Diseño De Barrera Nj En Mathcad

-1-

Strength Properties of New Jersey Barrier

f'c ≔ 3000 psi Barrier dimensions: a ≔ 21 in Bar No.: A1 ≔ 4 S ≔ 8 in Bar Diameter: A1 d1 ≔ ―― in 8 A2 ≔ 4 b ≔ 5 in

fy ≔ 60 ksi

lbf γc ≔ 150 ―― ft 3

c ≔ 3 in

d ≔ 5 in

e ≔ 6 in

f ≔ 10 in

A3 ≔ 4

A4 ≔ 4

A5 ≔ 4

A2 d2 ≔ ―― in 8

A3 d3 ≔ ―― in 8

A4 d4 ≔ ―― in 8

A5 d5 ≔ ―― in 8

-2-

Strength Properties of NewJersey Barrier
Typical cover for horizontal bars: coverh ≔ 2 in + d5 coverh = 2.5 in

Barrier Width: Wbarrier ≔ d + e + f Barrier Height: H≔a+b+c H = 29 in Wbarrier = 21 in

Total Area of bars on Tension Side for Mwall (Same Area in both faces) π As ≔ ― ⎛d1 2 + d2 2 + d3 2 + d5 2 ⎞ ⋅⎝ ⎠ 4 As = 0.79 in 2 Awall = 423.5 in 2

1 ( Awall ≔ f ⋅ H + b ⋅ e + (d + e) ⋅ c + ― e ⋅ a + c ⋅ d) ) ) ( (2

-3-

1 ( Awall ≔ f ⋅ H + b ⋅ e + (d Strength Properties of New Jersey Barrier ) ) ( + e) ⋅ c + ― e ⋅ a + c ⋅ d) ( 2 Thickness of uniform wall with same area as the New Jersey Barrier Awall tuni ≔ ―― H tuni = 14.6 in

Average Depth of Tension: dave ≔ tuni − coverh Wall Moment Capacity: ⎛ As ⋅ fy ⎞ ―――― ⎜ ⎟ .85 ⋅ f'c ⋅ H ⎟ ⎜d − ―――― HMw ≔ As ⋅ fy ⋅ ave ⎜ ⎟ 2 ⎝ ⎠ dave = 12.1 in

HMw =46.28 ft·kip

Total Wall Capacity

HMw Mw_uni ≔ ―― H

kip ⋅ ft Mw_uni = 19.15 ――― Moment Capacity per foot (vertical) of Wall ft

Vertical Moment Capacity of Wall (by average segments):

Segment #1: Tension area: π As1 ≔ ― ⎛d1 2 + d2 2 ⎞ ⋅⎝ ⎠ 4 Average tension bar depth: 2 f+e have1 ≔ ――― 2 have1 = 13 in As1 = 0.39 in 2

-4-

Strength Properties of New Jersey Barrier
⎛ d1 + d2 ⎞ ⎜―――⎟ ⎝ 2 ⎠ dave ≔ have1 − coverh − ――― 2

dave = 10.25 in

Moment Capacity of segment #1: ⎛ As ⋅ fy ⎞ ―――― ⎜ ⎟ .85 ⋅ f'c ⋅ a ⎟ ⎜d − ―――― Mn1 ≔ As1 ⋅ fy ⋅ ave ⎜ ⎟ 2 ⎝ ⎠

Mn1 = 19.26 kip ⋅ ft

Segment #2: π As2 ≔ ―d3 2 4 As2 = 0.2 in 2 Area of Tension Bar

Average Tension bar depth: 2 f+2 e+d have2 ≔ ―――― 2 d3 dave ≔ have2 − coverh − ― 2 have2 = 18.5 in

dave = 15.75 in

Moment Capacity ofsegment #2: ⎛ As ⋅ fy ⎞ ―――― ⎜ ⎟ .85 ⋅ f'c ⋅ b ⎟ ⎜d − ―――― Mn2 ≔ As2 ⋅ fy ⋅ ave ⎜ ⎟ 2 ⎝ ⎠

Mn2 = 13.65 kip ⋅ ft

-5-

Strength Properties of New Jersey Barrier
Segment #3: π ⋅ As3 ≔ ― d4 2 4 Average Tension depth: have3 ≔ f + e + d d4 dave ≔ have3 − coverh − ― 2 have3 = 21 in dave = 18.25 in As3 = 0.2 in 2

Area of Tension Bar

Moment Capacity of Segment 3 ⎛ As ⋅ fy ⎞ ―――― ⎜ ⎟ .85 ⋅f'c ⋅ c ⎟ ⎜d − ―――― Mn3 ≔ As3 ⋅ fy ⋅ ave ⎜ ⎟ 2 ⎝ ⎠

Mn3 = 14.89 kip ⋅ ft

Tatal Vertical Moment Capacity of Wall: HMw ≔ Mn1 + Mn2 + Mn3 HMw Mw ≔ ―― H HMw = 47.8 kip ⋅ ft Total Wall Capacity

kip ⋅ ft Mw = 19.78 ――― ft

Moment Capacity per foot (vertical) of Wall

Compare to assuming depth

kip ⋅ ft Mw_uni = 19.15 ――― ft

OK

-6-

Strength Properties of New Jersey BarrierAverage Stregth about Horizontal Axis of Wall assuming uniform wall thickness: coverv ≔ 2 in Typical cover for vertical rebar dave = 12.35 in

d4 dave ≔ tuni − coverv − ― 2 π ⋅ 2 ― d4 4 As ≔ ――― S

in 2 As = 0.29 ―― ft

Horizontal Moment Capacity per foot of Barrier ⎛ As ⋅ fy ⎞ ――― ⎜ ⎟ .85 ⋅ f'c ⎟ ⎜d − ――― Mc_uni ≔ As ⋅ fy ⋅ ave ⎜ ⎟ 2 ⎝ ⎠

kip ⋅ ft Mc_uni = 17.77 ――― ft

Moment Stregth abouthorizontal Axis of Wall: Segment #1:

in 2 As = 0.29 ―― ft

Area of Tension per foot dave = 10.75 in

d4 dave ≔ have1 − coverv − ― 2

Average depth of Tension Bar

Horizontal Moment Capacity of Wall:

-7-

Strength Properties of New Jersey Barrier
⎛ As ⋅ fy ⎞ ――― ⎜ ⎟ .85 ⋅ f'c ⎟ ⎜d − ――― Mc1 ≔ As ⋅ fy ⋅ ave ⎜ ⎟ 2 ⎝ ⎠ Segment #2: In segment #2 & #3, the effective rebar is the dowel:d4 dave ≔ have2 − coverv − ― 2 in 2 As = 0.29 ―― ft Horizontal Capacity of Wall: ⎛ As ⋅ fy ⎞ ――― ⎜ ⎟ .85 ⋅ f'c ⎟ ⎜d − ――― Mc2 ≔ As ⋅ fy ⋅ ave ⎜ ⎟ 2 ⎝ ⎠ dave = 16.25 in kip ⋅ ft Mc1 = 15.41 ――― ft

kip ⋅ ft Mc2 = 23.5 ――― ft

Segment #3: d4 dave ≔ have3 − coverv − ― 2 in 2 As = 0.29 ―― ft Horizontal Moment Capacity of Segment #3: ⎛ As ⋅ fy ⎞ ――― ⎜ ⎟ .85 ⋅ f'c ⎟ ⎜d − ――― Mc3 ≔ As ⋅ fy ⋅ ave...