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User input in boxed regions

Section Properties:

b 1.5 in * :

Thickness of Section

d 9.25 in * :

Width of Section

I 112 / b * d 3^* : in 4^98.93

Material Properties:

E 29000 ksi * :

Get value from NDS Supplement

Loading Conditions:

L 10 :

Horizontal Span, adjust for one half the required bearing at each end (add .75" for wood/metal bearing, 1.5" for concrete/masonry bearing)

Units of Feet assumed

Pitch 0 :

Set as 0 if member is not pitched

DL_Conversion Pitch 2^122^+ sqrt 12 / (: 1

Converts Dead Loads acting along roof plane to horizontal span. Live loads are already assumed to act on the horizontal projection of beam.

Adjustment Factors:

C.M 1.0 :

Wet Service Factor

Note: If moisture conditions in the member will exceed 19% for an extended period of time, refer to the appropriate table in the Supplement to calculate the Wet Service Factor.

C.fu 1.0 :

Flat Use Factor (See Sect. 4.3.7 if this factor applies)

C.i 1.0 :

Incising Factor (See Section 4.3.8 if this factor applies)

C.t 1.0 :

Temperature Factor

Note: If member is not expected to experience "sustained exposure to elevated temperatures" (above 100 deg. F), Temperature Factor for all moisture conditions is 1. See Sect. 2.3.3.

Adjusted Modulus of Elasticity (See Table 4.3.1):

E' E C.M C.t * C.fu * C.i * (* : ksi 29000

Support Reactions (Leave unused spots as junk value X at end):

X 1000 :

Supports.Input 28 X X X 51 mat ft * :

Restraints.Input Pin Pin Pin Pin Pin 51 mat :

Enter "Pin" for Pinned, "Fix" for Fixed, only reads as many restraints as valid supports (i.e. X values get discarded)

i 1 Supports.Input rows range Supports.Input i el X ft * ≠ Supports i el Supports.Input i el : Restraints i el Restraints.Input i el : 21 line break if for

Supports ft 2821 mat

Load Cases:

LC.1 D S + :

Dead + Snow

LC.2 D L.r + :

Dead + Roof Live

LC.3 D .75 L.F * + .75 S * + :

Dead + .75(Floor Live) + .75(Snow)

LC.4 D .75 L.F * + .75 L.r * + :

Dead + .75(Floor Live) + .75(Roof Live)

LC.5 .6 D * .6 W * + :

.6(Dead) + .6(Wind)

LC.6 .6 D * .6 W.U * + :

.6(Dead) + .6(Uplift Wind)

Uniformly Distributed Dead Loads:

UDL 10000000000101 mat psf * :

UDL.b_tr 2000000000101 mat ft * :

UDL.Start 0000000000101 mat ft * :

UDL.End L 000000000101 mat ft * :

UDL.Desc Test Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. 101 mat :

i 1 UDL rows range UDL i el 0 ≠ UDL.Line i el UDL i el DL_Conversion * UDL.b_tr i el * : break if for

UDL.Line lbf ft / 2011 mat

Uniformly Distributed Live Loads:

ULL 5000000000101 mat psf * :

ULL.b_tr 2000000000101 mat ft * :

ULL.Start 0000000000101 mat ft * :

ULL.End 5000000000101 mat ft * :

ULL.Cat S Cat. Cat. Cat. Cat. Cat. Cat. Cat. Cat. Cat. 101 mat :

ULL.Desc Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. 101 mat :

i 1 ULL rows range ULL i el 0 ≠ ULL.Line i el ULL i el ULL.b_tr i el * : break if for

ULL.Line lbf ft / 1011 mat

Linearly Distributed Dead Loads:

LDL 0000000000101 mat psf * :

LDL.b_tr_A 0000000000101 mat ft * :

LDL.b_tr_B 0000000000101 mat ft * :

LDL.Start 0000000000101 mat ft * :

LDL.End 0000000000101 mat ft * :

LDL.Desc Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. 101 mat :

i 1 LDL rows range LDL i el 0 ≠ LDL.Lefts i el LDL i el LDL.b_tr_A i el * : LDL.Grads i el DL_Conversion LDL i el * LDL.b_tr_B i el LDL.b_tr_A i el - LDL.End i el LDL.Start i el - / (* : LDL.Rights i el LDL.Lefts i el LDL.Grads i el LDL.End i el LDL.Start i el - (* + : 31 line break if for

LDL.Grads lbf ft / ft / #

LDL.Lefts lbf ft / #

LDL.Rights lbf ft / #

Linearly Distributed Live Loads:

LLL 0000000000101 mat psf * :

LLL.b_tr_A 0000000000101 mat ft * :

LLL.b_tr_B 0000000000101 mat ft * :

LLL.Start 0000000000101 mat ft * :

LLL.End 0000000000101 mat ft * :

LLL.Cat Cat. Cat. Cat. Cat. Cat. Cat. Cat. Cat. Cat. Cat. 101 mat :

LDL.Desc Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. 101 mat :

i 1 LLL rows range LLL i el 0 ≠ LLL.Lefts i el LLL i el LLL.b_tr_A i el * : LLL.Grads i el LLL i el LLL.b_tr_B i el LLL.b_tr_A i el - LLL.End i el LLL.Start i el - / (* : LLL.Rights i el LLL.Lefts i el LLL.Grads i el LLL.End i el LLL.Start i el - (* + : 31 line break if for

LLL.Grads lbf ft / ft / #

LLL.Lefts lbf ft / #

LLL.Rights lbf ft / #

Concentrated Dead Loads:

CDL 200000000000101 mat lbf * :

CDL.Loc 6000000000101 mat ft * :

CDL.Desc Test Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. 101 mat :

Concentrated Live Loads:

CLL 0000000000101 mat lbf * :

CLL.Loc 0000000000101 mat ft * :

CLL.Cat Cat. Cat. Cat. Cat. Cat. Cat. Cat. Cat. Cat. Cat. 101 mat :

CLL.Desc Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. Desc. 101 mat :

Composing Basic Nodes List (Beam Start, Support Reactions, Beam End):

Nodes.ft 0 L 12 mat ft * :

U V Append U transpose V stack sort (transpose :

x Range is_in i 1 Range cols range Range i el x ≡ is_equal i el 1 : is_equal i el 0 : if for is_equal sum (0 > Membership Y : Membership N : if 21 line :

i 1 Supports rows range Supports i el Nodes.ft is_in N ≡ Nodes.ft Nodes.ft Supports i el Append : continue if 11 line for

Dead Load Node Locations:

Nodes.ft_D Nodes.ft : ft 0281014 mat

i 1 UDL.Line rows range UDL.Start i el Nodes.ft_D is_in N ≡ Nodes.ft_D Nodes.ft_D UDL.Start i el Append : continue if for

i 1 UDL.Line rows range UDL.End i el Nodes.ft_D is_in N ≡ Nodes.ft_D Nodes.ft_D UDL.End i el Append : continue if for

i 1 LDL.Lefts rows range LDL.Start i el Nodes.ft_D is_in N ≡ Nodes.ft_D Nodes.ft_D LDL.Start i el Append : continue if for

i 1 LDL.Lefts rows range LDL.End i el Nodes.ft_D is_in N ≡ Nodes.ft_D Nodes.ft_D LDL.End i el Append : continue if for

i 1 CDL rows range CDL i el 0 ≠ CDL.Loc i el Nodes.ft_D is_in N ≡ Nodes.ft_D Nodes.ft_D CDL.Loc i el Append : continue if continue if for

Nodes.ft_D ft 02681015 mat

All_Cats D L Lr S W Wu 61 mat :

Live Load Node Locations:

Nodes.ft_L Nodes.ft :

Nodes.ft_Lr Nodes.ft :

Nodes.ft_S Nodes.ft :

Nodes.ft_W Nodes.ft :

Nodes.ft_Wu Nodes.ft :

All_LL_Nodes.ft Nodes.ft_L Nodes.ft_Lr Nodes.ft_S Nodes.ft_W Nodes.ft_Wu 51 mat :

LL_Cats L Lr S W Wu 51 mat :

i 1 All_LL_Nodes.ft rows range Match LL_Cats i el : j 1 ULL.Line rows range ULL.Cat j el Match ≡ ULL.Start j el All_LL_Nodes.ft i el is_in N ≡ All_LL_Nodes.ft i el All_LL_Nodes.ft i el ULL.Start j el Append : continue if continue if for 21 line for

i 1 All_LL_Nodes.ft rows range Match LL_Cats i el : j 1 ULL.Line rows range ULL.Cat j el Match ≡ ULL.End j el All_LL_Nodes.ft i el is_in N ≡ All_LL_Nodes.ft i el All_LL_Nodes.ft i el ULL.End j el Append : continue if continue if for 21 line for

i 1 All_LL_Nodes.ft rows range Match LL_Cats i el : j 1 LLL.Lefts rows range LLL.Cat j el Match ≡ LLL.Start j el All_LL_Nodes.ft i el is_in N ≡ All_LL_Nodes.ft i el All_LL_Nodes.ft i el LLL.Start j el Append : continue if continue if for 21 line for

i 1 All_LL_Nodes.ft rows range Match LL_Cats i el : j 1 LLL.Lefts rows range LLL.Cat j el Match ≡ LLL.End j el All_LL_Nodes.ft i el is_in N ≡ All_LL_Nodes.ft i el All_LL_Nodes.ft i el LLL.End j el Append : continue if continue if for 21 line for

i 1 All_LL_Nodes.ft rows range Match LL_Cats i el : j 1 CLL rows range CLL j el 0 ≠ CLL.Cat j el Match ≡ CLL.Loc j el All_LL_Nodes.ft i el is_in N ≡ All_LL_Nodes.ft i el All_LL_Nodes.ft i el CLL.Loc j el Append : continue if continue if continue if for 21 line for

Nodes needed to process all load types (D, L, Lr, S, W, Wu):

Nodes.ft_All Nodes.ft_D All_LL_Nodes.ft 1 el All_LL_Nodes.ft 2 el All_LL_Nodes.ft 3 el All_LL_Nodes.ft 4 el All_LL_Nodes.ft 5 el 61 mat : ft 02681015 mat 0281014 mat 0281014 mat 02581015 mat 0281014 mat 0281014 mat 61 mat

Equivalent Nodal Loads:

w l Equiv_Loads.Uniform w l * 2 / - w l 2^* - 12 / w l * 2 / - w l 2^* 12 / 41 mat :

w.1 w.2 l Equiv_Loads.Linear_Inc l 20 / 7 w.1 * 3 w.2 * + (* - l 2^60 / 3 w.1 * 2 w.2 * + (* - l 20 / 3 w.1 * 7 w.2 * + (* - l 2^60 / 2 w.1 * 3 w.2 * + (* 41 mat :

w.1 w.2 l Equiv_Loads.Linear_Dec l 20 / 3 w.1 * 7 w.2 * + (* - l 2^60 / 2 w.1 * 3 w.2 * + (* - l 20 / 7 w.1 * 3 w.2 * + (* - l 2^60 / 3 w.1 * 2 w.2 * + (* 41 mat :

list find index i 1 list cols range list i el find ≡ index i : continue if for index 21 line :

item inputs number range rewrite number range is_in Y ≡ selection range number index : item item inputs selection el + : 21 line item item : if item 21 line :

Adding UDLs to DL Load Vector:

F.D 2 Nodes.ft_All 1 el length * 1 matrix :

i 1 UDL.Line rows range len.elem UDL.End i el UDL.Start i el - : D.input UDL.Line i el len.elem Equiv_Loads.Uniform : D.insert 1 - Nodes.ft_All 1 el UDL.Start i el index 2 * + : D.range D.insert D.insert 1 + D.insert 2 + D.insert 3 + 41 mat transpose : j 1 F.D rows range F.D_temp j el F.D j el D.input j D.range rewrite : for F.D F.D_temp : 61 line for

Adding LDLs to DL Load Vector:

i 1 LDL.Lefts rows range len.elem LDL.End i el LDL.Start i el - : LDL.Grads i el 0 ≥ w.1 LDL.Lefts i el : w.2 LDL.Lefts i el LDL.Grads i el len.elem * + : D.input w.1 w.2 len.elem Equiv_Loads.Linear_Inc : 31 line w.1 LDL.Lefts i el : w.2 LDL.Lefts i el LDL.Grads i el len.elem * + : D.input w.1 w.2 len.elem Equiv_Loads.Linear_Dec : 31 line if D.insert 1 - Nodes.ft_All 1 el LDL.Start i el index 2 * + : D.range D.insert D.insert 1 + D.insert 2 + D.insert 3 + 41 mat transpose : j 1 F.D rows range F.D_temp j el F.D j el D.input j D.range rewrite : for F.D F.D_temp : 61 line for

Adding CDLs to DL Load Vector:

item matrix_index load insertion rewrite_CL insertion matrix_index ≡ item item load + : item item : if item 21 line :

i 1 CDL rows range CDL i el 0 ≠ CDL.use i el CDL - i el : continue if for

i 1 CDL.use rows range D.insert 1 - Nodes.ft_All 1 el CDL.Loc i el index 2 * + : j 1 F.D rows range F.D_temp j el F.D j el j CDL.use i el D.insert rewrite_CL : for F.D F.D_temp : 31 line for

Adding ULLs to LL Load Vectors:

F.L 2 Nodes.ft_All 2 el length * 1 matrix :

F.Lr 2 Nodes.ft_All 3 el length * 1 matrix :

F.S 2 Nodes.ft_All 4 el length * 1 matrix :

F.W 2 Nodes.ft_All 5 el length * 1 matrix :

F.Wu 2 Nodes.ft_All 6 el length * 1 matrix :

All_LL_F F.L F.Lr F.S F.W F.Wu 51 mat :

Cat match_Cat LL_Cats transpose Cat index :

i 1 ULL.Line rows range len.elem ULL.End i el ULL.Start i el - : D.input ULL.Line i el len.elem Equiv_Loads.Uniform : D.insert 1 - Nodes.ft_All ULL.Cat i el match_Cat 1 + (el ULL.Start i el index 2 * + : D.range D.insert D.insert 1 + D.insert 2 + D.insert 3 + 41 mat transpose : j 1 All_LL_F ULL.Cat i el match_Cat el rows range LL.temp j el All_LL_F ULL.Cat i el match_Cat el j el D.input j D.range rewrite : for All_LL_F ULL.Cat i el match_Cat el LL.temp : 61 line for

F.L All_LL_F 1 el :

F.Lr All_LL_F 2 el :

F.S All_LL_F 3 el :

F.W All_LL_F 4 el :

F.Wu All_LL_F 5 el :

Adding LLLs to LL Load Vectors:

i 1 LLL.Lefts rows range len.elem LLL.End i el LLL.Start i el - : LLL.Grads i el 0 ≥ w.1 LLL.Lefts i el : w.2 LLL.Lefts i el LLL.Grads i el len.elem * + : D.input w.1 w.2 len.elem Equiv_Loads.Linear_Inc : 31 line w.1 LLL.Lefts i el : w.2 LLL.Lefts i el LLL.Grads i el len.elem * + : D.input w.1 w.2 len.elem Equiv_Loads.Linear_Dec : 31 line if D.insert 1 - Nodes.ft_All LLL.Cat i el match_Cat 1 + (el LLL.Start i el index 2 * + : D.range D.insert D.insert 1 + D.insert 2 + D.insert 3 + 41 mat transpose : j 1 All_LL_F LLL.Cat i el match_Cat el rows range LL.temp j el All_LL_F LLL.Cat i el match_Cat el j el D.input j D.range rewrite : for All_LL_F LLL.Cat i el match_Cat el LL.temp : 61 line for

F.L All_LL_F 1 el :

F.Lr All_LL_F 2 el :

F.S All_LL_F 3 el :

F.W All_LL_F 4 el :

F.Wu All_LL_F 5 el :

Adding CLLs to LL Load Vectors:

i 1 CLL rows range CLL i el 0 ≠ CLL.use i el CLL - i el : continue if for

i 1 CLL.use rows range D.insert 1 - Nodes.ft_All CLL.Cat i el match_Cat 1 + (el CLL.Loc i el index 2 * + : j 1 All_LL_F CLL.Cat i el match_Cat el rows range LL.temp j el All_LL_F CLL.Cat i el match_Cat el j el j CLL.use i el D.insert rewrite_CL : for All_LL_F CLL.Cat i el match_Cat el LL.temp : 31 line for

F.L All_LL_F 1 el :

F.Lr All_LL_F 2 el :

F.S All_LL_F 3 el :

F.W All_LL_F 4 el :

F.Wu All_LL_F 5 el :

F.All F.D F.L F.Lr F.S F.W F.Wu 61 mat :

Element stiffness matrices:

U V Append_Unsorted U transpose V stack transpose :

N1 N2 l N2 N1 - :

blank 011 mat :

l.all_elems blank blank blank blank blank blank 61 mat :

l.all_elems_init i el l.all_elems i el lengths_vector Append_Unsorted :

list get_lengths j 2 Nodes.ft_All list el length range lengths j 1 - el Nodes.ft_All list el transpose j 1 - el Nodes.ft_All list el transpose j el l : for l.all_elems_init list el l.all_elems list el lengths Append_Unsorted : l.all_elems_init list el 31 line :

l.all_elems_init 1 get_lengths 2 get_lengths 3 get_lengths 4 get_lengths 5 get_lengths 6 get_lengths 61 mat :

i 16 range len.list l.all_elems_init i el length : l.all_elems i el l.all_elems_init i el 112 len.list submatrix : 21 line for

l.all_elems ft 242214 mat 26213 mat 26213 mat 233214 mat 26213 mat 26213 mat 61 mat

Formula for local stiffness matrix of a beam element:

l k E I * l 3^/ 126 l * 12 - 6 l * 6 l * 4 l 2^* 6 l * - 2 l 2^* 12 - 6 l * - 126 l * - 6 l * 2 l 2^* 6 l * - 4 l 2^* 44 mat * :

Determining assembly coordinates for local matrices into global:

i 1 l.all_elems rows range j 1 l.all_elems i el cols range assembly_coords i j el 1 j 1 ≡ 1 - j 2 * (+ cases : for for

Initializing global stiffness matrices (Size = # of Elements + 1 or the # of Nodes * DOF):

i 1 l.all_elems rows range K i el l.all_elems i el length 1 + (2 * l.all_elems i el length 1 + (2 * matrix : for

Assembling global stiffness matrices:

K k coord Assemble_K U K : i 03 range j 03 range U coord i + coord j + el U coord i + coord j + el k i 1 + j 1 + el + : for for U 31 line :

i 1 K rows range j 1 l.all_elems i el cols range assembly_coord assembly_coords i j el : k l.all_elems i el transpose j el k : K.temp K i el k assembly_coord Assemble_K : K i el K.temp : K i el 51 line for for

Strip units from global K matrix for later calculation:

odd_range 11003 range :

even_range 01002 range :

K K.unitless i 1 K rows range j 1 K cols range i odd_range transpose is_in Y ≡ j odd_range transpose is_in Y ≡ K i j el K i j el ft lbf / * : K i j el K i j el 1 lbf / * : if j odd_range transpose is_in Y ≡ K i j el K i j el 1 lbf / * : K i j el K i j el 1 lbf ft * / * : if if for for K 21 line :

K.unitless K 1 el K.unitless K 2 el K.unitless K 3 el K.unitless K 4 el K.unitless K 5 el K.unitless K 6 el K.unitless 61 mat :

Enforcing boundary conditions @ supports in load matrices:

F nodes Enforce_BCs i 1 Supports rows range loc Supports i el : cond Restraints i el : F.index nodes loc index : cond Fix ≡ restrict 1221 mat : cond Pin ≡ restrict 111 mat : Error if if i 1 restrict rows range indexes i el 1 - 2 F.index * + restrict i el 1 - (+ : for i 1 indexes rows range enforce_at indexes i el : F enforce_at el 0 : 21 line for 61 line for F 21 line :

F.All_mod F.All 1 el Nodes.ft_All 1 el Enforce_BCs F.All 2 el Nodes.ft_All 2 el Enforce_BCs F.All 3 el Nodes.ft_All 3 el Enforce_BCs F.All 4 el Nodes.ft_All 4 el Enforce_BCs F.All 5 el Nodes.ft_All 5 el Enforce_BCs F.All 6 el Nodes.ft_All 6 el Enforce_BCs 61 mat :

Enforcing boundary conditions @ supports in stiffness matrices:

K nodes Modify_K i 1 Supports rows range loc Supports i el : cond Restraints i el : K.index nodes loc index : cond Fix ≡ restrict 1221 mat : cond Pin ≡ restrict 111 mat : Error if if i 1 restrict rows range indexes i el 1 - 2 K.index * + restrict i el 1 - (+ : for i 1 indexes rows range enforce_at indexes i el : g 1 K cols range K enforce_at g el 0 : for K enforce_at enforce_at el 1 : 31 line for 61 line for K 21 line :

K.mod K.unitless 1 el Nodes.ft_All 1 el Modify_K K.unitless 2 el Nodes.ft_All 2 el Modify_K K.unitless 3 el Nodes.ft_All 3 el Modify_K K.unitless 4 el Nodes.ft_All 4 el Modify_K K.unitless 5 el Nodes.ft_All 5 el Modify_K K.unitless 6 el Nodes.ft_All 6 el Modify_K 61 mat :

Solving for displacement matrices (strip load vector of units as well):

F F.unitless i 1 F rows range F i el F i el 1 lbf / * i odd_range transpose is_in Y ≡ F i el 1 lbf ft * / * cases : for F 21 line :

F.D_unitless F.All_mod 1 el F.unitless :

F.L_unitless F.All_mod 2 el F.unitless :

F.Lr_unitless F.All_mod 3 el F.unitless :

F.S_unitless F.All_mod 4 el F.unitless :

F.W_unitless F.All_mod 5 el F.unitless :

F.Wu_unitless F.All_mod 6 el F.unitless :

V get split get 1 ≡ i 1 V rows 3 range reindex_odd odd_range transpose i index : V.odd reindex_odd el V i el : 21 line for i 2 V rows 4 range reindex_even even_range transpose i index 1 - : V.even reindex_even el V i el : 21 line for if get 1 ≡ V.out V.odd : V.out V.even : if V.out 31 line :

U.D K.mod 1 el (1 -^F.D_unitless * :

R.D K.unitless 1 el U.D * F.All 1 el F.unitless - :

U.L K.mod 2 el (1 -^F.L_unitless * :

R.L K.unitless 2 el U.L * F.All 2 el F.unitless - :

U.Lr K.mod 3 el (1 -^F.Lr_unitless * :

R.Lr K.unitless 3 el U.Lr * F.All 3 el F.unitless - :

U.S K.mod 4 el (1 -^F.S_unitless * :

R.S K.unitless 4 el U.S * F.All 4 el F.unitless - :

U.S K.mod 4 el (1 -^F.S_unitless * :

R.S K.unitless 4 el U.S * F.All 4 el F.unitless - :

U.W K.mod 5 el (1 -^F.W_unitless * :

R.W K.unitless 5 el U.W * F.All 5 el F.unitless - :

U.Wu K.mod 6 el (1 -^F.Wu_unitless * :

R.Wu K.unitless 6 el U.Wu * F.All 6 el F.unitless - :

U.All U.D U.L U.Lr U.S U.W U.Wu 61 mat :

R.All R.D R.L R.Lr R.S R.W R.Wu 61 mat :

R_vector filter R.Y_filtered Supports length 1 matrix : counter 1 : j 1 R_vector rows range R_vector sum (0 ≠ R_vector j el abs .001 < continue R.Y_filtered counter el R_vector j el : counter counter 1 + : 21 line if R.Y_filtered R_vector : if for R.Y_filtered 41 line :

i 1 U.All rows range U.Y i el U.All i el 1 split : U.M i el U.All i el 0 split : R.Y i el R.All i el 1 split filter : R.M i el R.All i el 0 split filter : 41 line for

Results (D, L, Lr, S, W, Wu):

Nodal displacements in inches:

U.Y transpose in * in #

Nodal rotations in degrees:

U.M transpose deg #

Vertical reactions in lbs:

R.Y transpose #

Moment reactions in lbft:

R.M transpose #

Load Combinations (Y-Reactions, lbs):

D R.Y 1 el :

L.F R.Y 2 el :

L.r R.Y 3 el :

S R.Y 4 el :

W R.Y 5 el :

W.U R.Y 6 el :

Dead + Snow

Dead + Roof Live

Dead + .75(Floor Live) + .75(Snow)

LC.1 LC.1 lbf * :

LC.2 LC.2 lbf * :

LC.3 LC.3 lbf * :

LC.1 lbf #

LC.2 lbf #

LC.3 lbf #

Dead + .75(Floor Live) + .75(Roof Live)

.6(Dead) + .6(Wind)

.6(Dead) + .6(Uplift Wind)

LC.4 LC.4 lbf * :

LC.5 LC.5 lbf * :

LC.6 LC.6 lbf * :

LC.4 lbf #

LC.5 lbf #

LC.6 lbf #

Singlularity Functions for load types:

w x a V.Uniform SF w x a - (1^* - : x a ≥ SF 0 : cases :

w x a M.Uniform SF w 2 / x a - (2^* - : x a ≥ SF 0 : cases :

m x a V.Linear SF m 2 / x a - (2^* - : x a - a ≥ SF 0 : cases :

m x a M.Linear SF m 6 / x a - (3^* - : x a - a ≥ SF 0 : cases :

p x a V.Conc SF p - : x a ≥ SF 0 : cases :

p x a M.Conc SF p x a - (* - : x a ≥ SF 0 : cases :

Shear Diagrams:

i 010001 range i L ≤ temp_vector i 1 + el i : break if for

Load Start V.Function_Uniform i 010001 range i L ≤ V.Values i 1 + el Load i ft * Start V.Uniform : break if 11 line for V.Values 21 line :

Load Start V.Function_Linear i 010001 range i L ≤ V.Values i 1 + el Load i ft * Start V.Linear : break if 11 line for V.Values 21 line :

Load Location V.Function_Conc i 010001 range i L ≤ V.Values i 1 + el Load i ft * Location V.Conc : break if 11 line for V.Values 21 line :

LC Num V.Function_Support i 010001 range i L ≤ V.Values i 1 + el LC Num el i ft * Supports Num el V.Conc : break if 11 line for V.Values 21 line :

Initializing Dead and Live Load Shear Vectors:

V.DL temp_vector rows 1 matrix :

V.LL temp_vector rows 5 matrix :

Combining Unform Shears:

i 1 UDL.Line rows range V.DL V.DL UDL.Line i el UDL.Start i el V.Function_Uniform + : UDL.End i el L ft * < V.DL V.DL UDL.Line i el - UDL.End i el V.Function_Uniform + : continue if V.DL 31 line for

i 1 ULL.Line rows range Column ULL.Cat i el match_Cat : Changed_col V.LL Column col : Changed_col Changed_col ULL.Line i el ULL.Start i el V.Function_Uniform + : j 1 Changed_col rows range V.LL j Column el V.LL j Column el Changed_col j el + : for ULL.End i el L ft * < Changed_col Changed_col ULL.Line i el - ULL.End i el V.Function_Uniform + : j 1 Changed_col rows range V.LL j Column el V.LL j Column el Changed_col j el + : for 21 line continue if 51 line for

Combining Linear Shears:

i 1 LDL.Line rows range V.DL V.DL LDL.Line i el LDL.Start i el V.Function_Linear + : LDL.End i el L ft * < V.DL V.DL LDL.Line i el - LDL.End i el V.Function_Linear + : continue if V.DL 31 line for

i 1 LLL.Line rows range Column LLL.Cat i el match_Cat : Changed_col V.LL Column col : Changed_col Changed_col ULL.Line i el ULL.Start i el V.Function_Uniform + : j 1 Changed_col rows range V.LL j Column el V.LL j Column el Changed_col j el + : for ULL.End i el L ft * < Changed_col Changed_col ULL.Line i el - ULL.End i el V.Function_Uniform + : j 1 Changed_col rows range V.LL j Column el V.LL j Column el Changed_col j el + : for 21 line continue if 51 line for

Combining Concentrated Shears:

i 1 CDL rows range V.DL V.DL CDL i el CDL.Loc i el V.Function_Conc + : V.DL 21 line for

i 1 CLL rows range Column CLL.Cat i el match_Cat : Changed_col V.LL Column col : Changed_col Changed_col CLL i el CLL.Loc i el V.Function_Conc + : j 1 Changed_col rows range V.LL j Column el V.LL j Column el Changed_col j el + : for 41 line for

Combining Support Shears:

V.Supports temp_vector rows 1 matrix :

LC Combine_V.Supports i 1 Supports rows range V.Supports V.Supports LC i V.Function_Support + : 11 line for V.Supports 21 line :

Beam Analysis for Sawn Lumber Design (According to NDS 2024)

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