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# 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

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
    ——————————  ——————————

Fig. 2 - Moment diagram | 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.