Answered: 6 kN/m ania B IC A aM emer JA 21 -3 m-…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Determine the normal force, shear force, and moment at point C. Assume A as a pin support and B as a roller support. Draw the shear and bending moment diagram.

6 kN/m
ania
B
IC
A
aM emer
JA 21
-3 m-
3 m-

Expert Solution

Step 1

Draw the free-body diagram of the beam.

Write the equilibrium equation for the sum of vertical forces.

$\begin{array}{rcl} \sum_{} F_{y} & = & 0 \\ R_{A} + R_{B} & = & \frac{1}{2} \times 6 \times 3 + 6 \times 3 \\ R_{A} + R_{B} & = & 27 kN . . . (1) \end{array}$

Write the equilibrium equation for the sum of the moment about point A.

$\begin{array}{rcl} \sum_{} M_{A} & = & 0 \\ (\frac{1}{2} \times 6 \times 3) \times (\frac{2}{3} \times 3) + (6 \times 3) \times (3 + 1.5) - R_{B} \times 6 & = & 0 \\ R_{B} \times 6 & = & 99 \\ R_{B} & = & 16.5 kN \end{array}$

Substitute the value of $R_{B}$ in equation (1).

$\begin{array}{rcl} R_{A} + 16.5 & = & 27 \\ R_{A} & = & 10.5 kN \end{array}$

Step 2

Calculate the shear force at point A.

$\begin{array}{rcl} V_{A} & = & R_{A} \\ = & 10.5 kN (↑) \end{array}$

Calculate the shear force at point C.

$\begin{array}{rcl} V_{C} & = & 10.5 - \frac{1}{2} \times 6 \times 3 \\ = & 1.5 kN (↑) \end{array}$

Calculate the shear force at point B.

$\begin{array}{rcl} V_{B} & = & R_{B} \\ = & 16.5 kN (↓) \end{array}$

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