A cantilever beam of constant cross section is subjected to a positive moment $M$ and a positive axial force $F$ as shown. The normal stress due to the axial force $F$ is 200 MPa and the maximum compressive stress due to the moment $M$ is 100 MPa. If the point A is located on the top surface and the point B is located on the centroidal axis of the beam, the stress elements at these points are (with stresses shown in MPa)
To solve this problem, we need to calculate the stress at points A and B in the cantilever beam subjected to an axial force \(F\) and a bending moment \(M\).
Concepts and Calculations
- Axial Stress: The axial stress \(\sigma_a\) due to the force \(F\) is given directly as 200 MPa (tensile).
- Bending Stress: The stress caused by the bending moment \(M\) can be calculated using the formula: \(\sigma_b = \frac{M \cdot y}{I}\), where \(y\) is the distance from the neutral axis and \(I\) is the moment of inertia of the cross-section.
- The maximum compressive stress at the top surface due to \(M\) is given as 100 MPa (compressive).
Stress at Point A (Top Surface)
- \(\sigma_a = 200 \text{ MPa} \, (\text{tensile})\)
- \(\sigma_b = -100 \text{ MPa} \, (\text{compressive})\).
- Total Stress at A: \(\sigma_A = \sigma_a + \sigma_b = 200 - 100 = 100 \text{ MPa (tensile)}\)
Stress at Point B (Centroidal Axis)
- \(\sigma_a = 200 \text{ MPa} \, (\text{tensile})\)
- \(\sigma_b = 0 \text{ MPa}\) (since \(y = 0\) at the centroidal axis).
- Total Stress at B: \(\sigma_B = \sigma_a + \sigma_b = 200 \text{ MPa (tensile)}\)
Conclusion
The stress elements at points A and B are:
- Point A: 100 MPa (tensile)
- Point B: 200 MPa (tensile)
Correct Solution
The solution matches with the provided correct answer image.
Important Questions from Analytical Aptitude
- The assumption that the probability of occurrence of a word in a string depends ONLY on the preceding word is called a ______ assumption.
- Which ONE of the following options represents the correct mapping of the phonetic features in Column X to their Sanskrit equivalents in Column Y?
Column X:
Phonetic featuresColumn Y:
Sanskrit termsP. voicing 1. prāṇa Q. retroflex 2. tālavya R. palatal 3. ghōṣa S. aspiration 4. mūrdhanya - Which ONE of the options represents the CORRECT mapping between the morphological concepts in Column X and the examples in Column Y?
Column X:
Morphological ConceptsColumn Y:
ExamplesP. Suppletion 1. bookmaker – bookie Q. Conversion 2. deer – deer R. Zero morpheme 3. bad – worst S. Hypocorism 4. arrive – arrival T. Derivation 5. (a) doctor – (to) doctor 
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Which one of the following is a part of a possible trajectory of the ant during the movement?A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.
What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?
