strap_footing_eqns.pdf

 ANTILEVER EVER) FOOTINGS DESIGN OF STRAP (C ANTIL Desig Desig n Steps and Equations For an example on Design of Strap Footing click here

(a)

(b)

(a) Strap Footing with non-uniform strap bean thickness (b) Strap Footing with uniform strap bean thickness 1 of 6

 Advanced Foundation Engineering Design Equations for Strap Footings Dr. Adnan A. Basma

P1

P2 S l2

l1

 Strap Beam  h  L2 x B2

 L1 x B1

 e

B1

 R1

 R2

 L1

 L2

 b1

 Strap Beam

 B2

 b2 l2

l1

STEP 1 – DIMENSION FOOTINGS (Determine L1, B1, L2 and B2)  Allowable load

P = P1 + P2

Ultimate load

Pu = [1.4DL1 + 1.7LL1] + [1.4DL2 + 1.7LL2]

Ultimate ratio

r u =

Pu P

, Ultimate applied pressure qu = qa x r u

!Mcol. 2 = 0 R1 (S " e) " Pu1 S = 0 ....................................................................... (1)

!MR1 = 0 Pu2 (S " e) " R2 (S " e) " Pu1 e = 0 .................................................. (2)

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 Advanced Foundation Engineering Design Equations for Strap Footings Dr. Adnan A. Basma

!F = 0 Pu1 + Pu2 " R1 " R2 = 0 .................................................................. (3)

To solve these three equations assume a value for e, a) Find R1 by eq. (1)  b) Find R2 by eq. (2). c) Check eq. (3). If eq. (3) is not satisfied, then repeat 1 and 2 until eq. (3) is satisfied.

qu = r u qa

( 

Footing 1: L1 = 2 x & e )

' 

Footing 2: let k2 =

B2 =

L2 B2

l 1  %

# 2  $

and

B1 =

R1 qu L 1

 (1.0 means footing 2 is square)

R2 k 2 qu

and

L2 = k2 B2

Note: In step (c) above, any value of e will do, however, the best selection is the one that gives B1 = B2

STEP 2 – DRAW SHEAR AND MOMENT DIAGRAMS (L - DIRECTION) qu1, L = qu x B1 qu2, L = qu x B2

The general shape of the shear and bending moment diagrams are shown on the next page.

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 Advanced Foundation Engineering Design Equations for Strap Footings Dr. Adnan A. Basma

P1

P2 S l2

l1

 Strap Beam

qu1, L

qu2, L

Constant Shear in Strap Beam = V Strap

+   V(kN)

"

Top Steel Footing 1 Top Steel, Strap Beam, Mu(strap)

Top Steel Footing 2

"  

M(kN.m)

+  Moment drawn on tension side Bottom Steel Footing 2

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 Advanced Foundation Engineering Design Equations for Strap Footings Dr. Adnan A. Basma

STEP 3 – DEPTH OF CONCRETE, d' Estimate d' for footing 1 by 3-way punching shear under column 1 and for  footing 2 by 4-way punching shear under column 2. (Use Equations For Punching Shear  or approximate d' by Structural Depth of Concrete table for punching shear failure).

Note: Usually punching shear govern over wide beam so there is no need to check against wide beam.

STEP 4 – REINFORCEMENT IN L-DIRECTION The calculations below are repeated for both footings. 1. Select the appropriate moments (refer to moment diagram) and estimate the moment per meter by Mu(x)/m = Mu(x)/B. 2. Using Mu(x)/m, d', f c' and f y  estimate the reinforcement As  (refer to Equations for Reinforcement  or the percent reinforcement can be obtained directly from Percent Steel Tables).

STEP 5 – REINFORCEMENT IN B-DIRECTION For Footing 1

L1' = Mu1 =

For Footing 2

B1 " b1

L2' =

2 qu 2

*L 1 '+2

Mu2 =

B2 " b2 2 qu 2

*L 2 '+2

Using Mu`-, d', f c' and f y estimate the reinforcement As (refer to Equations for  Reinforcement or the percent reinforcement can be obtained directly from Percent Steel Tables).

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 Advanced Foundation Engineering Design Equations for Strap Footings Dr. Adnan A. Basma

STEP 6 – DEPTH AND REINFORCEMENT OF STRAP BEAM Depth h of strap beam:  Assume that the width of the trap = b (with of the smallest of column 1 or 2). The shear stress, ,u =

Vstrap b h

- ,c = 8.87 f ' c . Solve for h.

Reinforcement of strap beam: Select the appropriate moments (refer to moment diagram) Mu(strap). Using Mu(strap), d', f c' and f y  estimate the reinforcement As  (refer to Equations for Reinforcement  or the percent reinforcement can be obtained directly from Percent Steel Tables). As is the total reinforcement in strap beam.

For an exampl e on Design of Strap Footi ng click here

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 Advanced Foundation Engineering Design Equations for Strap Footings Dr. Adnan A. Basma