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In the Calcs.com Beam Analysis and Wood Beam calculators, a downward load is entered as a positive number, and support reactions that push up are positive. Shear, moment and deflection are plotted along the beam: a positive moment plots above the axis, and a downward deflection is negative. In the Wood Beam calculator, the strong axis (X-X) is the axis with the higher moment of inertia. This article shows each convention with US-unit screenshots from three calculators.

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Worked example

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Symbols

The article uses these symbols, with the names the sheets use.

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Example 1: a fixed-roller beam under a uniform load

A 20 ft beam is fixed at the left end and on a roller at the right end. It carries one downward uniform load of 1 kip/ft over its full length. This one beam shows every sign in the Beam Analysis calculator: the load, the shear, a negative moment at the fixed support, a positive moment in the span, a downward deflection, and upward reactions with a moment reaction. The run is on Beam Analysis in a US customary project. The edits are:
  • Supports: Fixed at 0 ft and Roller at 20 ft
  • Distributed Load: 1000 plf at the start and the end, from 0 ft to 20 ft (the default load is replaced)
Everything else stays as the sheet opens.
1

Set the supports

In Position of Supports from Left, set the first support to Fixed at 0 ft and the second to Roller at 20 ft.Position of Supports from Left with a Fixed support at 0 ft and a Roller support at 20 ft.
2

Enter the load

In Simple Loads, replace the default load with a Distributed Load of 1000 plf at the start and the end, from 0 ft to 20 ft. The load is entered as a positive number and the diagram draws it as an arrow pointing down.Distributed Loads table with a Distributed Load with a start magnitude of 1000 plf, an end magnitude of 1000 plf, a start location of 0 ft and an end location of 20 ft.Simple Loads with a diagram of a 20 ft beam with a fixed support on the left, a roller support on the right and Distributed Load 1 of 1000 plf pointing down along its length.
3

Read the summary and the reactions

The Summary shows a Moment Demand M∗M^* of −50 000 lb·ft, a Shear Demand V∗V^* of 12 500 lb, a Deflection δ\delta of −0.0715 in, a Maximum Lateral Reaction R∗R^* of 12 500 lb and a Maximum Moment Reaction Rm∗R_m^* of 50 000 lb·ft. The reactions diagram shows 12 500 lb up at the fixed end, with a curved arrow for the moment reaction, and 7500 lb up at the roller.Summary with a Moment Demand of minus 50 000 pound-feet, a Shear Demand of 12 500 pounds, a Deflection of minus 0.0715 inches, a Maximum Lateral Reaction of 12 500 pounds and a Maximum Moment Reaction of 50 000 pound-feet, above a reactions diagram with 12 500 pounds and a curved moment arrow at the left end and 7500 pounds at the right end, and the start of the shear graph.
4

Read the graphs

The shear graph starts at +12 500 lb at the fixed end, crosses zero at about 12.5 ft and ends at −7500 lb. The moment graph starts at −50 000 lb·ft at the fixed end, crosses zero at 5 ft, peaks at about +28 000 lb·ft near 12.5 ft and returns to zero at the roller. The deflection graph is below the axis, lowest at about −0.07 in. In the last diagram the load arrows point down and the reaction arrows point up.Moment graph from minus 50 000 pound-feet at the left end, crossing zero at 5 ft, peaking near 28 000 pound-feet and returning to zero at 20 ft, a deflection graph below the axis with its lowest point about minus 0.07 inches, and a diagram of the downward load with reactions of 12 500 pounds with a moment arrow and 7500 pounds.
5

Check the reactions per support

Per-Support Analysis lists a reaction of 12 500 lb, a moment of −50 000 lb·ft and a shear of 12 500 lb at 0 ft, and a reaction of 7500 lb, a moment of 0 and a shear of −7500 lb at 20 ft. The moment and shear columns match the moment and shear graphs at each support.Support Demands Table with 12 500 pounds of reaction, minus 50 000 pound-feet of moment and 12 500 pounds of shear at position 0, and 7500 pounds of reaction, 0 moment and minus 7500 pounds of shear at position 20.
Inputs, Calcs.com output and a hand check

Inputs

CalculatorBeam Analysis
Span LL20 ft
SupportsFixed at 0 ft, Roller at 20 ft
Uniform load ww1000 plf, downward

Calcs.com output

Reaction at the fixed end12 500 lb up
Moment at the fixed end−50 000 lb·ft
Reaction at the roller7500 lb up
Peak span momentabout +28 000 lb·ft
Deflection−0.0715 in

Hand check

✓Total load: wL=1000×20=20 000wL = 1000 \times 20 = 20\,000 lb
✓Roller reaction: 3wL/8=3×20 000/8=3wL/8 = 3 \times 20\,000 / 8 = 7500 lb
✓Fixed-end reaction: 5wL/8=5×20 000/8=5wL/8 = 5 \times 20\,000 / 8 = 12 500 lb
✓Fixed-end moment: wL2/8=1000×202/8=wL^2/8 = 1000 \times 20^2 / 8 = 50 000 lb·ft, negative because it is a hogging moment
✓Peak span moment: 9wL2/128=9×1000×400/128=9wL^2/128 = 9 \times 1000 \times 400 / 128 = 28 125 lb·ft

The reactions, the end moment and the peak span moment match the closed-form solution for a beam fixed at one end and simply supported at the other. This is a sanity check only. The deflection depends on the section and is not hand-checked. Beam Analysis.

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Loads

A vertical load is entered as a positive number when it acts downward, and the load diagrams draw it as an arrow pointing down. This is the same in Beam Analysis, in the Wood Beam calculator and for the axial load on a column. The Wood Beam Loads panel draws a floor load and the self-weight as arrows pointing down. Loads panel of the Wood Beam calculator with a diagram of a 25 ft beam with a Floor Load and a Self-weight, both drawn as arrows pointing down, and a Distributed Loads table with a Floor Load of 20 psf dead and 40 psf live load.

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Shear, moment and deflection

The shear, moment and deflection graphs follow the same rules in Beam Analysis (below the Summary) and in the Diagrams panel of the Wood Beam calculator.
  • Shear: under a downward load the shear is positive at the left support and negative at the right.
  • Moment: a positive (sagging) moment plots above the axis, and a negative (hogging) moment plots below it. In Example 1, the fixed support gives a negative moment at that end.
  • Deflection: a downward deflection is negative and plots below the axis.
Diagrams panel of the Wood Beam calculator with a shear graph from 4000 pounds to minus 4000 pounds, a moment graph above the axis peaking near 25 000 pound-feet, a deflection graph below the axis with its lowest point near minus 0.5 inches.

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Reactions

Support reactions that push up on the beam are positive. In Beam Analysis, the reactions diagram draws them as arrows pointing up, and for a fixed support it also draws the moment reaction as a curved arrow. In Example 1 the curved arrow reads counter-clockwise at the fixed end. When a reaction is linked to another calculator, the value is carried through as it appears in the reaction table, with no sign change. See Linking loads and reactions between calculators.

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Strong and weak axis

In the Wood Beam calculator, Member Orientation in Design Conditions chooses whether the member bends about the strong axis (X-X) or the weak axis (Y-Y). X-X is the axis with the higher moment of inertia. For the 5-1/2x16 24F-1.8E member in the Wood Beam screenshots, the strong axis moment of inertia is 1877 in⁴ and the weak axis is 222 in⁴. Design Conditions panel with the Member Orientation row set to Strong (X-X), with Weak (Y-Y) as the other option, above the Service Condition, Temperature Range and deflection limit inputs. Open the description of Member Orientation to see the Bending Axis and the Loading Axis, and a picture of each orientation. In the pictures, the strong axis case has the deep side of the member upright, in line with the load. Member Orientation description with a Lookup Data of Bending Axis X-X and Loading Axis y, the text that X-X refers to the axis with the higher moment of inertia, and pictures of a timber beam loaded for strong axis bending and for weak axis bending. Member Properties panel with a width of 5.5 in, a depth of 16 in, a cross-sectional area of 88 in squared, a strong axis moment of inertia of 1877 in to the fourth and a weak axis moment of inertia of 222 in to the fourth. The Summary draws a Primary Loading arrow on the section, which shows the direction of the main load. Summary of the Wood Beam calculator with a section 5.5 in wide and 16 in deep with a Primary Loading arrow pointing down onto the top, above the member name and the utilization results.

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Column loads and bracing

The Wood Column calculator measures positions up from the bottom of the column, and the diagram is labeled Distance from Bottom of Column (ft). Column loads are listed in the Axial, Lateral & Moment Loads table and entered in the Load Magnitudes window, opened with Edit… on a load row. Axial, Lateral & Moment Loads about X-axis table of the Wood Column calculator with a Floor Load at 12 ft and a load magnitude of D: 0 lb, 4000 lb, 0 lb, with an Edit link. The window has three load columns: the X-Direction Lateral Load PxP_x, the Y-Direction Axial Load NyN_y and the Moment Load MM. The preset opens with a dead load of 4000 lb and a live load of 8500 lb axial, and 0 lateral and moment. The screenshots below have a live lateral load of 500 lb and a moment of 1000 lb·ft entered so that the arrows show. Load Magnitudes window with a (D) Dead Load of 0 pounds lateral, 4000 pounds axial and 0 moment, and an (L) Live Load of 500 pounds lateral, 8500 pounds axial and 1000 pound-feet moment. In the Wood Beam calculator, the setting Load Direction When Linking to Column sets whether the load is Lateral (Px) or Axial (Ny) when a beam is linked to a column. Axial (Ny) is selected as the sheet opens. Wood Beam Loads panel with the Point & Moment Loads table and the Load Direction When Linking to Column setting, with the options Lateral (Px) and Axial (Ny) and Axial (Ny) selected. On the Wood Column loads diagram, an axial load is an arrow pointing down, a positive lateral load is an arrow pointing left, and a positive moment is a counter-clockwise curved arrow. Column loads diagram with a Floor Load at 12 ft, a lateral load of 500 lb drawn as an arrow pointing left, axial loads of 4000 lb dead and 8500 lb live drawn as arrows pointing down, and a moment of 1000 lb-ft drawn as a counter-clockwise curved arrow. In Key Properties, the Continuous Bracing for Strong Axis Buckling and Continuous Bracing for Weak Axis Buckling questions say whether the column has continuous bracing against buckling about each axis. The preset opens with both set to No. Key Properties of the Wood Column calculator with a 6x8 D.Fir-L No. 1 member, a column height of 12 ft and the Continuous Bracing for Strong Axis Buckling and Weak Axis Buckling questions both set to No. Continuous Bracing for Weak Axis Buckling and for Lateral Torsional Buckling set to No, above a table of supports with a Pinned (Base) support at 0 ft and a Roller (Axial Free) support at 12 ft.

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Common questions

A downward deflection is negative in the Summary and plots below the axis. In Example 1 the load acts downward and the deflection is −0.0715 in.
A fixed support under a downward load gives a hogging moment, which plots below the axis as a negative value. In Example 1 the moment at the fixed end is −50 000 lb·ft, and the moment in the span is positive.
In the Wood Beam calculator, the strong axis is X-X, the axis with the higher moment of inertia, and the weak axis is Y-Y. You choose between them with Member Orientation in Design Conditions.
On the Wood Column loads diagram, a positive lateral load is drawn as an arrow pointing left and a positive moment as a counter-clockwise curved arrow. Axial loads are drawn pointing down.

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Next steps

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