-------------------------------------------------------------------------------- Example 1 - rivt Doc | R Holland | v-1.0.0a13 | 2026-07-11 - 02:30PM -------------------------------------------------------------------------------- 0.1 | 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 https://www.rivt.info . 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 - 2 | 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 - 3 | 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] ============= ============ ========= ================== ========== D₃ spc₁ D₁ D₄ D₂ ============= ============ ========= ================== ========== 10.00 p_sf 2.00 ft 3.80 p_sf 3.00 k_ft 2.10 p_sf ————— ————— ————— ————— ————— partitions DL beam spacing joists DL fixed machinery DL plywood 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] =================== =================== ll₁ dl₁ =================== =================== 128.00 ft·p_sf 3.64 k_ft ————— ————— Live load [ASCE7-05 Dead load [ASCE7-05 2.3.2] 2.3.2] =================== =================== 0.1 - 4 | 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: (from file) ========================== ============================================ 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 │ │ fb_1 < Fb_1 └ ▮ ========= ========== =============== ======= ============ ▮ [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) ============= ========= ==================== ============= E₁ spn₁ ω₁ inertia₁ ============= ========= ==================== ============= 29000.00 k_si 16.00 ft 3.77 k_ft 4860.00 inch4 ————— ————— ————— ————— modulus of beam span Total load [ASCE7-05 rectangle - I elasticity - 2.3.2] (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.