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Reinforced Masonry Pier

MSJC -08 and earlier

LRFD

A Pier is defined as an isolated vertical member whose horizontal dimension measured at right angles to its thickness is not less than 3xthickness nor greater than 6xthickness. Also its height is less than 5 times its lkentgh. If it does not meet these restricitons it is then typically a wall or a pier

value table column vlookup k 1 : j 1 : j table rows ≤ j j 1 + : table j 1 el value ≡ result k 1 el table j column el : k k 1 + : 21 line 0 if for result 31 line :

Forces

Factored (strength level) axial force

P.r 3.6 kip * :

Factored (strength level) moment force

M.r 80 kip * ft * :

Factored (strength level) shear force

V.r 12.4 kip * :

Forces P.r M.r V.r 13 mat :

Reduction Factors

Reinforced Msry

Axial

φ.a 0.9 :

Bending

φ.b 0.9 :

Shear

φ.s 0.8 :

Geometry of Section

Width of Section ("x" direction)

b.pier 7.625 in * :

Height of Section ("y" direction)

h.pier 32 in * :

Height of Pier

H.pier 18.5 ft * :

Reinforcment effective in compression

R.tied Yes :

Location of Centroid from top

Y.p h.pier 2 / :

Y.p in 16

Section Properties:

Area of section

A.g b.pier h.pier * :

A.g in 2^244

I.gx b.pier h.pier 3^* 12 / :

Moment of inertia

I.gx in 4^20821.3333

I.gy h.pier b.pier 3^* 12 / :

Moment of inertia

I.gy in 4^1182.1927

r.gx I.gx A.g / (sqrt :

r.gy I.gy A.g / (sqrt :

Radius of gyration

r.gx in 9.2376

r.gy in 2.2011

Design radius of gyration

r.gd r.gx r.gy 12 mat min :

r.gd in 2.2011

Material Properties

Type of Msry

Msry Concrete :

Enter "Concrete" or "Clay"

Masonry Strength

f'.m 1500 psi * :

E.factor Msry Concrete ≡ 900 Msry Clay ≡ 700 Error if if :

Steel Strength

F.s 60 ksi * :

Steel MOE

E.s 29000 ksi * :

Masonry MOE

E.m E.factor f'.m * :

E.m ksi 1350

Reinforcment Layout

Click in box then can drag corner to expand Top: Enter Bar Number Bottom: Enter depth from compression face to bar OK to enter same depth for multiple bars

Reinf 55554 in * 12 in * 20 in * 28 in * 24 mat :

n 1 : n Reinf cols ≤ n n 1 + : temp Reinf 1 n el 8 / (2^π 4 / * 1 * in 2^* : ReinfA 1 n el n in 2^* : ReinfA 2 n el temp : 31 line for 11 line

This converts the bar size to an area

Area of bars

ReinfA in 2^1234 0.3068 0.3068 0.3068 0.3068 24 mat

Total reinforcment

A.stot ReinfA 2 n el n 1 ReinfA cols sum :

A.stot in 2^1.2272

Enter Value for Depth of N.A. Can close "area" in order to iterate value

Depth to NA

c 6.71 in * :

Depth of compression block

a c 0.8 * :

a in 5.368

ε.m Msry Concrete ≡ 0.0025 Msry Clay ≡ 0.0035 Check Input if if :

Maximum allowable strain in Masonry

n 1 : n Reinf cols ≤ n n 1 + : S.strain 1 n el n : S.strain 2 n el ε.m c / Reinf 2 n el c - (* : 21 line for

Loop to find strain in reinforcment

S.strain in in / 1234 0.001 - 0.002 0.005 0.0079 24 mat

Top row: label only Bottom row: strain Negative indicates compression

Loop to find stess in reinforcment

n 1 : n Reinf cols ≤ n n 1 + : S.stress 1 n el n 1 * ksi * : S.elastic S.strain 2 n el E.s * : S.stress 2 n el S.elastic 0 ksi * < R.tied Yes ≡ S.elastic abs F.s > 1 F.s * - S.elastic if 0 ksi * if S.elastic F.s > F.s S.elastic if if : 31 line for

'n' is multiplied by 1ksi so that the lable displayes correctly

Check if steel is effective in compression.

Limit the compression steel to the allowalbe

Limit the tension stress to the allowable

Stess in reinforcment

S.stress ksi 1234 29.2809 - 57.1572 606024 mat

n 1 : n S.stress cols ≤ n n 1 + : S.force 1 n el n 1 * kip * : S.force 2 n el S.stress 2 n el ReinfA 2 n el * : 21 line for

S.stress 22 el ksi 57.1572

Negative forces = compression

Force in reinforcment

S.force kip 1234 8.9833 - 17.5356 18.4078 18.4078 24 mat

S.force_net S.force 2 n el n 1 S.force cols sum :

S.force_net kip 45.3679

Force of compression block

M.force 1 - (0.8 f'.m * a * b.pier * (* :

M.force kip 49.1172 -

Total force

F.ncomp M.force S.force_net + :

F.ncomp kip 3.7493 -

Nominal axial strength of section

P.n 1 - (F.ncomp * :

Moments

Moment stength - Reinforcment

n 1 : n Reinf cols ≤ n n 1 + : S.arm 1 n el n 1 * in * : Arm Reinf 2 n el Y.p - : S.arm 2 n el Arm : 31 line for

S.arm in 123412 - 4 - 41224 mat

S.moment S.force 2 n el S.arm 2 n el * (n 1 S.arm cols sum :

S.moment kip ft * 27.6818

Moment strength - Maosnry

M.arm a 2 / Y.p - :

M.arm in 13.316 -

M.moment M.arm M.force * :

M.moment kip ft * 54.5037

Total moment

M.n S.moment M.moment + :

M.n kip ft * 82.1855

Eccentricty of Section

e.section M.n P.n / : in 263.0414

e.forces M.r P.r / : in 266.6667

Axial Only Checks

Reduction factor for slenderness

Sldr H.pier r.gd / :

Slenderness

Sldr 100.8565

For slenderness ≤ 99

For slenderness > 99

R1 1 H.pier 140 r.gd * / (2^(- :

R2 70 r.gd * H.pier / (2^:

R2 0.4817

R1 0.481

R Sldr 99 ≤ R1 R1 if :

R 0.481

Maximum Axial Load Capacity

P.cmax R.tied Yes ≡ 0.8 0.8 f'.m * A.g A.stot - (* F.s A.stot * + (* R * R.tied No ≡ 0.8 0.8 f'.m * A.g A.stot - (* (* R * Entry Error if if :

P.cmax kip 140.4416

Section Capcity

Capacity

Utilization

Check

P.c φ.a P.cmax * φ.a P.n * 12 mat min :

U.a P.r P.c / :

P.c kip 3.3744

U.a 1.0669

P.chk U.a 1 ≤ OK NG if :

P.chk NG

U.b M.r M.c / :

M.c φ.b M.n * :

M.c kip ft * 73.9669

U.b 1.0816

M.chk U.b 1 ≤ OK NG if :

M.chk NG

U.s V.r V.c / :

V.c # :

U.s #

V.chk U.s 1 ≤ OK NG if :

V.chk #