Overhanging-Beam Reactions

\sum M_{A} = 0 \Rightarrow R_{B} = \frac{\sum P _{i} a _{i}}{L}

An overhanging simple beam (pin and roller) can have a negative (uplift) reaction if a load sits on a long overhang. Always write ΣM about one support and ΣFy. Check signs.

$R_{A}, R_{B}$ (kN): Support reactions
$L$ (m): Distance between supports

Step-by-step solved example

Supports at A and B, AB=6 m, overhang BC=2 m. 10 kN at C. Reactions?

Overhang point load can lift a far support (negative reaction).

1. ΣMB
RA×6 − 10×2 = 0? Wait ΣMA: RB×6 − 10×8 = 0 → RB = 80/6 = 13.33 kN up.
2. ΣFy
RA + 13.33 = 10 → RA = −3.33 kN (down, hold-down).

Answer: RA = −3.33 kN (down), RB = 13.33 kN (up)

10 practice questions

0/10 correct

1.A negative vertical reaction means

2.Overhang load tends to

3.Simple span L with midspan P (no overhang): each R=

4.ΣM about A eliminates

5.A roller cannot provide

6.Check: RA+RB must equal

7.Double overhang with equal end loads is

8.Units of reaction are

9.If the overhang load is zero, signs of RA, RB are

10.Internal hinge would add