Structural Analysis

The load-shear-moment relationships

Building the shear diagram

Building the moment diagram and finding the maximum

Inflection points and sign convention

The AISC Table 3-23 standard cases

Overhangs and continuous beams

Exam strategy

Key equations

Worked examples

Common pitfalls

• •Using $wL^2/8$ when the load is a point load, not a UDL. A central point load gives $PL/4$, a cantilever UDL gives $wL^2/2$ — match the AISC Table 3-23 case (support and load type) exactly.
• •Mixing $\text{kip}$ and $\text{lb}$ or $\text{ft}$ and $\text{in}$. In $M=wL^2/8$
• •Looking for the maximum moment under the point load. The moment peaks where shear crosses zero; if the shear stays positive through a load, the peak is farther along the span (Example 3).
• •Forgetting that an overhang creates a hogging support moment $wL_o^2/2$ that often governs over the positive span moment — design both regions.
• •Sign-convention slips: handbook §1.6.7 takes positive moment as sagging (bottom fiber in tension). A concentrated applied couple jumps the moment diagram but does not change the shear.
• •Flipping the sign of $V_2-V_1=\int w\,dx$. The integral form is positive; the shear drops under a downward UDL because the signed $w$
• •Not closing the diagrams. The shear must return to zero at the far end of the beam; if it does not, a reaction or load is wrong — fix it before drawing the moment diagram.

References

• NCEES PE Civil Reference Handbook — §4.1.7 Moment, Shear, and Deflection Diagrams
• NCEES PE Civil Reference Handbook — §1.6.7 Beams (load-shear-moment relations and sign conventions)
• AISC Steel Construction Manual, 15th ed. — Table 3-23, Shears, Moments and Deflections — The source the handbook adapts for standard beam cases.