Flexural Analysis of Beams Flashcards
Stress due to bending
Flexure
This is the concrete cracked - elastic stress stage
Service Stage
Bending moment where cracks will begin to occur.
Cracking Moment
This is the ultimate strength stage
Failure
This is the uneconomical stage before collapse occur
Uncracked concrete stage
If the steel does not yield, the concrete is still on the ______ stage
Elastic Stage
It is the moment that causes the stress in the extreme tension fiber to reach the modulus of rupture
Cracking Moment
Stage of Working stress design where the criteria is Ma < Mcr
Stage 1: Uncracked Concrete Stage
Stage of working stress design where the criteria is Ma > Mcr
Stage 2: Concrete Cracked - Elastic Stresses Stage
are the loads that are assumed to actually occur when a structure is in use or service.
Service Loads or Working Loads
It is the clear distance between bars
Spacing
For members with parallel layers of rebar, the minimum spacing should be ____
At least one bar diameter but not less than 1 in
For members with two or more layers of rebar, the upper layers must be _____ in the bottom layers
directly above
Clear spacing for members with two or more layers of rebar
at least 1 inch clear vertically
For this member the clear distance between longitudinal bars must be at least 1-1/2 bar diameter but not less than 1-1/2 inch
Spirally reinforced and tied reinforced compression members
In walls and slabs other than concrete joists, primarily flexural reinforcement must NOT be spaced ____
greater than 3 times the wall or slab thickness nor 18 inches
For flexural members, the clear horizontal distance is ____
db > 1 in
For Compression members, tied or spirally, the clear horizontal distance is _____
1.5 db > 1.5 inches
d stands for
effective depth
d’ stands for
effective cover
ft stands for
tensile stress
fr stands for
modulus of rupture
h stands for
depth
b stands for
width
Formula for Modulus of Elasticity
(Concrete, Normal Weight)
Ec = 4700 √fc’
Formula for Modulus of Elasticity
(Steel)
Es = 200,000 Mpa
Formula for allowable stress on concrete
fc = 0.45fc’
Formula for allowable stress on steel
fs = 0.5fy
Formula for Rupture (Normal weight of concrete)
fr = 0.62 λ √fc’
Formula for modular ratio
n = Es/Ec
Ma stands for
actual moment due to load
symbol for allowable moment of steel
Ms
symbol for allowable moment of concrete
Mc
nb stands for
number of bars
db stands for
bar diameter
To solve for cracking moment (Mcr), use formula ___
fr = Mcr(y) / Ig
Specified cover (mm) for cast against and permanently in contact with ground
75 mm
Specified cover (mm) for concrete exposed to weather or in contact with ground.
No. 19 through No. 57 bars
50 mm
Specified cover (mm) for concrete exposed to weather or in contact with ground.
No. 16, MW200 or MD200 wire, and smaller
40 mm
Specified cover (mm) for concrete not exposed to weather or in contact with ground.
Slab, joists, and wall member
No.43 and 57 bars
40 mm
Specified cover (mm) for concrete not exposed to weather or in contact with ground.
Slab, joists, and wall member
No. 36 bar and smaller
20 mm
Specified cover (mm) for concrete not exposed to weather or in contact with ground.
Beams, columns, pedestals, and tension ties
40 mm
Reinforcement for beams, columns, pedestals, and tension ties
✓ Primary Reinforcement
✓ Stirrups
✓ Ties
✓ Spirals
✓ Hoops
Reinforcement for slabs, joists, and walls
✓ No. 43 and No. 57 bars
✓ No. 36 and smaller bars
3 Advantages of Concrete Cover
✓ Helps steel to not be exposed on weather
✓ Helps avoid corrosion
✓ Enhances fire resistance
Three distinct stages before collapse occur:
- The uncracked concrete stage (uneconomical)
- The concrete cracked - elastic stresses stage (service stage)
- The ultimate-strength stage (failure)
