Civil Engineering - Strength of Materials - Discussion

5. 

The section modulus of a rectangular light beam 25 metres long is 12.500 cm3. The beam is simply supported at its ends and carries a longitudinal axial tensile load of 10 tonnes in addition to a point load of 4 tonnes at the centre. The maximum stress in the bottom most fibre at the mid span section, is

[A]. 13.33 kg/cm2 tensile
[B]. 13.33 kg/cm2 compressive
[C]. 26.67 kg/cm2 tensile
[D]. 26.67 kg/cm2 compressive
[E]. none of these.

Answer: Option C

Explanation:

No answer description available for this question.

Aspire said: (Sep 21, 2016)  
How to solve this?

Ramachandraraju said: (Sep 21, 2016)  
Anybody give explanation about this.

Akscivilian said: (Sep 27, 2016)  
Question is wrong ,there is needed cross-sectional area, not given so we can't find the answer.

B.S = M/Z + P/A.
M = WL/4.

But A is not given.

Deb said: (Jun 19, 2017)  
Please, someone solve it clearly.

Thakur said: (Nov 19, 2017)  
Please explain the details.

Paul said: (Jan 5, 2018)  
How to find out A? Please explain in detail.

Muthu said: (Jul 27, 2019)  
Please explain the answer.

Pranjul said: (Aug 13, 2019)  
Area calculate from bending equation M = f * Z and f = force/area.

Basanth Babu said: (Nov 22, 2019)  
The cross sectional area of the beam is needed to solve this problem.

Vipin Sainath said: (Apr 12, 2020)  
Bending Stress (Sigma) = M/Z x P/A.

First, we have to calculate Depth and Breadth ..From span/depth ratio we get Depth
Span/20 = 25m/20 = 1.25m or 125cm so D= 125cm, Then B/D=0.5 to 0.67 from this ratio we get breadth B,

B = Dx0.5 = 125X0.5 = 62.5 say B= 60cm, So we got B and D.
M/Z = (4000x2500/4) / 12.6 = 2,00,000 kg/cm2.

P/A = 10000/7500 =1.33 kg/cm2.
Therefore, Sigma = 200000 kg/cm2 x 1.33 kg/cm2 = 266000 Kg/cm2 or 26.6 Kg/m2
finally we got Max stress = 26.6kg/m2.

Shraddha said: (Sep 7, 2020)  
@Vipin Sainath.

Why Σ = (M/Z)*(P/A)?

Kajal said: (Sep 23, 2020)  
@Vipin Sainath.

Why multiplying p/A?

Chris said: (Mar 11, 2021)  
@Shraddha @Kajal.

P/A represents stress.
The bending formula:
M/I = f/y.
Stress f = P/A.
Section Modulus Z = I/y.

Shahid Khan said: (Nov 24, 2021)  
Here is the solution:

Length= 2.5m=250 cm,
Z=12500 cm^3,
Z=bh^2/6=12500,
Bh^2=75000,
H=50cm.
B=30 cm.

Sigma=m/z + p/A.
M=4000*250/4=250000,
A=1500 cm2.

Sigma =250000/12500 +10000/1500,
= 20+6.66,
= 26.66 kg/cm2.

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