Steel Joist Analysis Calculator

For Steel Joists Considered as Simple-Span Beams
Subjected to Non-Standard Loads

Input Data

Joist Data:
Designation =  
Span, L = ft.
Modulus, E = psi
Inertia, Ix = in.^4
Original Design or Capacity Loads:
Full Uniform:
w = plf
  Start End
Distributed: b (ft.) wb (plf) e (ft.) we (plf) Point Loads: a (ft.) P (lbs.)
1# 1#
2# 2#
3# 3#
4# 4#
5# 5#
6# 6#
7# 7#
8# 8#
  9#
Moments: c (ft.) M (ft-lbs)   10#
1#   11#
2#   12#
3#   13#
4#   14#
  15#
New Design Loads:
Full Uniform:  
w = plf  
  Start End
Distributed: b (ft.) wb (plf) e (ft.) we (plf) Point Loads: a (ft.) P (lbs.)
1# 1#
2# 2#
3# 3#
4# 4#
5# 5#
6# 6#
7# 7#
8# 8#
  9#
Moments: c (ft.) M (ft-lbs)   10#
1#   11#
2#   12#
3#   13#
4#   14#
  15#

Results of Joist Analysis:

Original Design or Capacity Loads:
End Reactions:
RL = lbs. RR = lbs.
Minimum Design Web Member Shear:
Vw(min) = lbs.  
Maximum Moments:
+Mx(max) = ft-lbs @ x = ft.
-Mx(max) = ft-lbs @ x = ft.
*Maximum Deflections:
- Δ(max) = in. @ x = ft.
+Δ(max) = in. @ x = ft.
Δ(ratio) =  
*Note: deflections shown above include a 15% increase above the values calculated using traditional
"simple-beam" flexure in order to more closely match actual test results obtained by SJI.
New Design Loads:
End Reactions:
RL = lbs. RR = lbs.
Maximum Moments:
+Mx(max) = ft-lbs @ x = ft.
-Mx(max) = ft-lbs @ x = ft.
*Maximum Deflections:
- Δ(max) = in. @ x = ft.
+Δ(max) = in. @ x = ft.
Δ(ratio) =  
*Note: deflections shown above include a 15% increase above the values calculated using traditional
"simple-beam" flexure in order to more closely match actual test results obtained by SJI.
Maximum Stress Ratios:
S.R. = for Shear @ x = ft.
S.R. = for Moment @ x = ft.

Note: this worksheet can be used to determine the
total equivalent uniform load required to size a joist
for non-standard loads. The user can input all the
new, non-standard loads beginning at Row #35, and
then full uniform load at Cell B17 can be iterated
until both the stress ratios for shear and moment
are <= 1.0 everywhere the along the entire span.

User Designated Points to Calculate:
x1 = ft.  
x2 = ft.  
Results for User Designated Points for Original Design or Capacity Loads:
  For x1:   For x2:
Vx1 = lbs. Vx2 = lbs.
Mx1 = ft-lbs. Mx2 = ft-lbs.
qx1 = deg. qx2 = deg.
Δx1 = in. Δx2 = in.
Results for User Designated Points for New Design Loads:
  For x1:   For x2:
Vx1 = lbs. Vx2 = lbs.
Mx1 = ft-lbs. Mx2 = ft-lbs.
qx1 = deg. qx2 = deg.
Δx1 = in. Δx2 = in.
Maximum Stress Ratios (for 50 Joist Segments):
S.R. = for Shear @ x = ft.
S.R. = for Moment @ x = ft.
Maximum Stress Ratios (at User Designated Points):
S.R. =   for Shear @ x = ft.
S.R. =   for Moment @ x = ft.


x
The approximate moment of inertia of the joist is:
Ix = 26.767*W(LL)*(L-0.33)^3/1000000
where: W(LL) = uniform live load based on deflection of
          1/360 of span from Joist Load Table (plf)
          L = joist span from center to center of supports (ft.)
          (Note: joist design span = L-0.33'.)
The full uniformly distributed load, 'w',
usually includes the self-weight of the joist.
The full uniformly distributed load, 'w',
usually includes the self-weight of the joist.
Up to 8 distributed loads may be input.
These loads may be full or partial in
length and may be varying in value
(triangular or trapezoidal).
Do not use "Space Bar" to clear contents of unused cells.
"Highlight" those cells which are to be cleared
and click on the Right Mouse
Button and select "Clear Contents".
'b' is the distance from the left end of the
joist to the beginning (left side)
of the distributed load.
See Nomenclature illustration above.
'wb' is the value of the distributed load
at the beginning (left side) of the load.
See Nomenclature illustration above.
'e' is the distance from the left end of the
joist to the end (right side) of
the distributed load.
See Nomenclature illustration above..
'we' is the value of the distributed load
at the end (right side) of the load.
See Nomenclature illustration above.
Up to 15 point (concentrated) loads may be input.
Do not use "Space Bar" to clear contents of unused cells.
"Highlight" those cells which are to be cleared and click
on the Right Mouse Button and select
"Clear Contents".
'a' is the distance from the left
end of the joist to the point load.
See Nomenclature illustration above.
The value of 'P' is positive (+)
downward and negative (-) upward.
See Nomenclature illustration above.
Up to 4 externally applied moments may be input.
Do not use "Space Bar" to clear
contents of unused cells.
"Highlight" those cells which are to be cleared and
click on the Right Mouse Button and select "Clear Contents".
'c' is the distance from the left end of
the joist to the applied moment.
See Nomenclature illustration above
The value of 'M' is positive (+)
counterclockwise and negative (-) clockwise.
See Nomenclature illustration above.
'RL' is the vertical reaction at left end of joist.
Sign convention: positive (+) = upward.
The minimum design web shear capacity (per SJI)
= 25% of maximum end reaction for K-series and
LH-series joists
= 50% of maximum end reaction for H-series joists
'+M(max)' is the maximum positive moment in joist.
Positive (+) moment = tension in bottom of joist.
'-M(max)' is the maximum negative moment in joist.
Negative (-) moment = tension in top of joist.
'-D(max)' is the maximum negative deflection in joist.
Negative deflection is in downward direction.

Note: original calculated deflections were increased by
15% to more closely match actual test results by SJI.

'+D(max)' is the maximum positive deflection in joist.
Positive deflection is in upward direction.

Note: original calculated deflections were
increased by 15% to more closely match actual test results by SJI.

'D(ratio)' is the absolute maximum deflection
ratio and is calculated as follows:
  D(ratio) = L/n     where: n = L*12/ABS(D(max))
'RR' is the vertical reaction at right end of joist.
Sign convention: positive (+) = upward.
'x' is the location of the maximum positive
moment from left end of joist.
'x' is the location of the maximum negative
moment from left end of joist.
'x' is the location of the maximum negative
deflection from left end of joist.
'x' is the location of the maximum positive
deflection from left end of joist.
S.R. = maximum stress ratio for shear in the joist.
S.R. = maximum stress ratio for moment in the joist.
'x' is the location of the maximum
shear stress ratio from left end of joist.
'x' is the location of the maximum
moment stress ratio from left end of joist.
Shear at distance = x1 from left end of joist.
Sign convention: positive (+) = upward.

Note: Per SJI Spec's. for K-series and LH-series joists,
the minimum design web shear = 25% of the maximum joist end reaction.
(Value is 50% for older H-series joists.)

Moment at distance = x1 from left end of joist.
Sign convention: positive (+) = tension in bottom of joist.
Slope (rotation) at distance = x from left end of joist.
Sign convention: positive (+) = counterclockwise.

Note: original calculated slopes (rotations)
were increased by 15% to more closely
match actual test results by SJI.

Deflection at distance = x from left end of joist.
Sign convention: positive (+) = upward.

Note: original calculated deflections were increased
by 15% to more closely match actual test results by SJI.

Shear at distance = x2 from left end of joist.
Sign convention: positive (+) = upward.
Note: Per SJI Spec's. for K-series and LH-series

joists, the minimum design web shear = 25%
of the maximum joist end reaction.
(Value is 50% for older H-series joists.)

Moment at distance = x2 from left end of joist.
Sign convention: positive (+) = tension in bottom of joist
Slope (rotation) at distance = x from left end of joist.
Sign convention: positive (+) = counterclockwise.

Note: original calculated slopes (rotations) were
increased by 15% to more closely match actual test results by SJI.

Deflection at distance = x from left end of joist.
Sign convention: positive (+) = upward.


Note: original calculated deflections were
increased by 15% to more closely match actual test results by SJI.

Shear at distance = x1 from left end of joist.
Sign convention: positive (+) = upward.
Moment at distance = x1 from left end of joist.
Sign convention: positive (+) = tension in bottom of joist.
Slope (rotation) at distance = x from left end of joist.
Sign convention: positive (+) = counterclockwise.

Note: original calculated slopes (rotations)
were increased by 15% to more closely match actual test results by SJI.

Deflection at distance = x from left end of joist.
Sign convention: positive (+) = upward.

Note: original calculated deflections were
increased by 15% to more closely match actual test results by SJI.

Shear at distance = x2 from left end of joist.
Sign convention: positive (+) = upward.
Moment at distance = x2 from left end of joist.
Sign convention: positive (+) = tension in bottom of joist.
Slope (rotation) at distance = x from left end of joist.
Sign convention: positive (+) = counterclockwise.

Note: original calculated slopes (rotations)
were increased by 15% to more closely match actual test results by SJI.

Deflection at distance = x from left end of joist.
Sign convention: positive (+) = upward.

Note: original calculated deflections were
increased by 15% to more closely match actual test results by SJI.

S.R. = maximum stress ratio for shear in the joist.
S.R. = maximum stress ratio for moment in the joist.
'x' is the location of the maximum shear
stress ratio from left end of joist.
'x' is the location of the maximum moment
stress ratio from left end of joist.
'x' is the location of the maximum shear
stress ratio from left end of joist.
'x' is the location of the maximum moment
stress ratio from left end of joist.

Disclaimer: This calculator are not intended to be used for the design of actual structures, but only for schematic (preliminary) understanding of structural design principals. For the design of an actual structure, a competent professional should be consulted.

‘Calculations courtesy of Alex Tomanovich, PE