(11C) Concrete Beam Reinforcement Ratio and Area of Reinforcement

[buddyd16]

Recently acquired an HP 11c after having used TI's my whole life.

Here is a little program to calculate the required reinforcement ratio and required area of reinforcing steel.

setup:
Design Moment - Mu (ft-kips) STO 1
Cross Section Width - b (in) STO 2
Effective Depth to Tension Steel - d (in) STO 3
Concrete 28-day Compressive Strength - f'c (ksi) STO 4
Steel Yield Strength - fy (ksi) STO 5

Code:


Keystroke        Checksum        Comment
F LBL A        42,21,11    
RCL 1        45   1        Mu
RCL 2        45   2        b
RCL 3        45   3        d
G x^2        43   11        d^2
*            20    
.            48    
9            9    
*            20            0.9*b*d^2
/            10            Mu/0.9*b*d^2
1            1    
2            2    
*            20            conv. ft to in = 12*ans
STO 6        44   6        Ku
1            1    
RCL 6        45   6    
2            2    
*            20            2*Ku
RCL 4        45   4        F'c
.                48    
8            8    
5            5    
*            20            0.85*F'c
/            10            2*Ku/0.85*F'c
-            30            1 - (2*Ku/0.85*F'c)
√x            11            √1 - (2*Ku/0.85*F'c)
-            30            1-√1 - (2*Ku/0.85*F'c)
RCL 4        45   4        F'c
.            48    
8            8    
5            5    
*            20            0.85*F'c
*            20            (0.85*F'c)*1-√1 - (2*Ku/0.85*F'c)
RCL 5        45   5    
/            10            ρ
ENTER        36            copy ρ to stack
ENTER        36            copy ρ to stack
RCL 2        45   2        b
RCL 3        45   3        d
*            20    
*            20            As = ρ*b*d
G RTN        43   32        As in X register
                        ρ in Y register

[Gamo]

buddyd16

Would be nice if you include some example cases from your program.

By the way how do you like it so far on the HP-11C ?

Gamo

[buddyd16]

The 11c is quite nice. I used a TI-89 exclusively from high school through the earlier part of my career then switch to a Casio fx-115ES PLUS when it came time to take my licensing exam and then put that away about a year later and back to the TI-89.

The 11c has a much more solid feel than the TI-89 and the Casio feels like a toy in comparison. I read a lot of posts here and other locations before I decided to give RPN and an HP calculator a try and I must say the legend about the HP buttons is spot on, very purposeful feel to the button presses.

The "simplicity" of the 11c is a little refreshing to use there is no interface or CAS system to make some inputs cumbersome everything gets out of the way so you can just do the math.

The keystroke programming and the logic operators are a bit fascinating and wonderfully simple to piece together once you know how to input the problem in RPN. I started down this whole path because I wanted to relearn some higher level math and programming and took a bit of a math and programming history detour that led first to the sliderule and now calculators.

RPN in general I'm liking so far, some things take a bit of thought before entering them in as I've become so reliant on dropping parenthesis everywhere in formulas, partly because I ran into a PEMDAS order bug in the past which always made me paranoid and also because thats the way it was taught throughout my schooling. It's a bit like learning a new language I'm still translating what I'm doing to infix notation in my head eventually you get to the point where you think in that language as well as speak it.

as for an example of the program:
Given a Beam with the following:
Mu = 149.95 ft-kips
b = 48 in
d = 14.75 in
F'c = 3 ksi
Fy = 60 ksi

the program returns:
rho = As/bd = 0.00332 (y register)
As = 2.35098 in^2 (x register)

Verified by the Standard formula for phi*Mn = 0.9*As*Fy*(d-a/2) where a = As*Fy/(0.85*F'c*b)

a = 1.15244 in
phi*Mn = 1799.4 in-kips * 1 ft/12 in = 149.95 ft-kips

verification that a phi of 0.9 is appropriate is still left up to the end user. I'm still learning the logic operators and goto methods and may implement that check sometime in the future.