VIPSolutionsAct like a helpful tutor and exlain me : Give step-by-step solution with explanation and final answer: only answer '' what criteria would you use in order to safely neglect the weight of the beam?''L | F 2.(10pts). (1). find an expression for the internal shear force (V) and bending moment (My) acting at a position x, some arbitrary distance from the root of the cantilever beam. Neglect the ‘weight of the beam. (2). What if you now include the weight of the beam, say a uniform woper unit length; how do these expressions (V and My) change? Given your answer, what criteria would you use in order to safely neglect the weight of the beam?
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Act like a helpful tutor and exlain me :
Give step-by-step solution with explanation and final answer:
only answer '' what criteria would you use in order to safely neglect the weight of the beam?''L
|
F
2.(10pts). (1). find an expression for the internal shear force (V) and bending moment (My)
acting at a position x, some arbitrary distance from the root of the cantilever beam. Neglect the
‘weight of the beam.
(2). What if you now include the weight of the beam, say a uniform woper unit length; how do
these expressions (V and My) change? Given your answer, what criteria would you use in order
to safely neglect the weight of the beam?
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Asked by: manish kumar
Created at: 2025-10-02 11:08:00
Asked by: manish kumar
Created at: 2025-10-02 11:08:00
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## Criteria to Safely Neglect the Weight of the Beam
To **safely neglect the weight of the beam**, you should compare the effect of the beam’s own weight to the effect of the applied load (**F**).
### Step-by-Step Criteria:
1. **Calculate the Total Beam Weight:**
- If the weight per unit length is \( w_ \) and the beam length is \( L \), the total weight of the beam is:
\[
W_{\text{beam}} = w_ \cdot L
\]
2. **Compare with the Applied Load:**
- Compare \( W_{\text{beam}} \) with the applied load \( F \).
3. **Neglect the Weight If:**
- The beam’s weight is **much smaller** than the applied load. A typical engineering rule is:
\[
W_{\text{beam}} \ll F
\]
- Or, more specifically, if:
\[
w_ L \leq .1F
\]
(i.e., the beam’s total weight is less than 10% of the applied load, its effect on shear and moment is usually negligible.)
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### **Final Answer:**
> **You can safely neglect the weight of the beam if the total weight of the beam (\(w_ L\)) is much smaller than the applied load (\(F\)), such as less than 10% of \(F\).**
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