section to A = P
e 
/(0.5f
cc,all
).