Example 1 - rivt Doc#

0.11 | Summary and Loads#

This rivt file example calculates the maximum stress and deflection in a simply supported, uniformly loaded beam using E-B theory [0.1.1] . It also serves as an annotated example of a single rivt doc with multiple sections that is not part of a report.

The example illustrates the use of some of the most common API functions, commands and tags. Further details are provided in the rivt user manual .

The file may be formatted as a text, PDF or HTML doc by changing the type parameter in the PUBLISH command at the end of each rivt file (Doc-API rv.D). Published files are found in the _published folder.


0.1 - 22 | Load Combinations#

Dead and live loads effects are taken from ASCE 7-05 [0.1.2]


Table 1: Load Effects (stored: t001-1.csv)

Equation No.

Load Combination

16-1

1.4(D+F)

16-2

1.2(D+F+T) + 1.6(L+H) + 0.5(Lr or S or R)

16-3

1.2(D+F+T) + 1.6(Lr or S or R) + (f1L or 0.8W)


0.1 - 33 | Loads and Geometry#

Successive value definitions are formatted as a table. Variable values are defined with the define operator. The line tag [T] labels and numbers the table.

Table 2: Define Unit Loads

variable

value

[value]

description

D_1

3.80 p_sf

0.18 kPA

joists DL

D_2

2.10 p_sf

0.10 kPA

plywood DL

D_3

10.00 p_sf

0.48 kPA

partitions DL

D_4

3.00 k_ft

43.78 kN_m

fixed machinery DL

L_1

40.00 p_sf

1.92 kPA

ASCE7-O5 LL

b_1

10.00 inch

254.00 mm

beam width

h_1

18.00 inch

457.20 mm

beam depth

E_1

29000.00 k_si

199947.96 MPA

modulus of elasticity

Fb_1

20000.00 p_si

137.90 MPA

allowable stress

The VALTABLE command reads variable values from a file in the rvsrc/data folder. The description is the table title, followed by the max column width.


Table 3: Beam Geometry (rvsrc/data/beam1.csv)

variable

value

[value]

description

spc_1

2.00 ft

0.61 m

beam spacing

spn_1

16.00 ft

4.88 m

beam span

_images/beam1.png

Fig. 1 - Beam Diagram#

Uniform Distributed Loads


Eq. 1: Dead load [ASCE7-05 2.3.2]

dl₁ = 1.2⋅(D₄ + spc₁⋅(D₁ + D₂ + D₃))

dl₁ = 3.64 k_ft     [dl₁] = 53.09 kN_m   | Dead load [ASCE7-05 2.3.2]

D₄                  D₂          D₁         spc₁          D₃
——————————————————  ——————————  —————————  ————————————  —————————————
3.00 k_ft           2.10 p_sf   3.80 p_sf  2.00 ft       10.00 p_sf
—————               —————       —————      —————         —————
fixed machinery DL  plywood DL  joists DL  beam spacing  partitions DL
——————————————————  ——————————  —————————  ————————————  —————————————

Eq. 2: Live load [ASCE7-05 2.3.2]

ll₁ = 1.6⋅L₁⋅spc₁

ll₁ = 0.13 k_ft     [ll₁] = 1.87 kN_m   | Live load [ASCE7-05 2.3.2]

L₁           spc₁
———————————  ————————————
40.00 p_sf   2.00 ft
—————        —————
ASCE7-O5 LL  beam spacing
———————————  ————————————

Eq. 3: Total load [ASCE7-05 2.3.2]

ω₁ = dl₁ + ll₁

ω₁ = 3.77 k_ft     [ω₁] = 54.96 kN_m   | Total load [ASCE7-05 2.3.2]

dl₁                  ll₁
———————————————————  ———————————————————
3.64 k_ft            128.00 ft·p_sf
—————                —————
Dead load [ASCE7-05  Live load [ASCE7-05
2.3.2]               2.3.2]
———————————————————  ———————————————————

0.1 - 44 | Beam Response#

The following lines import the beam geometry from an external file, calculate section properties from imported functions and calculate the maximum moment, bending stress and mid-span deflection.

Table 4: Beam functions (rvsrc/scripts/sectprop.py)

Function

Docstring

rectsect(b, d)

section modulus of rectangle

rectinertia(b, d)

moment of inertia of rectangle

midspan_delta(ln, w, e, i)

mid-span deflection of simply supported beam with UDL


Eq. 4: rectangle - S (sectprop.py)

section₁ = rectsect(b₁, h₁)

section₁ = 540.00 in3     [section₁] = 8849.01 cm3   | rectangle - S (sectprop.py)

h₁          b₁
——————————  ——————————
18.00 inch  10.00 inch
—————       —————
beam depth  beam width
——————————  ——————————

Eq. 5: rectangle - I (sectprop.py)

inertia₁ = rectinertia(b₁, h₁)

inertia₁ = 4860.0 in4     [inertia₁] = 202288.5 cm4   | rectangle - I (sectprop.py)

h₁          b₁
——————————  ——————————
18.0 inch   10.0 inch
—————       —————
beam depth  beam width
——————————  ——————————
_images/ss-beam2.png

Fig. 2 - Moment diagram#

_images/ss-beam1.png

Fig. 3 - Deflection diagram#

Maximum bending stress formula


Eq.6:

     M₁
σ₁ = ──
     S₁

Eq. 7: Mid-span UDL moment

            2
     ω₁⋅spn₁
m₁ = ────────
        8

m₁ = 120.52 ft-kip     [m₁] = 163.40 mkN   | Mid-span UDL moment

spn₁       ω₁
—————————  ————————————————————
16.00 ft   3.77 k_ft
—————      —————
beam span  Total load [ASCE7-05
-          2.3.2]
—————————  ————————————————————

Eq. 8: Bending stress

         m₁
fb₁ = ────────
      section₁

fb₁ = 2678.2 p_si     [fb₁] = 18.5 MPA   | Bending stress

m₁                   section₁
———————————————————  —————————————
120.5 ft2·k_ft       540.0 inch3
—————                —————
Mid-span UDL moment  rectangle - S
-                    (sectprop.py)
———————————————————  —————————————


Eq.9: Stress ratio

▮ fb₁ < Fb₁
▮
▮ [1] fb₁    [2] Fb₁     ratio [1]/[2]    check    reference
▮ —————————  ——————————  ———————————————  ———————  ————————————
▮ 2.68 k_si  20.00 k_si  0.13             OK       Stress ratio
▮ —————————  ——————————  ———————————————  ———————  ————————————

Eq. 10: mid-span deflection (sectprop.py)

δ₁ = midspan_δ(spn₁, ω₁, E₁, inertia₁)

δ₁ = 0.04 inch     [δ₁] = 1.00 mm   | mid-span deflection (sectprop.py)

spn₁       ω₁                    E₁             inertia₁
—————————  ————————————————————  —————————————  —————————————
16.00 ft   3.77 k_ft             29000.00 k_si  4860.00 inch4
—————      —————                 —————          —————
beam span  Total load [ASCE7-05  modulus of     rectangle - I
-          2.3.2]                elasticity     (sectprop.py)
—————————  ————————————————————  —————————————  —————————————

[0.1.1]

“Euler–Bernoulli beam theory”, Wikipedia, Wikimedia Foundation. [Online].https://en.wikipedia.org/wiki/Euler_Bernoulli_beam_theory.[Accessed: Jun. 15, 2026].

[0.1.2]

ASCE/SEI 7-05, Minimum Design Loads for Buildings and Other Structures,American Society of Civil Engineers, 2005.