In the question in the image you can see a T-beam, but instead for solution assume inverted T-beam and solve according to that. Nothing else changes. Question No. 2A simply supported beam with overhanging is loaded as shown. Calculate the maximum tensile stress and maximumcompressive stress due to bending.200 mm30 kN/m2 m200 mm63 ANSFD60 kN2.1 m87 kN40 mm66.15 kN mBMD(+)60 Nm40 mm

Answered: In the question in the image you can…

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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In the question in the image you can see a T-beam, but instead for solution assume inverted T-beam and solve according to that. Nothing else changes.

Question No. 2
A simply supported beam with overhanging is loaded as shown. Calculate the maximum tensile stress and maximum
compressive stress due to bending.
200 mm
30 kN/m
2 m
200 mm
63 AN
SFD
60 kN
2.1 m
87 kN
40 mm
66.15 kN m
BMD
(+)
60 Nm
40 mm

Expert Solution

Step 1

Draw the figure.

Step 2

It is required to determine the centroid.

$\begin{array}{rcl} y & = & \frac{A_{1} y_{1} + A_{2} y_{2}}{A_{1} + A_{2}} \\ = & \frac{(200 \times 40) (\frac{200}{2}) + (200 \times 40) (\frac{40}{2} + 200)}{(200 \times 40) + (200 \times 40)} \\ = & 160 mm from top \end{array}$

It is required to determine the moment of inertia.

$\begin{array}{rcl} I_{x} & = & \frac{B_{1} D_{1}^{3}}{12} + A_{1} h_{1}^{2} + \frac{B_{2} D_{2}^{3}}{12} + A_{2} h_{2}^{2} \\ = & \frac{40 \times 200^{3}}{12} + (40 \times 200) {(\frac{200}{2} - 160)}^{2} + \frac{200 \times 40^{3}}{12} + (40 \times 200) {((\frac{40}{2} + 200) - 160)}^{2} \\ = & (55.47 \times 10^{6}) + (29.87 \times 10^{6}) \\ = & 85.34 \times 10^{6} {mm}^{4} \end{array}$

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