Calculation Examples

Interactive deflection model

The calculator uses elastic service-load equations and requires the user to select the serviceability criterion instead of assuming L/360L/360 for every member.

Beam Deflection

Concept and model scope

Service-load elastic deflection with a user-selected project criterion instead of a universal L/360 assumption

Elastic deflection0.386 in
Selected L/360 limit0.800 in
Deflection ratio0.483
Within modeled limit
Use unfactored service loads and the deflection criterion actually required by the applicable building code, project specification and supported nonstructural elements. This linear-elastic tool does not evaluate vibration, ponding, camber, composite action, creep or connection flexibility.

Example 1: Rolled W-Shape Shear Strength

A W18x50 beam has Fy=50 ksiF_y=50\text{ ksi}, d=18.0 ind=18.0\text{ in}, tw=0.355 int_w=0.355\text{ in}, and h/tw=46.6h/t_w=46.6. Service loads are D=0.8 kip/ftD=0.8\text{ kip/ft} and L=1.2 kip/ftL=1.2\text{ kip/ft} over 24 ft. For this example use 1.2D+1.6L1.2D+1.6L.

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Example 2: Slender Unstiffened Web

A built-up girder has h=60 inh=60\text{ in}, tw=0.50 int_w=0.50\text{ in}, Fy=50 ksiF_y=50\text{ ksi}, E=29,000 ksiE=29,000\text{ ksi} and kv=5.34k_v=5.34.

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Example 3: Live-Load Deflection with an Explicit Criterion

For the W18x50, use Ix=800 in4I_x=800\text{ in}^4, span 24 ft, service live load 1.2 kip/ft1.2\text{ kip/ft}, and an explicitly selected L/360L/360 live-load criterion.

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Example 4: Total Service-Load Deflection

For the same beam, total service load is 0.8+1.2=2.0 kip/ft0.8+1.2=2.0\text{ kip/ft}. Suppose the project criterion for this check is L/240L/240.

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Example 5: Local Web Yielding — Interior Concentrated Force

A W24x68 has Fyw=50 ksiF_{yw}=50\text{ ksi}, tw=0.415 int_w=0.415\text{ in}, k=1.18 ink=1.18\text{ in}, and bearing length lb=6 inl_b=6\text{ in}.

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Example 6: Local Web Yielding — Near Member End

For the same W24x68 with lb=4 inl_b=4\text{ in}, use the near-end expression applicable to the example.

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Example 7: Web Crippling Arithmetic Check

For the W24x68 under the interior bearing load, let tf=0.585 int_f=0.585\text{ in}, d=23.7 ind=23.7\text{ in}, tw=0.415 int_w=0.415\text{ in}, lb=6 inl_b=6\text{ in}, and Fyw=50 ksiF_{yw}=50\text{ ksi}. Use the stated example expression:

Rn=0.80tw2[1+3(lbd)(twtf)1.5](EFywtftw)1/2.R_n=0.80t_w^2\left[1+3\left(\frac{l_b}{d}\right)\left(\frac{t_w}{t_f}\right)^{1.5}\right]\left(\frac{EF_{yw}t_f}{t_w}\right)^{1/2}.

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Corrected arithmetic

The previous version printed 1453 in the final multiplication even though the calculated dimensionless bracket was 1.453. The corrected expression above preserves the decimal and the resulting strength.

Example 8: Bearing Length from Local Web Yielding

A reaction Ru=120 kipsR_u=120\text{ kips} acts near the end of a W16x31 with Fyw=50 ksiF_{yw}=50\text{ ksi}, tw=0.275 int_w=0.275\text{ in}, and k=0.827 ink=0.827\text{ in}. For the stated example, take the applicable design factor as 1.00.

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Worked-example summary

Beam web shear transitions from yielding to buckling as slenderness increases. Serviceability uses service loads and a criterion selected from the governing project/code requirements; L/360L/360 is not universal. Concentrated forces require multiple local web checks, not only web yielding. Numerical work must preserve dimensional consistency and intermediate decimal factors; the corrected web-crippling example removes the prior 1453/1.453 transcription defect.