viga recortada puntal tensor

8/9/2019 Viga Recortada Puntal Tensor

1/8

1

CIE525: Assignment 5

Strut and Tie Models

Manish Kumar

1.1

Problem Statement

A 26-inch deep precast concrete T-beam has a 12 in. thick web and carries factored end reactions

of 75 kips and 15 kips in the vertical direction and horizontal directions as shown in the figure

below. Load is transferred to the supporting corbel via a bearing plate that is 412 inches in

plan. Assume that the concrete compressive strength is 6000 psi and that ASTM Grade A615

Grade 60 rebar is used. Design and detail the reinforcement at the end of the beam using strut-

and-tie procedures. Draw elevations and sections that show all reinforcement and the bearing

plate. Your solution must include a drawing of the strut-and-tie model.

1.2 Solution

The solution process for analyzing concrete members, as outlined in Wight and MacGregor

(2009)and class notes (Whittaker, 2012), employed here is:

1. Identify and isolate the D (discontinuous) regions in the given member/structure

2. Draw an equivalent strut-and-tie model for the D-regions to transmit the forces


2/8


3/8

3

Figure 2: Strut-and-tie model for the D-region

In the figure above, dashed line represents struts and solid line represents the ties.

1.2.3 Step 3: Compressive Strength of Nodal Zones and Struts

The compressive strength of the nodal zones is given by:

'0.85ce n cf f

Nodal zone A, E: Node A is a CCT node for which 0.8n . Hence effective strength of

concrete in the nodal zone A is given as '

0.85 0.85 0.8 6 4.08ce n cf f ksi .

Nodal zone B, F: This node is surrounded by three compressive struts and can be treated as

CCC, for which 1n .'

0.85 0.85 1 6 5.1ce n c

f f ksi

Nodal zone C, D: These nodes includes more than one tie, hence 0.6n ,

'0.85 0.85 0.6 6 3.06ce n cf f ksi

Struts AF, BF, BC, BE: These struts have room to expand and are assumed as bottle shaped

struts, which gives 0.75s ,'

0.85 0.85 0.75 6 3.8ce s cf f ksi


4/8


5/8

5

1.2.6 Step 6: Steel Required in the Ties

For the tie AB:

90AB

T k

2902

0.75 60

ust

y

FA in

f

2 #9 bars can be provided here. However, the development length for #9 bars is not available

here so an angle can be provided at the support and bars can be welded to the angle. The bearing

area of the angle would be based on the bearing strength of concrete of the concrete which

should not be less than nodal zone strength of A. The required bearing area is:

27522.6

0.65 0.85 6in

Required bearing area calculated through nodal zone strength is:

27524.5

0.75 4.08in

Hence area of2

24.5 in is required for the angle. A 3 3 1 / 2 angle is provided at the corner

along the 12"width of the beam.

For the tie CF:

100.4CF

T k

2100.42.23

0.75 60

ust

y

FA in

f

9 #5 bars can be used in three layers with 3 bars in each layer, as shown in Figure 4.Layers

should be equally spaced at 3" . Use #5 bars inside the top corners of the closed stirrups.


6/8

6

Figure 4: Shear reinforcement provided for tie CF

For the tie CD:

As the force in CD is same to CF, it will have the same area requirement of2

2.23 in . 4 #8 bars

can be provided in the bottom which provides an equivalent force of 142.2 ( 100.4 )k k .

However, these need to be developed as well to acquire the full strength of the bars. The

development length for #8 bars is 54.8 inch, however available development length is only about

10 inches. So, either a mechanical anchor or U bars need to be provided.

The area of required U bars is:

2142.23.16

0.75 60sA in

Use 2 #8 U bars which bend adjacent to the end of the beam.

The actual effective width of tie is now calculated as bar diameter plus twice the cover, which is

equal to 4"tw

1.2.7 Adequacy of Strut-widths

It is necessary to find out widths of each strut and show that it will fit the given beam. Let us

assume a prismatic strut with thickness equal to the beams thickness of 12". In order to find out

the width, minimum of nodal zone compressive strength and corresponding strut compressive

strength will govern. Only strut AF and FE are checked, as they are expected to be critical.

Strut AF: Compressive strength of strut AF will govern 3.8cef ksi . Required width is:


7/8

7

1063.1"

0.75 3.8 12w

Provided width is calculated as cos sin 4 cos 45 4 sin 45 5.6"o os t bw w l

Hence provided width is Ok!

Strut FE: Nodal zone strength of E will govern 4.08cef ksi , required width is:

1062.9"

0.75 4.08 12w

Beam can accommodate this width at top.

1.2.8

Crack Control

Longitudinal cracking can occur along the strut if the applied load is greater than twice the

cracking force 2n

C . Hence for strut AF:

'2 2 0.55 2 0.55 5.4 12 6 427n s cC w b f k

As factored load (106 k) is less than longitudinal cracking force in the strut, design is ok.

Also we have used 0.75s

assuming bottle shaped struts which require that adequate shear

reinforcement conforming to ACI 318 (ACI, 2011)must be provided, which requires:

sin 0.003si ii

A

bs

Let us provide two horizontal #4 U-shaped bars enclosing the strut AF, which gives:

4 0.2sin 45 0.0033 0.003

12 14

Hence provided design is OK!

1.3

Final Design

The final design of the dapped end of the beam is shown inFigure 5


8/8

8

Figure 5: Design of the dapped end of the beam

References

ACI (2011). "Building code requirements for structural concrete and commentary." Report ACI

318-11, American Concrete Institute, USA.

Whittaker, A. S. (2012). "CIE 525: Concrete Design Class Notes."University at Buffalo, NY.

Wight, J. K., and MacGregor, J. G. (2009). "Reinforced concrete: Mechanics and design (5th

edition)." Pearson Prentice Hall, Upper Saddle River, NJ.

viga recortada puntal tensor

Documents