Concrete Cheat Sheat

Beams Rectangle Analysis Cracking Moment

  

Where: Mcr= Moment



f r=7.5 Ig= Moment of Inertia Yt=distance from centroid to tensile fiber Elastic Stresses  – Concrete Cracked

  

Where: n=modular ratio E=modulus of elasticity

  

Transformed Area

Where: b=base d=distance from center of steel to top compressive fiber x=distance from top compressive fiber to neutral axis As=Area of Steel Moment of Inertia

T-Beams Design Dimensions: Minimum thickness from ACI Table 9.5a Width= ½ thickness

           

Analysis

Design Find: beff =1/4 beam span 8*slab thickness + bw ½ Clear distance

Check: beff =1/4 beam span 8*hf  + bw ½ Clear distance As min

                                                         

Weight: w=

Calculate:

ρ (assuming ∅=0.9) Compare with As min Select Reinforcement:

             

Check:

For Slabs: Shrink & Temp. Steel

Find:

                                                               

Assume large of:

N.A

If N.A. is in flange:

Trial Steel Area:

New Z

If N.A. is not in flange:

                                                                                                                                                                                                                                                                                                                                                                                                                                                              

Bending Stresses

Doubly Reinforced Beams

Analysis

Find:

Design

Until As is consistent then compare with As min

Find:

Ultimate Flexural Moments

Find:

’

Strength Analysis

If  sy:

Check Safety Factor:

’

’

’

’

If  sy: Solve for c

Then find:

’

If  s0.00207 f s =f y otherwise f s =s Es

If bars are different sizes: Solve for c

If not strong enough use smaller compressive steel.

           Development Lengths

Where: cb=Center of tension bar to nearest concrete surface or center to center spacing Ktr=0 (ACIU 12.2.3)

Shear Is reinforcement needed: Calculate Vu at distance d from support Calculate:

Columns Axially Loaded: Find Area of Concrete (Ag):

  

                                                                                                                                                                                                       

If Bundled Bars: Imaginary bar centroid is used Development +20% for 3 bars +40% for 4 bars For Hooks:

If

 stirrups are needed

Calculate: Theoretical stirrup spacing-

Where

Maximum spacing for min area  –

Max Spacing:

Length after turn: 90 degree = 12db 180 degree = 4db For Compression:

Assuming Ast=0.02Ag Then Find Ast  with selected Ag

Ties- =0.65 Spacing of ties = lesser of 16*longitudinal bar diameter or 48*tie diameter (#3bar ties for #10 or smaller long. Bars, #4 for larger) Spiral-=0.75 Find Ac (area of core inside the spiral)

Solve for spacing (s)

Where

Check V at different distances for spacing changes. Simple Beam Deflections Instantaneous dead load-

Eccentricly Loaded: Plastic Centroid-

Reduction Factor:

Design-

Splices Compresssion:  for 60kpsi or less  for 60kpsi

,

If MaMcr Ma=Mcr

,

Find Transformed area & moment of inertia as on the front.

Tension:

,

Find ρg on Interaction diagram

Calculate:

Otherwise:

Crack Width (Gergely-Lutz)

Where: Βh=ratio of distance to NA from extreme tensile concrete to extreme tensile steel f s=0.6f y dc=Outermost cover to centroid of bar A=tension area of concretecentroid of bars to outer layer divided by the number of bars Properties

Span Formulas

Inst. Dead + Live: As with dead only

Simple-

Inst. Live

Fixed-

Long Term

Cantilever-

Where: =Time factor (2 for 5+yrs, 1.4 for 1 yr, 1.2 for 0.5yr, 1 for 3 months) ’

ρ =compression steel

Footings WallAssume 12 in h with d=8.5in

                                                                       Find Required Depth

Where bw =base width (assumed 1ft for wall footing) If d is met-

Where a is the column width

Find steel as usual Find Development Length Longitudinal Temp & Shrinkage steel

Rectangular footings-

Depth Required for 2 way (punch)

Depth Required for 1 way shear

If all depths are ok-

Combined footing: Find Center of gravity-

Footing length =2x+distance to property line Footing Width = x Create sheer & Moment diagrams solve as Rectangular footing.