Tables and Functions

Masonry Pier - STR 56facf58-bd4b-45ce-bf10-8022d7cc7513 138 4 5 decimal

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Reinforced Masonry Pier

MSJC 2013

Strength Design

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 length. If it does not meet these restricitons it is then typically a wall or a column. Calculation assumes that the pier is grouted solid Note - There is NO 4/3 INCREASE in the 2013 code.

Tables and Functions

Yes no Matrix YN Yes No 21 mat :

Masonry Material MOE Matrix MasMat# Concrete 900 Clay 70022 mat :

Allowable Msry Reinf Stress MsryStlMatSTR# Grade 40 40 ksi * Grade 50 50 ksi * Grade 60 60 ksi * 32 mat :

Mortar Types MortarType# M S N 31 mat :

M/Vd shear factor options Mshearfactor# Compute using M&V Input M.U V.U d# max * / abs 1 Min Manually define Enter Value 22 mat :

Unity Check Function for Condition Formatting U# U.a# fcheck U# U.a# > Out# NG white red ButtonGlossy 14 mat : U# 0 ≥ Out# OK white green ButtonGlossy 14 mat : Out# Check Negative white yellow ButtonGlossy 14 mat : if if Out# 21 line :

U U.a fcheck

Forces

Required Axial
(Factored) P.U 5 kip * :

Required Moment
(Factored) M.U 5 kip * ft * :

Required Shear
(Factored) V.U 3 kip * :

Reduction Factors

Axial φ.a# 0.9 :

Bending φ.b# 0.9 :

Shear φ.v# 0.8 :

Combined Axial and Bending φ.p_m# 0.8 :

Geometry of Section

Width (in X-direction) b.pier# 7.625 in * :

Depth 
(in Y-direction) h.pier# 32 in * :

Height of pier H.pier# 18.5 ft * :

"Yes"
"No"

Is the Reinf. Tied? i.e. effective in compression?

Tied#

Location of the
geo. centroid Y.p# h.pier# 2 / : in 16

Materials

Specified compressive 
strength f'.m# 1500 psi * :

"Concrete"
"Clay"

Masonry Type

E.factor#

Partially grouted factor γ.gv# 1 :

Note: Grout strength shall be min 2,000psi or exceed f'm Mortar shall equal or exceed f'm

Pier is assumed as fully grouted

"Grade 40"
"Grade 50"
"Grade 60"

Steel Reinforcment

f.y#

MOE - Steel Reinf. E.s# 29000 ksi * :

f.y# ksi 60

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

Reinforcment Layout
Top = Bar #
Bottom = depth to bar (form comp. face) Reinf# 55554 in * 12 in * 20 in * 28 in * 24 mat :

Area and Depth of Reinforcement n 1 Reinf# cols range A.s# n el Reinf# 1 n el 8 / in * (2^π 4 / * : d# n el Reinf# 2 n el : 21 line for

This converts the bar size to an area

A.stot# A.s# sum : in 2^1.2272

Total reinforcment

Shear Design Input:

Area of Steel
Shear reinf. A.sv# 0 in 2^* : in 2^0

Spacing of shear
reinf. S.asv# 4 in * :

Shear depth d.v# d# Max : in 28

"Compute using M&V Input"
"Manually define"

Shear factor M/Vd - Use input values or manually define?

M_Vd#

M_Vd# 0.7143

Additional Reduction factor to
axial load "helping" shear capacity R.v# 0.75 :

Note: The code uses 1/4 x axial load P.u to resist shear. This reduction will reduce this axial load further. It is not required and would typically be equal to 1.0 . It is directly applied to the axial load "P.U"

Partially grouted factor γ.gv# 1 :

Note: Piers are always fully grouted

Calculations

Section Properties:

Area of section

A.g# b.pier# h.pier# * : in 3^9606.2992 1 m / *

Moment of inertia

I.gx# b.pier# h.pier# 3^* 12 / : in 4^20821.3333

Moment of inertia

I.gy# h.pier# b.pier# 3^* 12 / : in 4^1182.1927

Radius of gyration

r.gx# I.gx# A.g# / (sqrt : in 9.2376

r.gy# I.gy# A.g# / (sqrt : in 2.2011

Design radius of gyration

r.gd# r.gx# r.gy# 12 mat min : in 2.2011

Material Properties

Masonry MOE

E.m# E.factor# f'.m# * : ksi 1350

E.factor# 900

Maximum compressive masonry strain

E.factor# 700 ≡ ε.m# 0.0035 : ε.m# 0.0025 : if

ε.m# 0.0025

Reduction factor for slenderness

Slenderness

h_r# H.pier# r.gd# / : 100.8565

H.pier# h.pier# b.pier# Min / 29.1148

Reduction for Slenderness

h_r# 99 ≤ R.s# 1 h_r# 140 / (2^- : R.s# 70 h_r# / (2^: if

R.s# 0.4817

P.nmax# 0.8 0.8 f'.m# * A.g# A.stot# - (* Tied# Yes ≡ f.y# A.stot# * 0 kip * if + (* R.s# * : kip 140.6443

Maximum Axial Force

The following calulcations are a series of functions All of which depend on the location of the neutral axis. This is done so that multiple locations of the neutral can be definded and the results recorded, graphed or compated. Also recall that functions can use variables definded outside the function (but not vice versa). To be consistent with the calulcation setup, we will use ## for variables inside these functions. However by doing this it adds a conseridable amount of variables that must be input into each function

Strain in Steel function
(note tension steel has negative strain) c## d## ε.m## ε.sx ε.m## c## / c## d## - (* :

Stress in Steel Function
(note positive stress means compression) c## d## Tied## E.s## f.y## ε.m## σ.s 0 ksi * c## d## ε.m## ε.sx 0 ksi * ≥ (Tied## No ≡ (& f.y## c## d## ε.m## ε.sx f.y## E.s## / ≥ f.y## - c## d## ε.m## ε.sx f.y## - E.s## / ≤ E.s## c## d## ε.m## ε.sx * cases :

Steel Force Function c## d## A.s## Tied## E.s## f.y## ε.m## F.s c## d## Tied## E.s## f.y## ε.m## σ.s A.s## * :

Compressive Force Function c## h.pier## f'.m## b.pier## d## A.s## C.m a# 0.8 c## * h.pier## Min : 0.8 f'.m## * a# b.pier## * c## d## i el < 0 A.s## i el if i 1 d## rows sum - (* 21 line :

Distance from h/2 to Comp. Force c## h.pier## Y.cm a# 0.8 c## * h.pier## Min : h.pier## 2 / a# 2 / - 21 line :

Nominal Axial Capacity Based on Eccentrically Applied Axial
Send As and d to the force function for each bar/depth c## h.pier## f'.m## b.pier## d## A.s## Tied## E.s## f.y## ε.m## P.nx c## h.pier## f'.m## b.pier## d## A.s## C.m c## d## i el A.s## i el Tied## E.s## f.y## ε.m## F.s i 1 A.s## rows sum + :

Nominal Moment Capacity based on Eccentricity c## h.pier## f'.m## b.pier## d## A.s## Tied## E.s## f.y## ε.m## M.nx c## h.pier## f'.m## b.pier## d## A.s## C.m c## h.pier## Y.cm * c## d## i el A.s## i el Tied## E.s## f.y## ε.m## F.s h.pier## 2 / d## i el - (* (i 1 A.s## rows sum + :

Call Functions and find Nominal Strengths

Nominal Strengths - 
Itterate though different values of "c" to find moment and axial strengths i 1 h.pier# 1.4 * 0.1 in * / trunc range c# i 0.1 * in * : P_M.n i 1 el c# h.pier# f'.m# b.pier# d# A.s# Tied# E.s# f.y# ε.m# M.nx kip ft * / eval : P_M.n i 2 el c# h.pier# f'.m# b.pier# d# A.s# Tied# E.s# f.y# ε.m# P.nx kip / P.nmax# kip / H.pier# h.pier# b.pier# Min / 30 > 0.05 f'.m# * A.g# * kip / 0.2 f'.m# * A.g# * kip / if Min eval : 31 line for

Now factor the nominal strengths and place them into 
a matrix that can be ploted i 1 P_M.n rows range φP_M.n i 1 el φ.p_m# P_M.n i 1 el * eval : φP_M.n i 2 el φ.p_m# P_M.n * i 2 el eval : 21 line for

Create a matrix of the forces acting on the member
these will also be ploted Pu_Mu 0 P.U kip / M.U kip ft * / P.U kip / M.U kip ft * / 032 mat : 05555032 mat

Use for spot checking N.A. Location and Functions Defined Above

c.check 10 in * :

n 1 d# rows range σ.sout n el c.check d# n el Tied# E.s# f.y# ε.m# σ.s : ε.sxout n el c.check d# n el ε.m# ε.sx : F.sout n el c.check d# n el A.s# n el Tied# E.s# f.y# ε.m# F.s : M.nout n el F.sout n el h.pier# 2 / d# n el - (* : 41 line for

σ.sout ksi 43.5 14.5 - 60 - 60 - 41 mat

ε.sxout in in / 0.0015 0.0005 - 0.0025 - 0.0045 - 41 mat

f.y# E.s# / 0.0021

F.sout kip 13.3456 4.4485 - 18.4078 - 18.4078 - 41 mat

M.nout kip ft * 13.3456 1.4828 - 6.1359 18.4078 41 mat

Shear - Calcs

Net shear area

A.nv# b.pier# d.v# * : in 2^213.5

Max Nominal Shear Capacity

Max Shear

M_Vd Limit

V.nmax1# A.nv# 6 * f'.m# 1 ksi * / sqrt * 1 * ksi * γ.gv# * : kip 1568.8982

M_vdlim1# 0.25 :

V.nmax2# A.nv# 4 * f'.m# 1 ksi * / sqrt * 1 * ksi * γ.gv# * : kip 1045.9321

M_vdlim2# 1 :

MV.nmax# M_vdlim1# V.nmax1# M_vdlim2# V.nmax2# 22 mat :

Assemble matrix and find max

V.nmax# MV.nmax# 1 col MV.nmax# 2 col kip / M_Vd# linterp kip * : kip 1245.1573

V.nm# 12 / 4 1.75 M_Vd# * - (* f'.m# 1 ksi * / sqrt * ksi * A.nv# * P.U R.v# * 4 / + : kip 360.4767

Nominal masonry shear strength

Nominal steel Reinf. shear strength

V.ns# 12 / A.sv# S.asv# / * f.y# * d.v# * : kip 0

Nominal Shear capacity

V.n# V.nmax# V.nm# V.ns# + (γ.gv# * (Min : kip 360.4767

Section capacity

V.c# V.n# φ.v# * : kip 288.3813

PLOT FORMATTING

Function to round to nearest indicated number

x n roundc n 0 ≡ invalid argument n error x 0 ≡ 0 magnitude 10 x abs n / 10 log 0 round^: x magnitude / n < x magnitude / 0 round magnitude * x magnitude 10 * / 0 round magnitude * 10 * if 21 line if if :

Plot Formatting XYPlot.XLimMin 1 el 0 : XYPLOT.YLimMin 1 el 0 : XYPlot.XLimMax 1 el P_M.n 1 col max eval 1.05 * : XYPlot.YLimMax 1 el P_M.n 2 col max eval 1.05 * : XYPlot.YTick 1 el XYPlot.YLimMax 1 el 10 / XYPlot.YLimMax 1 el 100 < 110 if roundc : XYPlot.XTick 1 el XYPlot.XLimMax 1 el 10 / XYPlot.XLimMax 1 el 100 < 110 if roundc (: 71 line

RESULTS

Shear

Utilization

U.v# V.U V.c# / : 0.0104

U.a 1 :

U.v# U.a fcheck φP_M.n P_M.n Pu_Mu 3 1 sys