Formula Sheets Construction Materials - Construction Materials & Management - Civil

 Page 1


GA TE CE 2026 F orm ula Sheet: Construction Materials
1. Structural Steel - Comp osition and Prop erties
• Mo dulus of elasticit y:
E
s
= 2×10
5
N/mm
2
where:
– E
s
: Mo dulus of elasticit y of steel (constan t for structural steel)
• Stress-strain relationship (elastic region):
s = E
s
·?
where:
– s : Stress (N/mm²)
– ? : Strain (dimensionless)
• Yield strength (t ypical for mild steel, IS 2062):
f
y
= 250 N/mm
2
( for F e 250 grade)
• Ultimate tensile strength:
f
u
= 410 N/mm
2
( for F e 250 grade)
• Allo w able stress (W orking Stress Design):
s
allo w
=
f
y
?
where:
– ? : F actor of safet y (t ypically 1.67 for tension)
2. Concrete - Constituen ts and Mix Design
• W ater-cemen t ratio (Abrams’ la w):
f
c
=
k
1
k
w/c
2
where:
– f
c
: Compressiv e strength of concrete (N/mm²)
– w/c : W ater-cemen t ratio (b y w eigh t)
– k
1
, k
2
: Empirical constan ts
• Concrete mix prop ortion (b y w eigh t):
Cemen t : Fine Aggregate : Coarse Aggregate = 1 : x : y
where:
– x , y : Prop ortions of fine and coarse aggregates
• V olume of concrete:
V
concrete
=
M
cemen t
?
cemen t
+
M
fine
?
fine
+
M
coarse
?
coarse
+
M
w ater
?
w ater
where:
– M : Mass of eac h constituen t (kg)
– ? : Densit y (kg/m³, e.g., ?
cemen t
˜ 1440 , ?
w ater
= 1000 )
1
Page 2


GA TE CE 2026 F orm ula Sheet: Construction Materials
1. Structural Steel - Comp osition and Prop erties
• Mo dulus of elasticit y:
E
s
= 2×10
5
N/mm
2
where:
– E
s
: Mo dulus of elasticit y of steel (constan t for structural steel)
• Stress-strain relationship (elastic region):
s = E
s
·?
where:
– s : Stress (N/mm²)
– ? : Strain (dimensionless)
• Yield strength (t ypical for mild steel, IS 2062):
f
y
= 250 N/mm
2
( for F e 250 grade)
• Ultimate tensile strength:
f
u
= 410 N/mm
2
( for F e 250 grade)
• Allo w able stress (W orking Stress Design):
s
allo w
=
f
y
?
where:
– ? : F actor of safet y (t ypically 1.67 for tension)
2. Concrete - Constituen ts and Mix Design
• W ater-cemen t ratio (Abrams’ la w):
f
c
=
k
1
k
w/c
2
where:
– f
c
: Compressiv e strength of concrete (N/mm²)
– w/c : W ater-cemen t ratio (b y w eigh t)
– k
1
, k
2
: Empirical constan ts
• Concrete mix prop ortion (b y w eigh t):
Cemen t : Fine Aggregate : Coarse Aggregate = 1 : x : y
where:
– x , y : Prop ortions of fine and coarse aggregates
• V olume of concrete:
V
concrete
=
M
cemen t
?
cemen t
+
M
fine
?
fine
+
M
coarse
?
coarse
+
M
w ater
?
w ater
where:
– M : Mass of eac h constituen t (kg)
– ? : Densit y (kg/m³, e.g., ?
cemen t
˜ 1440 , ?
w ater
= 1000 )
1
3. Concrete - Short-T erm Prop erties
• Compressiv e strength (28-da y c haracteristic strength):
f
ck
= Grade of concrete (e.g., 20, 25, 30 N/mm
2
for M20, M25, M30)
• Mo dulus of elasticit y of concrete (IS 456:2000):
E
c
= 5000
v
f
ck
where:
– E
c
: Mo dulus of elasticit y (N/mm²)
– f
ck
: Characteristic compressiv e strength (N/mm²)
• P oisson’s ratio:
?˜ 0.15-0.2
4. Concrete - Long-T erm Prop erties
• Creep co e?icien t:
? =
?
creep
?
elastic
where:
– ? : Creep co e?icien t (v aries with age, t ypically 1.5–2.0 p er IS 456:2000)
– ?
creep
: Creep strain
– ?
elastic
: Elastic strain
• Shrinkage strain:
?
sh
= k·
0.0003
v
t
where:
– ?
sh
: Shrinkage strain (mm/mm )
– k : F actor based on concrete t yp e (t ypically 0.8–1.0)
– t : Age of concrete (da ys)
• Mo dulus of rupture (flexural strength):
f
cr
= 0.7
v
f
ck
where:
– f
cr
: Mo dulus of rupture (N/mm²)
5. Tim b er - Prop erties (Supplemen tary)
• Allo w able stress in b ending:
s
b,allo w
=
f
b
?
where:
– s
b,allo w
: Allo w able b ending stress (N/mm²)
– f
b
: Characteristic b ending strength (N/mm², v aries b y sp ecies)
– ? : F actor of safet y (t ypically 2.5–3.0)
• Mo dulus of elasticit y:
E
t
˜ 8000-12000 N/mm
2
( dep ends on tim b er sp ecies)
2
Page 3


GA TE CE 2026 F orm ula Sheet: Construction Materials
1. Structural Steel - Comp osition and Prop erties
• Mo dulus of elasticit y:
E
s
= 2×10
5
N/mm
2
where:
– E
s
: Mo dulus of elasticit y of steel (constan t for structural steel)
• Stress-strain relationship (elastic region):
s = E
s
·?
where:
– s : Stress (N/mm²)
– ? : Strain (dimensionless)
• Yield strength (t ypical for mild steel, IS 2062):
f
y
= 250 N/mm
2
( for F e 250 grade)
• Ultimate tensile strength:
f
u
= 410 N/mm
2
( for F e 250 grade)
• Allo w able stress (W orking Stress Design):
s
allo w
=
f
y
?
where:
– ? : F actor of safet y (t ypically 1.67 for tension)
2. Concrete - Constituen ts and Mix Design
• W ater-cemen t ratio (Abrams’ la w):
f
c
=
k
1
k
w/c
2
where:
– f
c
: Compressiv e strength of concrete (N/mm²)
– w/c : W ater-cemen t ratio (b y w eigh t)
– k
1
, k
2
: Empirical constan ts
• Concrete mix prop ortion (b y w eigh t):
Cemen t : Fine Aggregate : Coarse Aggregate = 1 : x : y
where:
– x , y : Prop ortions of fine and coarse aggregates
• V olume of concrete:
V
concrete
=
M
cemen t
?
cemen t
+
M
fine
?
fine
+
M
coarse
?
coarse
+
M
w ater
?
w ater
where:
– M : Mass of eac h constituen t (kg)
– ? : Densit y (kg/m³, e.g., ?
cemen t
˜ 1440 , ?
w ater
= 1000 )
1
3. Concrete - Short-T erm Prop erties
• Compressiv e strength (28-da y c haracteristic strength):
f
ck
= Grade of concrete (e.g., 20, 25, 30 N/mm
2
for M20, M25, M30)
• Mo dulus of elasticit y of concrete (IS 456:2000):
E
c
= 5000
v
f
ck
where:
– E
c
: Mo dulus of elasticit y (N/mm²)
– f
ck
: Characteristic compressiv e strength (N/mm²)
• P oisson’s ratio:
?˜ 0.15-0.2
4. Concrete - Long-T erm Prop erties
• Creep co e?icien t:
? =
?
creep
?
elastic
where:
– ? : Creep co e?icien t (v aries with age, t ypically 1.5–2.0 p er IS 456:2000)
– ?
creep
: Creep strain
– ?
elastic
: Elastic strain
• Shrinkage strain:
?
sh
= k·
0.0003
v
t
where:
– ?
sh
: Shrinkage strain (mm/mm )
– k : F actor based on concrete t yp e (t ypically 0.8–1.0)
– t : Age of concrete (da ys)
• Mo dulus of rupture (flexural strength):
f
cr
= 0.7
v
f
ck
where:
– f
cr
: Mo dulus of rupture (N/mm²)
5. Tim b er - Prop erties (Supplemen tary)
• Allo w able stress in b ending:
s
b,allo w
=
f
b
?
where:
– s
b,allo w
: Allo w able b ending stress (N/mm²)
– f
b
: Characteristic b ending strength (N/mm², v aries b y sp ecies)
– ? : F actor of safet y (t ypically 2.5–3.0)
• Mo dulus of elasticit y:
E
t
˜ 8000-12000 N/mm
2
( dep ends on tim b er sp ecies)
2
• Deflection of tim b er b eam (simply supp orted, UDL):
d =
5wL
4
384E
t
I
where:
– d : Maxim um deflection (mm)
– w : Uniformly distributed l oad (kN/m)
– L : Span length (mm)
– I : Momen t of inertia (mm?)
3