Solution to Problem 403 | Shear and Moment Diagrams

Tags:

Problem 403
Beam loaded as shown in Fig. P-403.

Click here to read or hide the general instruction

Write shear and moment equations for the beams in the following problems. In each problem, let x be the distance measured from left end of the beam. Also, draw shear and moment diagrams, specifying values at all change of loading positions and at points of zero shear. Neglect the mass of the beam in each problem.

Solution 403

Click here to show or hide the solution

From the load diagram:
$\Sigma M_B = 0$
$5R_D + 1(30) = 3(50)$
$R_D = 24 \, \text{kN}$

$\Sigma M_D = 0$
$5R_B = 2(50) + 6(30)$
$R_B = 56 \, \text{kN}$

Segment AB:
$V_{AB} = -30 \, \text{kN}$

$M_{AB} = -30x \, \text{kN}\cdot\text{m}$

Segment BC:
$V_{BC} = -30 + 56$

$V_{BC} = 26 \, \text{kN}$

$M_{BC} = -30x + 56(x - 1)$

$M_{BC} = 26x - 56 \, \text{kN}\cdot\text{m}$

Segment CD:
$V_{CD} = -30 + 56 - 50$

$V_{CD} = -24 \, \text{kN}$

$M_{CD} = -30x + 56(x - 1) - 50(x - 4)$

$M_{CD} = -30x + 56x - 56 - 50x + 200$

$M_{CD} = -24x + 144 \, \text{kN}\cdot\text{m}$

To draw the Shear Diagram:

In segment AB, the shear is uniformly distributed over the segment at a magnitude of -30 kN.
In segment BC, the shear is uniformly distributed at a magnitude of 26 kN.
In segment CD, the shear is uniformly distributed at a magnitude of -24 kN.

To draw the Moment Diagram:

The equation M_AB = -30x is linear, at x = 0, M_AB = 0 and at x = 1 m, M_AB = -30 kN·m.
M_BC = 26x - 56 is also linear. At x = 1 m, M_BC = -30 kN·m; at x = 4 m, M_BC = 48 kN·m. When M_BC = 0, x = 2.154 m, thus the moment is zero at 1.154 m from B.
M_CD = -24x + 144 is again linear. At x = 4 m, M_CD = 48 kN·m; at x = 6 m, M_CD = 0.

Log in or register to post comments
179217 reads

MATHalino.com

For Suckerfish Menu

Solution to Problem 403 | Shear and Moment Diagrams

Strength of Materials

Our Online Reviewers

Recent comments

Recent Updates

MATHalino.com

For Suckerfish Menu

You are here

Solution to Problem 403 | Shear and Moment Diagrams

Strength of Materials

Our Online Reviewers

Search this site

Recent comments

Recent Updates