Question 1 of 4 · Distributed Loads, Shear & Bending · Intermediate · About 22 min

Partially loaded access beam

A simply supported $6\,\mathrm{m}$ beam has a pin at $A$ ( $x=0$ ) and roller at $B$ ( $x=6$ ). A uniform downward load of acts only on . Determine both vertical reactions, the piecewise internal shear and sagging moment , and the largest positive moment. Use in metres from .

A horizontal beam 6.0 m long. Pin support at the left end A, roller support at the right end B. Evenly spaced downward arrows, joined by a thin line along their tops, from 1.0 m to 5.0 m along the beam only. There is no load on the first or last 1.0 m. One row of dimensions under the beam, split into 1.0 m, 4.0 m and 1.0 m. A second row below it for the full 6.0 m. Labels: A; B; 3 kN/m; 1.0 m; 4.0 m; 1.0 m; 6.0 m — Schematic, not to scale unless dimensions are given.

Given

$L=6$ m
$w=3$ kN/m on $1\le x\le5$ m
Sagging bending moment positive

Find

$A_y,B_y$
All segments of $V(x), M(x)$

Assumptions

All members and connections are idealised as specified in the question.
Use g = 9.81 m/s^2 where gravitational acceleration is required.

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Partially loaded access beam

Given

Find

Assumptions

Worked solution